Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point.

PubMed

Najafi, M N; Nezhadhaghighi, M Ghasemi

2017-03-01

We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas, taking into account the particle-particle interaction and the remote Coulomb disorder on an equal footing within the Thomas-Fermi-Dirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Using Schramm-Loewner (SLE) evolution, we numerically demonstrate that the ungated graphene has conformal invariance and the random zero-charge density contours are SLE_{κ} with κ=1.8±0.2, consistent with c=-3 conformal field theory.

[Gene method for inconsistent hydrological frequency calculation. I: Inheritance, variability and evolution principles of hydrological genes].

PubMed

Xie, Ping; Wu, Zi Yi; Zhao, Jiang Yan; Sang, Yan Fang; Chen, Jie

2018-04-01

A stochastic hydrological process is influenced by both stochastic and deterministic factors. A hydrological time series contains not only pure random components reflecting its inheri-tance characteristics, but also deterministic components reflecting variability characteristics, such as jump, trend, period, and stochastic dependence. As a result, the stochastic hydrological process presents complicated evolution phenomena and rules. To better understand these complicated phenomena and rules, this study described the inheritance and variability characteristics of an inconsistent hydrological series from two aspects: stochastic process simulation and time series analysis. In addition, several frequency analysis approaches for inconsistent time series were compared to reveal the main problems in inconsistency study. Then, we proposed a new concept of hydrological genes origined from biological genes to describe the inconsistent hydrolocal processes. The hydrologi-cal genes were constructed using moments methods, such as general moments, weight function moments, probability weight moments and L-moments. Meanwhile, the five components, including jump, trend, periodic, dependence and pure random components, of a stochastic hydrological process were defined as five hydrological bases. With this method, the inheritance and variability of inconsistent hydrological time series were synthetically considered and the inheritance, variability and evolution principles were fully described. Our study would contribute to reveal the inheritance, variability and evolution principles in probability distribution of hydrological elements.

Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates

NASA Astrophysics Data System (ADS)

Finkelshtein, D.; Kondratiev, Yu.; Kutoviy, O.; Molchanov, S.; Zhizhina, E.

2014-10-01

We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate, which provides a stochastic changing of lengths by a free diffusion law. The birth and death rates are length dependent, which corresponds to a selection effect. We study an asymptotic behavior of a density for an infinite collection of genotypes. The cases of space homogeneous and space heterogeneous densities are considered.

Environmental Stochasticity and the Speed of Evolution

NASA Astrophysics Data System (ADS)

Danino, Matan; Kessler, David A.; Shnerb, Nadav M.

2018-03-01

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

Environmental Stochasticity and the Speed of Evolution

NASA Astrophysics Data System (ADS)

Danino, Matan; Kessler, David A.; Shnerb, Nadav M.

2018-07-01

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

Hydrodynamic Limit of Multiple SLE

NASA Astrophysics Data System (ADS)

Hotta, Ikkei; Katori, Makoto

2018-04-01

Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm-Loewner evolution (SLE) as the number of slits N goes to infinity. When the N slits grow from points on the real line R in a simultaneous way and go to infinity within the upper half plane H, an ordinary differential equation describing time evolution of the conformal map g_t(z) was derived in the N → ∞ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on R studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner's semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner's semicircle law determines the time evolution of the SLE hull, K_t \\subset H\\cup R, in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from -a < 0, and determine the multiple SLE in the hydrodynamic limit. After reporting these exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull K_t in the hydrodynamic limit.

Influence of vectors' risk-spreading strategies and environmental stochasticity on the epidemiology and evolution of vector-borne diseases: the example of Chagas' disease.

PubMed

Pelosse, Perrine; Kribs-Zaleta, Christopher M; Ginoux, Marine; Rabinovich, Jorge E; Gourbière, Sébastien; Menu, Frédéric

2013-01-01

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control.

Influence of Vectors’ Risk-Spreading Strategies and Environmental Stochasticity on the Epidemiology and Evolution of Vector-Borne Diseases: The Example of Chagas’ Disease

PubMed Central

Pelosse, Perrine; Kribs-Zaleta, Christopher M.; Ginoux, Marine; Rabinovich, Jorge E.; Gourbière, Sébastien; Menu, Frédéric

2013-01-01

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas’ disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control. PMID:23951018

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

On the physical realizability of quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Stochasticity versus determinism: consequences for realistic gene regulatory network modelling and evolution.

PubMed

Jenkins, Dafyd J; Stekel, Dov J

2010-02-01

Gene regulation is one important mechanism in producing observed phenotypes and heterogeneity. Consequently, the study of gene regulatory network (GRN) architecture, function and evolution now forms a major part of modern biology. However, it is impossible to experimentally observe the evolution of GRNs on the timescales on which living species evolve. In silico evolution provides an approach to studying the long-term evolution of GRNs, but many models have either considered network architecture from non-adaptive evolution, or evolution to non-biological objectives. Here, we address a number of important modelling and biological questions about the evolution of GRNs to the realistic goal of biomass production. Can different commonly used simulation paradigms, in particular deterministic and stochastic Boolean networks, with and without basal gene expression, be used to compare adaptive with non-adaptive evolution of GRNs? Are these paradigms together with this goal sufficient to generate a range of solutions? Will the interaction between a biological goal and evolutionary dynamics produce trade-offs between growth and mutational robustness? We show that stochastic basal gene expression forces shrinkage of genomes due to energetic constraints and is a prerequisite for some solutions. In systems that are able to evolve rates of basal expression, two optima, one with and one without basal expression, are observed. Simulation paradigms without basal expression generate bloated networks with non-functional elements. Further, a range of functional solutions was observed under identical conditions only in stochastic networks. Moreover, there are trade-offs between efficiency and yield, indicating an inherent intertwining of fitness and evolutionary dynamics.

The Stochastic Evolution of a Protocell: The Gillespie Algorithm in a Dynamically Varying Volume

PubMed Central

Carletti, T.; Filisetti, A.

2012-01-01

We propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some specific molecules, belonging to the reactions set. This allows us to study the stochastic evolution of a protocell, whose volume increases because of the production of container molecules. Several protocell models are considered and compared with the deterministic models. PMID:22536297

First-passage times for pattern formation in nonlocal partial differential equations

NASA Astrophysics Data System (ADS)

Cáceres, Manuel O.; Fuentes, Miguel A.

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

First-passage times for pattern formation in nonlocal partial differential equations.

PubMed

Cáceres, Manuel O; Fuentes, Miguel A

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

A damage analysis for brittle materials using stochastic micro-structural information

NASA Astrophysics Data System (ADS)

Lin, Shih-Po; Chen, Jiun-Shyan; Liang, Shixue

2016-03-01

In this work, a micro-crack informed stochastic damage analysis is performed to consider the failures of material with stochastic microstructure. The derivation of the damage evolution law is based on the Helmholtz free energy equivalence between cracked microstructure and homogenized continuum. The damage model is constructed under the stochastic representative volume element (SRVE) framework. The characteristics of SRVE used in the construction of the stochastic damage model have been investigated based on the principle of the minimum potential energy. The mesh dependency issue has been addressed by introducing a scaling law into the damage evolution equation. The proposed methods are then validated through the comparison between numerical simulations and experimental observations of a high strength concrete. It is observed that the standard deviation of porosity in the microstructures has stronger effect on the damage states and the peak stresses than its effect on the Young's and shear moduli in the macro-scale responses.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process

NASA Astrophysics Data System (ADS)

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-01

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

An upper limit on the stochastic gravitational-wave background of cosmological origin.

PubMed

Abbott, B P; Abbott, R; Acernese, F; Adhikari, R; Ajith, P; Allen, B; Allen, G; Alshourbagy, M; Amin, R S; Anderson, S B; Anderson, W G; Antonucci, F; Aoudia, S; Arain, M A; Araya, M; Armandula, H; Armor, P; Arun, K G; Aso, Y; Aston, S; Astone, P; Aufmuth, P; Aulbert, C; Babak, S; Baker, P; Ballardin, G; Ballmer, S; Barker, C; Barker, D; Barone, F; Barr, B; Barriga, P; Barsotti, L; Barsuglia, M; Barton, M A; Bartos, I; Bassiri, R; Bastarrika, M; Bauer, Th S; Behnke, B; Beker, M; Benacquista, M; Betzwieser, J; Beyersdorf, P T; Bigotta, S; Bilenko, I A; Billingsley, G; Birindelli, S; Biswas, R; Bizouard, M A; Black, E; Blackburn, J K; Blackburn, L; Blair, D; Bland, B; Boccara, C; Bodiya, T P; Bogue, L; Bondu, F; Bonelli, L; Bork, R; Boschi, V; Bose, S; Bosi, L; Braccini, S; Bradaschia, C; Brady, P R; Braginsky, V B; Brand, J F J van den; Brau, J E; Bridges, D O; Brillet, A; Brinkmann, M; Brisson, V; Van Den Broeck, C; Brooks, A F; Brown, D A; Brummit, A; Brunet, G; Bullington, A; Bulten, H J; 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Mukherjee, S; Mukhopadhyay, H; Mullavey, A; Müller-Ebhardt, H; Munch, J; Murray, P G; Myers, E; Myers, J; Nash, T; Nelson, J; Neri, I; Newton, G; Nishizawa, A; Nocera, F; Numata, K; Ochsner, E; O'Dell, J; Ogin, G H; O'Reilly, B; O'Shaughnessy, R; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pagliaroli, G; Palomba, C; Pan, Y; Pankow, C; Paoletti, F; Papa, M A; Parameshwaraiah, V; Pardi, S; Pasqualetti, A; Passaquieti, R; Passuello, D; Patel, P; Pedraza, M; Penn, S; Perreca, A; Persichetti, G; Pichot, M; Piergiovanni, F; Pierro, V; Pinard, L; Pinto, I M; Pitkin, M; Pletsch, H J; Plissi, M V; Poggiani, R; Postiglione, F; Principe, M; Prix, R; Prodi, G A; Prokhorov, L; Punken, O; Punturo, M; Puppo, P; Putten, S van der; Quetschke, V; Raab, F J; Rabaste, O; Rabeling, D S; Radkins, H; Raffai, P; Raics, Z; Rainer, N; Rakhmanov, M; Rapagnani, P; Raymond, V; Re, V; Reed, C M; Reed, T; Regimbau, T; Rehbein, H; Reid, S; Reitze, D H; Ricci, F; Riesen, R; Riles, K; Rivera, B; Roberts, P; Robertson, N A; Robinet, F; Robinson, C; Robinson, E L; Rocchi, A; Roddy, S; Rolland, L; Rollins, J; Romano, J D; Romano, R; Romie, J H; Röver, C; Rowan, S; Rüdiger, A; Ruggi, P; Russell, P; Ryan, K; Sakata, S; Salemi, F; Sandberg, V; Sannibale, V; Santamaría, L; Saraf, S; Sarin, P; Sassolas, B; Sathyaprakash, B S; Sato, S; Satterthwaite, M; Saulson, P R; Savage, R; Savov, P; Scanlan, M; Schilling, R; Schnabel, R; Schofield, R; Schulz, B; Schutz, B F; Schwinberg, P; Scott, J; Scott, S M; Searle, A C; Sears, B; Seifert, F; Sellers, D; Sengupta, A S; Sentenac, D; Sergeev, A; Shapiro, B; Shawhan, P; Shoemaker, D H; Sibley, A; Siemens, X; Sigg, D; Sinha, S; Sintes, A M; Slagmolen, B J J; Slutsky, J; van der Sluys, M V; Smith, J R; Smith, M R; Smith, N D; Somiya, K; Sorazu, B; Stein, A; Stein, L C; Steplewski, S; Stochino, A; Stone, R; Strain, K A; Strigin, S; Stroeer, A; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, K-X; Sung, M; Sutton, P J; Swinkels, B L; Szokoly, G P; Talukder, D; Tang, L; Tanner, D B; Tarabrin, S P; Taylor, J R; Taylor, R; Terenzi, R; Thacker, J; Thorne, K A; Thorne, K S; Thüring, A; Tokmakov, K V; Toncelli, A; Tonelli, M; Torres, C; Torrie, C; Tournefier, E; Travasso, F; Traylor, G; Trias, M; Trummer, J; Ugolini, D; Ulmen, J; Urbanek, K; Vahlbruch, H; Vajente, G; Vallisneri, M; Vass, S; Vaulin, R; Vavoulidis, M; Vecchio, A; Vedovato, G; van Veggel, A A; Veitch, J; Veitch, P; Veltkamp, C; Verkindt, D; Vetrano, F; Viceré, A; Villar, A; Vinet, J-Y; Vocca, H; Vorvick, C; Vyachanin, S P; Waldman, S J; Wallace, L; Ward, H; Ward, R L; Was, M; Weidner, A; Weinert, M; Weinstein, A J; Weiss, R; Wen, L; Wen, S; Wette, K; Whelan, J T; Whitcomb, S E; Whiting, B F; Wilkinson, C; Willems, P A; Williams, H R; Williams, L; Willke, B; Wilmut, I; Winkelmann, L; Winkler, W; Wipf, C C; Wiseman, A G; Woan, G; Wooley, R; Worden, J; Wu, W; Yakushin, I; Yamamoto, H; Yan, Z; Yoshida, S; Yvert, M; Zanolin, M; Zhang, J; Zhang, L; Zhao, C; Zotov, N; Zucker, M E; Zweizig, J

2009-08-20

A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved gravitational-wave sources of astrophysical and cosmological origin. It should carry unique signatures from the earliest epochs in the evolution of the Universe, inaccessible to standard astrophysical observations. Direct measurements of the amplitude of this background are therefore of fundamental importance for understanding the evolution of the Universe when it was younger than one minute. Here we report limits on the amplitude of the stochastic gravitational-wave background using the data from a two-year science run of the Laser Interferometer Gravitational-wave Observatory (LIGO). Our result constrains the energy density of the stochastic gravitational-wave background normalized by the critical energy density of the Universe, in the frequency band around 100 Hz, to be <6.9 x 10(-6) at 95% confidence. The data rule out models of early Universe evolution with relatively large equation-of-state parameter, as well as cosmic (super)string models with relatively small string tension that are favoured in some string theory models. This search for the stochastic background improves on the indirect limits from Big Bang nucleosynthesis and cosmic microwave background at 100 Hz.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.

PubMed

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-27

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

Physical realizability of continuous-time quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno G.; Govia, Luke C. G.; Wilhelm, Frank K.

2018-05-01

Quantum walks are a promising methodology that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution and the physical assumptions underpinning them. We show that general direct implementations would require the complete solution of the underlying unitary dynamics and sophisticated reservoir engineering, thus weakening the benefits of experimental implementation.

A kinetic theory for age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Chou, Tom; Greenman, Chris

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.

Evolutionary Game Theory in Growing Populations

NASA Astrophysics Data System (ADS)

Melbinger, Anna; Cremer, Jonas; Frey, Erwin

2010-10-01

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2018-05-01

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.

PubMed

Lèbre, Sophie; Michel, Christian J

2010-12-01

We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field. Copyright © 2010 Elsevier Ltd. All rights reserved.

Sources and Sinks: A Stochastic Model of Evolution in Heterogeneous Environments

NASA Astrophysics Data System (ADS)

Hermsen, Rutger; Hwa, Terence

2010-12-01

We study evolution driven by spatial heterogeneity in a stochastic model of source-sink ecologies. A sink is a habitat where mortality exceeds reproduction so that a local population persists only due to immigration from a source. Immigrants can, however, adapt to conditions in the sink by mutation. To characterize the adaptation rate, we derive expressions for the first arrival time of adapted mutants. The joint effects of migration, mutation, birth, and death result in two distinct parameter regimes. These results may pertain to the rapid evolution of drug-resistant pathogens and insects.

Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

NASA Astrophysics Data System (ADS)

Sudakov, Ivan

Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

The Stochastic Evolutionary Game for a Population of Biological Networks Under Natural Selection

PubMed Central

Chen, Bor-Sen; Ho, Shih-Ju

2014-01-01

In this study, a population of evolutionary biological networks is described by a stochastic dynamic system with intrinsic random parameter fluctuations due to genetic variations and external disturbances caused by environmental changes in the evolutionary process. Since information on environmental changes is unavailable and their occurrence is unpredictable, they can be considered as a game player with the potential to destroy phenotypic stability. The biological network needs to develop an evolutionary strategy to improve phenotypic stability as much as possible, so it can be considered as another game player in the evolutionary process, ie, a stochastic Nash game of minimizing the maximum network evolution level caused by the worst environmental disturbances. Based on the nonlinear stochastic evolutionary game strategy, we find that some genetic variations can be used in natural selection to construct negative feedback loops, efficiently improving network robustness. This provides larger genetic robustness as a buffer against neutral genetic variations, as well as larger environmental robustness to resist environmental disturbances and maintain a network phenotypic traits in the evolutionary process. In this situation, the robust phenotypic traits of stochastic biological networks can be more frequently selected by natural selection in evolution. However, if the harbored neutral genetic variations are accumulated to a sufficiently large degree, and environmental disturbances are strong enough that the network robustness can no longer confer enough genetic robustness and environmental robustness, then the phenotype robustness might break down. In this case, a network phenotypic trait may be pushed from one equilibrium point to another, changing the phenotypic trait and starting a new phase of network evolution through the hidden neutral genetic variations harbored in network robustness by adaptive evolution. Further, the proposed evolutionary game is extended to an n-tuple evolutionary game of stochastic biological networks with m players (competitive populations) and k environmental dynamics. PMID:24558296

Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process.

PubMed

Greenman, C D; Cooke, S L; Marshall, J; Stratton, M R; Campbell, P J

2016-01-01

Breakage-fusion-bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. Here we study the evolution space of breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are [Formula: see text] qualitatively distinct evolutions involving [Formula: see text] breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the process to show these evolutions are not equally likely, and also describe how amplicons become localized. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples.

ENVIRONMENT: a computational platform to stochastically simulate reacting and self-reproducing lipid compartments

NASA Astrophysics Data System (ADS)

Mavelli, Fabio; Ruiz-Mirazo, Kepa

2010-09-01

'ENVIRONMENT' is a computational platform that has been developed in the last few years with the aim to simulate stochastically the dynamics and stability of chemically reacting protocellular systems. Here we present and describe some of its main features, showing how the stochastic kinetics approach can be applied to study the time evolution of reaction networks in heterogeneous conditions, particularly when supramolecular lipid structures (micelles, vesicles, etc) coexist with aqueous domains. These conditions are of special relevance to understand the origins of cellular, self-reproducing compartments, in the context of prebiotic chemistry and evolution. We contrast our simulation results with real lab experiments, with the aim to bring together theoretical and experimental research on protocell and minimal artificial cell systems.

Calibration of a stochastic health evolution model using NHIS data

NASA Astrophysics Data System (ADS)

Gupta, Aparna; Li, Zhisheng

2011-10-01

This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.

Evolution of the Climate Continuum from the Mid-Miocene Climatic Optimum to the Present

NASA Astrophysics Data System (ADS)

Aswasereelert, W.; Meyers, S. R.; Hinnov, L. A.; Kelly, D.

2011-12-01

The recognition of orbital rhythms in paleoclimate data has led to a rich understanding of climate evolution during the Neogene and Quaternary. In contrast, changes in stochastic variability associated with the transition from unipolar to bipolar glaciation have received less attention, although the stochastic component likely preserves key insights about climate. In this study, we seek to evaluate the dominance and character of stochastic climate energy since the Middle Miocene Climatic Optimum (~17 Ma). These analyses extend a previous study that suggested diagnostic stochastic responses associated with Northern Hemisphere ice sheet development during the Plio-Pleistocene (Meyers and Hinnov, 2010). A critical and challenging step necessary to conduct the work is the conversion of depth data to time data. We investigate climate proxy datasets using multiple time scale hypotheses, including depth-derived time scales, sedimentologic/geochemical "tuning", minimal orbital tuning, and comprehensive orbital tuning. To extract the stochastic component of climate, and also explore potential relationships between the orbital parameters and paleoclimate response, a number of approaches rooted in Thomson's (1982) multi-taper spectral method (MTM) are applied. Importantly, the MTM technique is capable of separating the spectral "continuum" - a measure of stochastic variability - from the deterministic periodic orbital signals (spectral "lines") preserved in proxy data. Time series analysis of the proxy records using different chronologic approaches allows us to evaluate the sensitivity of our conclusion about stochastic and deterministic orbital processes during the Middle Miocene to present. Moreover, comparison of individual records permits examination of the spatial dependence of the identified climate responses. Meyers, S.R., and Hinnov, L.A. (2010), Northern Hemisphere glaciation and the evolution of Plio-Pleistocene climate noise: Paleoceanography, 25, PA3207, doi:10.1029/2009PA001834. Thomson, D.J. (1982), Spectrum estimation and harmonic analysis: IEEE Proceedings, v. 70, p. 1055-1096.

Simple stochastic birth and death models of genome evolution: was there enough time for us to evolve?

PubMed

Karev, Georgy P; Wolf, Yuri I; Koonin, Eugene V

2003-10-12

The distributions of many genome-associated quantities, including the membership of paralogous gene families can be approximated with power laws. We are interested in developing mathematical models of genome evolution that adequately account for the shape of these distributions and describe the evolutionary dynamics of their formation. We show that simple stochastic models of genome evolution lead to power-law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation Models (BDIM), represent a special class of balanced birth-and-death processes, in which domain duplication and deletion rates are asymptotically equal up to the second order. The simplest, linear BDIM shows an excellent fit to the observed distributions of domain family size in diverse prokaryotic and eukaryotic genomes. However, the stochastic version of the linear BDIM explored here predicts that the actual size of large paralogous families is reached on an unrealistically long timescale. We show that introduction of non-linearity, which might be interpreted as interaction of a particular order between individual family members, allows the model to achieve genome evolution rates that are much better compatible with the current estimates of the rates of individual duplication/loss events.

Stochastic evolution in populations of ideas

PubMed Central

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244

Stochastic evolution in populations of ideas

NASA Astrophysics Data System (ADS)

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.

A Stochastic Evolutionary Model for Protein Structure Alignment and Phylogeny

PubMed Central

Challis, Christopher J.; Schmidler, Scott C.

2012-01-01

We present a stochastic process model for the joint evolution of protein primary and tertiary structure, suitable for use in alignment and estimation of phylogeny. Indels arise from a classic Links model, and mutations follow a standard substitution matrix, whereas backbone atoms diffuse in three-dimensional space according to an Ornstein–Uhlenbeck process. The model allows for simultaneous estimation of evolutionary distances, indel rates, structural drift rates, and alignments, while fully accounting for uncertainty. The inclusion of structural information enables phylogenetic inference on time scales not previously attainable with sequence evolution models. The model also provides a tool for testing evolutionary hypotheses and improving our understanding of protein structural evolution. PMID:22723302

Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui

2018-06-01

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness.

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Advances in planetary geology

NASA Technical Reports Server (NTRS)

Woronow, A. (Editor)

1981-01-01

Three dissertations are provided covering (1) the stochastic evolution of asteroidal regoliths and the origin of brecciated and gas-rich meteorites; (2) ridge systems on Mars; and (3) the morphology and evolution of Ganymede and Callisto.

Adaptive grid based multi-objective Cauchy differential evolution for stochastic dynamic economic emission dispatch with wind power uncertainty

PubMed Central

Lei, Xiaohui; Wang, Chao; Yue, Dong; Xie, Xiangpeng

2017-01-01

Since wind power is integrated into the thermal power operation system, dynamic economic emission dispatch (DEED) has become a new challenge due to its uncertain characteristics. This paper proposes an adaptive grid based multi-objective Cauchy differential evolution (AGB-MOCDE) for solving stochastic DEED with wind power uncertainty. To properly deal with wind power uncertainty, some scenarios are generated to simulate those possible situations by dividing the uncertainty domain into different intervals, the probability of each interval can be calculated using the cumulative distribution function, and a stochastic DEED model can be formulated under different scenarios. For enhancing the optimization efficiency, Cauchy mutation operation is utilized to improve differential evolution by adjusting the population diversity during the population evolution process, and an adaptive grid is constructed for retaining diversity distribution of Pareto front. With consideration of large number of generated scenarios, the reduction mechanism is carried out to decrease the scenarios number with covariance relationships, which can greatly decrease the computational complexity. Moreover, the constraint-handling technique is also utilized to deal with the system load balance while considering transmission loss among thermal units and wind farms, all the constraint limits can be satisfied under the permitted accuracy. After the proposed method is simulated on three test systems, the obtained results reveal that in comparison with other alternatives, the proposed AGB-MOCDE can optimize the DEED problem while handling all constraint limits, and the optimal scheme of stochastic DEED can decrease the conservation of interval optimization, which can provide a more valuable optimal scheme for real-world applications. PMID:28961262

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation

PubMed Central

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation. PMID:26761487

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

PubMed

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington's genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.

Toward the Darwinian transition: Switching between distributed and speciated states in a simple model of early life.

PubMed

Arnoldt, Hinrich; Strogatz, Steven H; Timme, Marc

2015-01-01

It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer (HGT). At a certain point, however, life made a transition to the modern era of individuality and vertical descent. Here we present a minimal model for stochastic processes potentially contributing to this hypothesized "Darwinian transition." The model suggests that HGT-dominated dynamics may have been intermittently interrupted by selection-driven processes during which genotypes became fitter and decreased their inclination toward HGT. Stochastic switching in the population dynamics with three-point (hypernetwork) interactions may have destabilized the HGT-dominated collective state and essentially contributed to the emergence of vertical descent and the first well-defined species in early evolution. A systematic nonlinear analysis of the stochastic model dynamics covering key features of evolutionary processes (such as selection, mutation, drift and HGT) supports this view. Our findings thus suggest a viable direction out of early collective evolution, potentially enabling the start of individuality and vertical Darwinian evolution.

Tsunamis: stochastic models of occurrence and generation mechanisms

USGS Publications Warehouse

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

Time Evolution of the Dynamical Variables of a Stochastic System.

ERIC Educational Resources Information Center

de la Pena, L.

1980-01-01

By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)

A stochastic model of firm growth

NASA Astrophysics Data System (ADS)

Bottazzi, Giulio; Secchi, Angelo

2003-06-01

Recently from analyses on different databases the tent-shape of the distribution of firm growth rates has emerged as a robust and universal characteristic of the time evolution of corporates. We add new evidence on this topic and we present a new stochastic model that, under rather general assumptions, provides a robust explanation for the observed regularity.

Detecting evolutionary forces in language change.

PubMed

Newberry, Mitchell G; Ahern, Christopher A; Clark, Robin; Plotkin, Joshua B

2017-11-09

Both language and genes evolve by transmission over generations with opportunity for differential replication of forms. The understanding that gene frequencies change at random by genetic drift, even in the absence of natural selection, was a seminal advance in evolutionary biology. Stochastic drift must also occur in language as a result of randomness in how linguistic forms are copied between speakers. Here we quantify the strength of selection relative to stochastic drift in language evolution. We use time series derived from large corpora of annotated texts dating from the 12th to 21st centuries to analyse three well-known grammatical changes in English: the regularization of past-tense verbs, the introduction of the periphrastic 'do', and variation in verbal negation. We reject stochastic drift in favour of selection in some cases but not in others. In particular, we infer selection towards the irregular forms of some past-tense verbs, which is likely driven by changing frequencies of rhyming patterns over time. We show that stochastic drift is stronger for rare words, which may explain why rare forms are more prone to replacement than common ones. This work provides a method for testing selective theories of language change against a null model and reveals an underappreciated role for stochasticity in language evolution.

Numerical Simulation and Quantitative Uncertainty Assessment of Microchannel Flow

NASA Astrophysics Data System (ADS)

Debusschere, Bert; Najm, Habib; Knio, Omar; Matta, Alain; Ghanem, Roger; Le Maitre, Olivier

2002-11-01

This study investigates the effect of uncertainty in physical model parameters on computed electrokinetic flow of proteins in a microchannel with a potassium phosphate buffer. The coupled momentum, species transport, and electrostatic field equations give a detailed representation of electroosmotic and pressure-driven flow, including sample dispersion mechanisms. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. To quantify uncertainty, the governing equations are reformulated using a pseudo-spectral stochastic methodology, which uses polynomial chaos expansions to describe uncertain/stochastic model parameters, boundary conditions, and flow quantities. Integration of the resulting equations for the spectral mode strengths gives the evolution of all stochastic modes for all variables. Results show the spatiotemporal evolution of uncertainties in predicted quantities and highlight the dominant parameters contributing to these uncertainties during various flow phases. This work is supported by DARPA.

INFRARED OBSERVATIONAL MANIFESTATIONS OF YOUNG DUSTY SUPER STAR CLUSTERS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-González, Sergio; Tenorio-Tagle, Guillermo; Silich, Sergiy, E-mail: sergiomtz@inaoep.mx

The growing evidence pointing at core-collapse supernovae as large dust producers makes young massive stellar clusters ideal laboratories to study the evolution of dust immersed in a hot plasma. Here we address the stochastic injection of dust by supernovae, and follow its evolution due to thermal sputtering within the hot and dense plasma generated by young stellar clusters. Under these considerations, dust grains are heated by means of random collisions with gas particles which result in the appearance of  infrared spectral signatures. We present time-dependent infrared spectral energy distributions that are to be expected from young stellar clusters. Our results aremore » based on hydrodynamic calculations that account for the stochastic injection of dust by supernovae. These also consider gas and dust radiative cooling, stochastic dust temperature fluctuations, the exit of dust grains out of the cluster volume due to the cluster wind, and a time-dependent grain size distribution.« less

Interpretation of scrape-off layer profile evolution and first-wall ion flux statistics on JET using a stochastic framework based on fillamentary motion

NASA Astrophysics Data System (ADS)

Walkden, N. R.; Wynn, A.; Militello, F.; Lipschultz, B.; Matthews, G.; Guillemaut, C.; Harrison, J.; Moulton, D.; Contributors, JET

2017-08-01

This paper presents the use of a novel modelling technique based around intermittent transport due to filament motion, to interpret experimental profile and fluctuation data in the scrape-off layer (SOL) of JET during the onset and evolution of a density profile shoulder. A baseline case is established, prior to shoulder formation, and the stochastic model is shown to be capable of simultaneously matching the time averaged profile measurement as well as the PDF shape and autocorrelation function from the ion-saturation current time series at the outer wall. Aspects of the stochastic model are then varied with the aim of producing a profile shoulder with statistical measurements consistent with experiment. This is achieved through a strong localised reduction in the density sink acting on the filaments within the model. The required reduction of the density sink occurs over a highly localised region with the timescale of the density sink increased by a factor of 25. This alone is found to be insufficient to model the expansion and flattening of the shoulder region as the density increases, which requires additional changes within the stochastic model. An example is found which includes both a reduction in the density sink and filament acceleration and provides a consistent match to the experimental data as the shoulder expands, though the uniqueness of this solution can not be guaranteed. Within the context of the stochastic model, this implies that the localised reduction in the density sink can trigger shoulder formation, but additional physics is required to explain the subsequent evolution of the profile.

Stochastic damage evolution in textile laminates

NASA Technical Reports Server (NTRS)

Dzenis, Yuris A.; Bogdanovich, Alexander E.; Pastore, Christopher M.

1993-01-01

A probabilistic model utilizing random material characteristics to predict damage evolution in textile laminates is presented. Model is based on a division of each ply into two sublaminas consisting of cells. The probability of cell failure is calculated using stochastic function theory and maximal strain failure criterion. Three modes of failure, i.e. fiber breakage, matrix failure in transverse direction, as well as matrix or interface shear cracking, are taken into account. Computed failure probabilities are utilized in reducing cell stiffness based on the mesovolume concept. A numerical algorithm is developed predicting the damage evolution and deformation history of textile laminates. Effect of scatter of fiber orientation on cell properties is discussed. Weave influence on damage accumulation is illustrated with the help of an example of a Kevlar/epoxy laminate.

Evolution and mass extinctions as lognormal stochastic processes

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics). (5) But the most striking new result is that the well-known `Molecular Clock of Evolution', namely the `constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms. (7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time. In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are the particular case of exponential growth.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations.

PubMed

Lande, Russell; Engen, Steinar; Sæther, Bernt-Erik

2017-10-31

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size. Published under the PNAS license.

Nonlinear Image Denoising Methodologies

DTIC Science & Technology

2002-05-01

53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

On orthogonality preserving quadratic stochastic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

On an aggregation in birth-and-death stochastic dynamics

NASA Astrophysics Data System (ADS)

Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

2014-06-01

We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.

Computation of direct and inverse mutations with the SEGM web server (Stochastic Evolution of Genetic Motifs): an application to splice sites of human genome introns.

PubMed

Benard, Emmanuel; Michel, Christian J

2009-08-01

We present here the SEGM web server (Stochastic Evolution of Genetic Motifs) in order to study the evolution of genetic motifs both in the direct evolutionary sense (past-present) and in the inverse evolutionary sense (present-past). The genetic motifs studied can be nucleotides, dinucleotides and trinucleotides. As an example of an application of SEGM and to understand its functionalities, we give an analysis of inverse mutations of splice sites of human genome introns. SEGM is freely accessible at http://lsiit-bioinfo.u-strasbg.fr:8080/webMathematica/SEGM/SEGM.html directly or by the web site http://dpt-info.u-strasbg.fr/~michel/. To our knowledge, this SEGM web server is to date the only computational biology software in this evolutionary approach.

Magnetohydrodynamic stability of stochastically driven accretion flows.

PubMed

Nath, Sujit Kumar; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K

2013-07-01

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.

A Simplified Treatment of Brownian Motion and Stochastic Differential Equations Arising in Financial Mathematics

ERIC Educational Resources Information Center

Parlar, Mahmut

2004-01-01

Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

Two Stochastic Phases of Tick-wise Price Fluctuation and the Price Prediction Generator

NASA Astrophysics Data System (ADS)

Tanaka-Yamawaki, Mieko; Tokuoka, Seiji

2007-07-01

We report in this paper the existence of two different stochastic phases in the tick-wise price fluctuations. Based on this observation, we improve our old method of developing the evolutional strategy to predict the direction of the tick-wise price movements. We obtain a stable predictive power even in the region where the old method had a difficulty.

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ju, Ping; Li, Hongyu; Gan, Chun

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes itmore » very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.« less

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

Reynolds, Andy

2002-11-01

It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

Provably unbounded memory advantage in stochastic simulation using quantum mechanics

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.; Liu, Qing; Thompson, Jayne; Vedral, Vlatko; Gu, mile

2017-10-01

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.

Evolution in health and medicine Sackler colloquium: Stochastic epigenetic variation as a driving force of development, evolutionary adaptation, and disease.

PubMed

Feinberg, Andrew P; Irizarry, Rafael A

2010-01-26

Neo-Darwinian evolutionary theory is based on exquisite selection of phenotypes caused by small genetic variations, which is the basis of quantitative trait contribution to phenotype and disease. Epigenetics is the study of nonsequence-based changes, such as DNA methylation, heritable during cell division. Previous attempts to incorporate epigenetics into evolutionary thinking have focused on Lamarckian inheritance, that is, environmentally directed epigenetic changes. Here, we propose a new non-Lamarckian theory for a role of epigenetics in evolution. We suggest that genetic variants that do not change the mean phenotype could change the variability of phenotype; and this could be mediated epigenetically. This inherited stochastic variation model would provide a mechanism to explain an epigenetic role of developmental biology in selectable phenotypic variation, as well as the largely unexplained heritable genetic variation underlying common complex disease. We provide two experimental results as proof of principle. The first result is direct evidence for stochastic epigenetic variation, identifying highly variably DNA-methylated regions in mouse and human liver and mouse brain, associated with development and morphogenesis. The second is a heritable genetic mechanism for variable methylation, namely the loss or gain of CpG dinucleotides over evolutionary time. Finally, we model genetically inherited stochastic variation in evolution, showing that it provides a powerful mechanism for evolutionary adaptation in changing environments that can be mediated epigenetically. These data suggest that genetically inherited propensity to phenotypic variability, even with no change in the mean phenotype, substantially increases fitness while increasing the disease susceptibility of a population with a changing environment.

Relevance of phenotypic noise to adaptation and evolution.

PubMed

Kaneko, K; Furusawa, C

2008-09-01

Biological processes are inherently noisy, as highlighted in recent measurements of stochasticity in gene expression. Here, the authors show that such phenotypic noise is essential to the adaptation of organisms to a variety of environments and also to the evolution of robustness against mutations. First, the authors show that for any growing cell showing stochastic gene expression, the adaptive cellular state is inevitably selected by noise, without the use of a specific signal transduction network. In general, changes in any protein concentration in a cell are products of its synthesis minus dilution and degradation, both of which are proportional to the rate of cell growth. In an adaptive state, both the synthesis and dilution terms of proteins are large, and so the adaptive state is less affected by stochasticity in gene expression, whereas for a non-adaptive state, both terms are smaller, and so cells are easily knocked out of their original state by noise. This leads to a novel, generic mechanism for the selection of adaptive states. The authors have confirmed this selection by model simulations. Secondly, the authors consider the evolution of gene networks to acquire robustness of the phenotype against noise and mutation. Through simulations using a simple stochastic gene expression network that undergoes mutation and selection, the authors show that a threshold level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during growth and development shapes any network's robustness, not only to noise but also to mutations. The authors also establish a relationship between developmental and mutational robustness.

Recent topographic evolution and erosion of the deglaciated Washington Cascades inferred from a stochastic landscape evolution model

NASA Astrophysics Data System (ADS)

Moon, Seulgi; Shelef, Eitan; Hilley, George E.

2015-05-01

In this study, we model postglacial surface processes and examine the evolution of the topography and denudation rates within the deglaciated Washington Cascades to understand the controls on and time scales of landscape response to changes in the surface process regime after deglaciation. The postglacial adjustment of this landscape is modeled using a geomorphic-transport-law-based numerical model that includes processes of river incision, hillslope diffusion, and stochastic landslides. The surface lowering due to landslides is parameterized using a physically based slope stability model coupled to a stochastic model of the generation of landslides. The model parameters of river incision and stochastic landslides are calibrated based on the rates and distribution of thousand-year-time scale denudation rates measured from cosmogenic 10Be isotopes. The probability distributions of those model parameters calculated based on a Bayesian inversion scheme show comparable ranges from previous studies in similar rock types and climatic conditions. The magnitude of landslide denudation rates is determined by failure density (similar to landslide frequency), whereas precipitation and slopes affect the spatial variation in landslide denudation rates. Simulation results show that postglacial denudation rates decay over time and take longer than 100 kyr to reach time-invariant rates. Over time, the landslides in the model consume the steep slopes characteristic of deglaciated landscapes. This response time scale is on the order of or longer than glacial/interglacial cycles, suggesting that frequent climatic perturbations during the Quaternary may produce a significant and prolonged impact on denudation and topography.

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Tauber, Uwe C.

2012-02-01

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Evolutionary stability concepts in a stochastic environment

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Stochastic YORP On Real Asteroid Shapes

NASA Astrophysics Data System (ADS)

McMahon, Jay W.

2015-05-01

Since its theoretical foundation and subsequent observational verification, the YORP effect has been understood to be a fundamental process that controls the evolution of small asteroids in the inner solar system. In particular, the coupling of the YORP and Yarkovsky effects are hypothesized to be largely responsible for the transport of asteroids from the main belt to the inner solar system populations. Furthermore, the YORP effect is thought to lead to rotational fission of small asteroids, which leads to the creation of multiple asteroid systems, contact binary asteroids, and asteroid pairs. However recent studies have called into question the ability of YORP to produce these results. In particular, the high sensitivity of the YORP coefficients to variations in the shape of an asteroid, combined with the possibility of a changing shape due to YORP accelerated spin rates can combine to create a stochastic YORP coefficient which can arrest or change the evolution of a small asteroid's spin state. In this talk, initial results are presented from new simulations which comprehensively model the stochastic YORP process. Shape change is governed by the surface slopes on radar based asteroid shape models, where the highest slope regions change first. The investigation of the modification of YORP coefficients and subsequent spin state evolution as a result of this dynamically influenced shape change is presented and discussed.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Cosmological stochastic Higgs field stabilization

NASA Astrophysics Data System (ADS)

Gong, Jinn-Ouk; Kitajima, Naoya

2017-09-01

We show that the stochastic evolution of an interacting system of the Higgs field and a spectator scalar field naturally gives rise to an enhanced probability of settling down at the electroweak vacuum at the end of inflation. Subsequent destabilization due to parametric resonance between the Higgs field and the spectator field can be avoided in a wide parameter range. We further argue that the spectator field can play the role of dark matter.

Biophysics, environmental stochasticity, and the evolution of thermal safety margins in intertidal limpets.

PubMed

Denny, M W; Dowd, W W

2012-03-15

As the air temperature of the Earth rises, ecological relationships within a community might shift, in part due to differences in the thermal physiology of species. Prediction of these shifts - an urgent task for ecologists - will be complicated if thermal tolerance itself can rapidly evolve. Here, we employ a mechanistic approach to predict the potential for rapid evolution of thermal tolerance in the intertidal limpet Lottia gigantea. Using biophysical principles to predict body temperature as a function of the state of the environment, and an environmental bootstrap procedure to predict how the environment fluctuates through time, we create hypothetical time-series of limpet body temperatures, which are in turn used as a test platform for a mechanistic evolutionary model of thermal tolerance. Our simulations suggest that environmentally driven stochastic variation of L. gigantea body temperature results in rapid evolution of a substantial 'safety margin': the average lethal limit is 5-7°C above the average annual maximum temperature. This predicted safety margin approximately matches that found in nature, and once established is sufficient, in our simulations, to allow some limpet populations to survive a drastic, century-long increase in air temperature. By contrast, in the absence of environmental stochasticity, the safety margin is dramatically reduced. We suggest that the risk of exceeding the safety margin, rather than the absolute value of the safety margin, plays an underappreciated role in the evolution of thermal tolerance. Our predictions are based on a simple, hypothetical, allelic model that connects genetics to thermal physiology. To move beyond this simple model - and thereby potentially to predict differential evolution among populations and among species - will require significant advances in our ability to translate the details of thermal histories into physiological and population-genetic consequences.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Stochastic hybrid systems for studying biochemical processes.

PubMed

Singh, Abhyudai; Hespanha, João P

2010-11-13

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

A Generative Angular Model of Protein Structure Evolution

PubMed Central

Golden, Michael; García-Portugués, Eduardo; Sørensen, Michael; Mardia, Kanti V.; Hamelryck, Thomas; Hein, Jotun

2017-01-01

Abstract Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modeled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modeling both “smooth” conformational changes and “catastrophic” conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence–structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof. PMID:28453724

Boson Hamiltonians and stochasticity for the vorticity equation

NASA Technical Reports Server (NTRS)

Shen, Hubert H.

1990-01-01

The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

Mean Field Games for Stochastic Growth with Relative Utility

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Minyi, E-mail: mhuang@math.carleton.ca; Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation errormore » estimate.« less

Evolution of probability densities in stochastic coupled map lattices

NASA Astrophysics Data System (ADS)

Losson, Jérôme; Mackey, Michael C.

1995-08-01

This paper describes the statistical properties of coupled map lattices subjected to the influence of stochastic perturbations. The stochastic analog of the Perron-Frobenius operator is derived for various types of noise. When the local dynamics satisfy rather mild conditions, this equation is shown to possess either stable, steady state solutions (i.e., a stable invariant density) or density limit cycles. Convergence of the phase space densities to these limit cycle solutions explains the nonstationary behavior of statistical quantifiers at equilibrium. Numerical experiments performed on various lattices of tent, logistic, and shift maps with diffusivelike interelement couplings are examined in light of these theoretical results.

Selective sweeps of mitochondrial DNA can drive the evolution of uniparental inheritance.

PubMed

Christie, Joshua R; Beekman, Madeleine

2017-08-01

Although the uniparental (or maternal) inheritance of mitochondrial DNA (mtDNA) is widespread, the reasons for its evolution remain unclear. Two main hypotheses have been proposed: selection against individuals containing different mtDNAs (heteroplasmy) and selection against "selfish" mtDNA mutations. Recently, uniparental inheritance was shown to promote adaptive evolution in mtDNA, potentially providing a third hypothesis for its evolution. Here, we explore this hypothesis theoretically and ask if the accumulation of beneficial mutations provides a sufficient fitness advantage for uniparental inheritance to invade a population in which mtDNA is inherited biparentally. In a deterministic model, uniparental inheritance increases in frequency but cannot replace biparental inheritance if only a single beneficial mtDNA mutation sweeps through the population. When we allow successive selective sweeps of mtDNA, however, uniparental inheritance can replace biparental inheritance. Using a stochastic model, we show that a combination of selection and drift facilitates the fixation of uniparental inheritance (compared to a neutral trait) when there is only a single selective mtDNA sweep. When we consider multiple mtDNA sweeps in a stochastic model, uniparental inheritance becomes even more likely to replace biparental inheritance. Our findings thus suggest that selective sweeps of beneficial mtDNA haplotypes can drive the evolution of uniparental inheritance. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

PubMed

Mangel, Marc

2015-05-01

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

PubMed Central

Chen, Bor-Sen; Lin, Ying-Po

2011-01-01

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network’s evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective. PMID:22084563

Stochastic modification of the Schrödinger-Newton equation

NASA Astrophysics Data System (ADS)

Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.

2015-07-01

The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

Stochastic processes constrain the within and between host evolution of influenza virus.

PubMed

McCrone, John T; Woods, Robert J; Martin, Emily T; Malosh, Ryan E; Monto, Arnold S; Lauring, Adam S

2018-05-03

The evolutionary dynamics of influenza virus ultimately derive from processes that take place within and between infected individuals. Here we define influenza virus dynamics in human hosts through sequencing of 249 specimens from 200 individuals collected over 6290 person-seasons of observation. Because these viruses were collected from individuals in a prospective community-based cohort, they are broadly representative of natural infections with seasonal viruses. Consistent with a neutral model of evolution, sequence data from 49 serially sampled individuals illustrated the dynamic turnover of synonymous and nonsynonymous single nucleotide variants and provided little evidence for positive selection of antigenic variants. We also identified 43 genetically-validated transmission pairs in this cohort. Maximum likelihood optimization of multiple transmission models estimated an effective transmission bottleneck of 1-2 genomes. Our data suggest that positive selection is inefficient at the level of the individual host and that stochastic processes dominate the host-level evolution of influenza viruses. © 2018, McCrone et al.

Chaotic ion motion in magnetosonic plasma waves

NASA Technical Reports Server (NTRS)

Varvoglis, H.

1984-01-01

The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficient D approximately equal to 1/v. Possible applications of this process to ion acceleration in flares and ion beam thermalization are discussed.

Solving multistage stochastic programming models of portfolio selection with outstanding liabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edirisinghe, C.

1994-12-31

Models for portfolio selection in the presence of an outstanding liability have received significant attention, for example, models for pricing options. The problem may be described briefly as follows: given a set of risky securities (and a riskless security such as a bond), and given a set of cash flows, i.e., outstanding liability, to be met at some future date, determine an initial portfolio and a dynamic trading strategy for the underlying securities such that the initial cost of the portfolio is within a prescribed wealth level and the expected cash surpluses arising from trading is maximized. While the tradingmore » strategy should be self-financing, there may also be other restrictions such as leverage and short-sale constraints. Usually the treatment is limited to binomial evolution of uncertainty (of stock price), with possible extensions for developing computational bounds for multinomial generalizations. Posing as stochastic programming models of decision making, we investigate alternative efficient solution procedures under continuous evolution of uncertainty, for discrete time economies. We point out an important moment problem arising in the portfolio selection problem, the solution (or bounds) on which provides the basis for developing efficient computational algorithms. While the underlying stochastic program may be computationally tedious even for a modest number of trading opportunities (i.e., time periods), the derived algorithms may used to solve problems whose sizes are beyond those considered within stochastic optimization.« less

Time series analysis for minority game simulations of financial markets

NASA Astrophysics Data System (ADS)

Ferreira, Fernando F.; Francisco, Gerson; Machado, Birajara S.; Muruganandam, Paulsamy

2003-04-01

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.

Coupling of c  =  ‑2 and c =\\frac{1}{2} and c  =  0 conformal field theories: the geometrical point of view

NASA Astrophysics Data System (ADS)

Najafi, M. N.

2018-04-01

The coupling of the c  =  ‑2, c=\\frac{1}{2} and c  =  0 conformal field theories are numerically considered in this paper. As the prototypes of the couplings, (c_1=-2)\\oplus (c_2=0) and (c_1=-2)\\oplus (c_2=\\frac{1}{2}) , we consider the Bak–Tang–Weisenfeld (BTW) model on the 2D square critical site-percolation and the BTW model on Ising-correlated percolation lattices respectively. Some geometrical techniques are used to characterize the presumable conformal symmetry of the resultant systems. Based on the numerical analysis of the diffusivity parameter (κ) in the Schramm–Loewner evolution (SLE) theory we propose that the algebra of the central charges of the coupled models is closed. This result is based on the analysis of the conformal loop ensemble (CLE) analysis. The diffusivity parameter in each case is obtained by calculating the fractal dimension of loops (and the corresponding exponent of mean-square root distance), the direct SLE mapping method, the left passage probability and the winding angle analysis. More precisely we numerically show that the coupling (c_1=-2)\\oplus (c_2=\\frac{1}{2}) results to 2D self-avoiding walk (SAW) fixed point corresponding to c  =  0 conformal field theory, whereas the coupling (c_1=-2)\\oplus (c_2=0) results to the 2D critical Ising fixed point corresponding to the c=\\frac{1}{2} conformal field theory.

Mechanisms for the target patterns formation in a stochastic bistable excitable medium

NASA Astrophysics Data System (ADS)

Verisokin, Andrey Yu.; Verveyko, Darya V.; Postnov, Dmitry E.

2018-04-01

We study the features of formation and evolution of spatiotemporal chaotic regime generated by autonomous pacemakers in excitable deterministic and stochastic bistable active media using the example of the FitzHugh - Nagumo biological neuron model under discrete medium conditions. The following possible mechanisms for the formation of autonomous pacemakers have been studied: 1) a temporal external force applied to a small region of the medium, 2) geometry of the solution region (the medium contains regions with Dirichlet or Neumann boundaries). In our work we explore the conditions for the emergence of pacemakers inducing target patterns in a stochastic bistable excitable system and propose the algorithm for their analysis.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

PubMed

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

Lognormals for SETI, Evolution and Mass Extinctions

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-12-01

In a series of recent papers (Refs. [1-5,7,8]) and in a book (Ref. [6]), this author suggested a new mathematical theory capable of merging Darwinian Evolution and SETI into a unified statistical framework. In this new vision, Darwinian Evolution, as it unfolded on Earth over the last 3.5 billion years, is defined as just one particular realization of a certain lognormal stochastic process in the number of living species on Earth, whose mean value increased in time exponentially. SETI also may be brought into this vision since the number of communicating civilizations in the Galaxy is given by a lognormal distribution (Statistical Drake Equation). Now, in this paper we further elaborate on all that particularly with regard to two important topics: The introduction of the general lognormal stochastic process L(t) whose mean value may be an arbitrary continuous function of the time, m(t), rather than just the exponential mGBM (t) =N0eμt typical of the Geometric Brownian Motion (GBM). This is a considerable generalization of the GBM-based theory used in Refs. [1-8]. The particular application of the general stochastic process L(t) to the understanding of Mass Extinctions like the K-Pg one that marked the dinosaurs' end 65 million years ago. We first model this Mass Extinction as a decreasing Geometric Brownian Motion (GBM) extending from the asteroid's impact time all through the ensuing 'nuclear winter'. However, this model has a flaw: the 'final value' of the GBM cannot have a horizontal tangent, as requested to enable the recovery of life again after this 'final extinction value'. That flaw, however, is removed if the rapidly decreasing mean value function of L(t) is the left branch of a parabola extending from the asteroid's impact time all through the ensuing 'nuclear winter' and up to the time when the number of living species on Earth started growing up again, as we show mathematically in Section 3. In conclusion, we have uncovered an important generalization of the GBM into the general lognormal stochastic process L(t), paving the way to a better, future understanding the evolution of life on Exoplanets on the basis of what Evolution unfolded on Earth in the last 3.5 billion years. That will be the goal of further research papers in the future.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Integrated Multiscale Modeling of Molecular Computing Devices. Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tim Schulze

2012-11-01

The general theme of this research has been to expand the capabilities of a simulation technique, Kinetic Monte Carlo (KMC) and apply it to study self-assembled nano-structures on epitaxial thin films. KMC simulates thin film growth and evolution by replacing the detailed dynamics of the system's evolution, which might otherwise be studied using molecular dynamics, with an appropriate stochastic process.

Stochastic 2-D galaxy disk evolution models. Resolved stellar populations in the galaxy M33

NASA Astrophysics Data System (ADS)

Mineikis, T.; Vansevičius, V.

We improved the stochastic 2-D galaxy disk models (Mineikis & Vansevičius 2014a) by introducing enriched gas outflows from galaxies and synthetic color-magnitude diagrams of stellar populations. To test the models, we use the HST/ACS stellar photometry data in four fields located along the major axis of the galaxy M33 (Williams et al. 2009) and demonstrate the potential of the models to derive 2-D star formation histories in the resolved disk galaxies.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Probability density function evolution of power systems subject to stochastic variation of renewable energy

NASA Astrophysics Data System (ADS)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy.

PubMed

Rajon, E; Venner, S; Menu, F

2009-10-01

Diversified bet-hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life-history traits defined as diversified bet-hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet-hedging dormancy strategies in a metapopulation using a two-patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet-hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet-hedging strategies that we hope will encourage new empirical studies of this topic.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

The adaptation rate of a quantitative trait in an environmental gradient

NASA Astrophysics Data System (ADS)

Hermsen, R.

2016-12-01

The spatial range of a species habitat is generally determined by the ability of the species to cope with biotic and abiotic variables that vary in space. Therefore, the species range is itself an evolvable property. Indeed, environmental gradients permit a mode of evolution in which range expansion and adaptation go hand in hand. This process can contribute to rapid evolution of drug resistant bacteria and viruses, because drug concentrations in humans and livestock treated with antibiotics are far from uniform. Here, we use a minimal stochastic model of discrete, interacting organisms evolving in continuous space to study how the rate of adaptation of a quantitative trait depends on the steepness of the gradient and various population parameters. We discuss analytical results for the mean-field limit as well as extensive stochastic simulations. These simulations were performed using an exact, event-driven simulation scheme that can deal with continuous time-, density- and coordinate-dependent reaction rates and could be used for a wide variety of stochastic systems. The results reveal two qualitative regimes. If the gradient is shallow, the rate of adaptation is limited by dispersion and increases linearly with the gradient slope. If the gradient is steep, the adaptation rate is limited by mutation. In this regime, the mean-field result is highly misleading: it predicts that the adaptation rate continues to increase with the gradient slope, whereas stochastic simulations show that it in fact decreases with the square root of the slope. This discrepancy underscores the importance of discreteness and stochasticity even at high population densities; mean-field results, including those routinely used in quantitative genetics, should be interpreted with care.

The adaptation rate of a quantitative trait in an environmental gradient.

PubMed

Hermsen, R

2016-11-30

The spatial range of a species habitat is generally determined by the ability of the species to cope with biotic and abiotic variables that vary in space. Therefore, the species range is itself an evolvable property. Indeed, environmental gradients permit a mode of evolution in which range expansion and adaptation go hand in hand. This process can contribute to rapid evolution of drug resistant bacteria and viruses, because drug concentrations in humans and livestock treated with antibiotics are far from uniform. Here, we use a minimal stochastic model of discrete, interacting organisms evolving in continuous space to study how the rate of adaptation of a quantitative trait depends on the steepness of the gradient and various population parameters. We discuss analytical results for the mean-field limit as well as extensive stochastic simulations. These simulations were performed using an exact, event-driven simulation scheme that can deal with continuous time-, density- and coordinate-dependent reaction rates and could be used for a wide variety of stochastic systems. The results reveal two qualitative regimes. If the gradient is shallow, the rate of adaptation is limited by dispersion and increases linearly with the gradient slope. If the gradient is steep, the adaptation rate is limited by mutation. In this regime, the mean-field result is highly misleading: it predicts that the adaptation rate continues to increase with the gradient slope, whereas stochastic simulations show that it in fact decreases with the square root of the slope. This discrepancy underscores the importance of discreteness and stochasticity even at high population densities; mean-field results, including those routinely used in quantitative genetics, should be interpreted with care.

SIApopr: a computational method to simulate evolutionary branching trees for analysis of tumor clonal evolution.

PubMed

McDonald, Thomas O; Michor, Franziska

2017-07-15

SIApopr (Simulating Infinite-Allele populations) is an R package to simulate time-homogeneous and inhomogeneous stochastic branching processes under a very flexible set of assumptions using the speed of C ++. The software simulates clonal evolution with the emergence of driver and passenger mutations under the infinite-allele assumption. The software is an application of the Gillespie Stochastic Simulation Algorithm expanded to a large number of cell types and scenarios, with the intention of allowing users to easily modify existing models or create their own. SIApopr is available as an R library on Github ( https://github.com/olliemcdonald/siapopr ). Supplementary data are available at Bioinformatics online. michor@jimmy.harvard.edu. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Stochastic stability in three-player games.

PubMed

Kamiński, Dominik; Miekisz, Jacek; Zaborowski, Marcin

2005-11-01

Animal behavior and evolution can often be described by game-theoretic models. Although in many situations the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only recently were evolutionarily stable strategies defined for multi-player games and their properties analyzed [Broom, M., Cannings, C., Vickers, G.T., 1997. Multi-player matrix games. Bull. Math. Biol. 59, 931-952]. Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze the stochastic stability of equilibria in games with multiple evolutionarily stable strategies. We also show that, in some games, a population may not evolve in the long run to an evolutionarily stable equilibrium.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations

NASA Astrophysics Data System (ADS)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2018-07-01

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation.

Stochastic Evolution of Augmented Born-Infeld Equations

NASA Astrophysics Data System (ADS)

Holm, Darryl D.

2018-06-01

This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are striking. Namely, the introduction of Stratonovich cylindrical noise into each of their Hamiltonian formulations introduces stochastic Lie transport into their dynamics in the same form for both theories. Moreover, the resulting stochastic partial differential equations retain their unperturbed form, except for an additional term representing induced Lie transport by the set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation for this remarkable similarity lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, which is done via pairing spatial correlation eigenvectors for cylindrical noise with the momentum map for the deterministic motion. This momentum map is responsible for the well-known analogy between hydrodynamics and electromagnetism. The momentum map for the Maxwell and Born-Infeld theories of electromagnetism treated here is the 1-form density known as the Poynting vector. Two appendices treat the Hamiltonian structures underlying these results.

Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum-measurement theory

NASA Astrophysics Data System (ADS)

Gambetta, Jay; Wiseman, H. M.

2002-07-01

Do stochastic Schrödinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schrödinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schrödinger equation introduced by Strunz, Diósi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.

Continuum Model for River Networks

NASA Astrophysics Data System (ADS)

Giacometti, Achille; Maritan, Amos; Banavar, Jayanth R.

1995-07-01

The effects of erosion, avalanching, and random precipitation are captured in a simple stochastic partial differential equation for modeling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.

From quantum to classical modeling of radiation reaction: A focus on stochasticity effects

NASA Astrophysics Data System (ADS)

Niel, F.; Riconda, C.; Amiranoff, F.; Duclous, R.; Grech, M.

2018-04-01

Radiation reaction in the interaction of ultrarelativistic electrons with a strong external electromagnetic field is investigated using a kinetic approach in the nonlinear moderately quantum regime. Three complementary descriptions are discussed considering arbitrary geometries of interaction: a deterministic one relying on the quantum-corrected radiation reaction force in the Landau and Lifschitz (LL) form, a linear Boltzmann equation for the electron distribution function, and a Fokker-Planck (FP) expansion in the limit where the emitted photon energies are small with respect to that of the emitting electrons. The latter description is equivalent to a stochastic differential equation where the effect of the radiation reaction appears in the form of the deterministic term corresponding to the quantum-corrected LL friction force, and by a diffusion term accounting for the stochastic nature of photon emission. By studying the evolution of the energy moments of the electron distribution function with the three models, we are able to show that all three descriptions provide similar predictions on the temporal evolution of the average energy of an electron population in various physical situations of interest, even for large values of the quantum parameter χ . The FP and full linear Boltzmann descriptions also allow us to correctly describe the evolution of the energy variance (second-order moment) of the distribution function, while higher-order moments are in general correctly captured with the full linear Boltzmann description only. A general criterion for the limit of validity of each description is proposed, as well as a numerical scheme for the inclusion of the FP description in particle-in-cell codes. This work, not limited to the configuration of a monoenergetic electron beam colliding with a laser pulse, allows further insight into the relative importance of various effects of radiation reaction and in particular of the discrete and stochastic nature of high-energy photon emission and its back-reaction in the deformation of the particle distribution function.

Shortcuts to adiabaticity using flow fields

NASA Astrophysics Data System (ADS)

Patra, Ayoti; Jarzynski, Christopher

2017-12-01

A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.

Effects of conformism on the cultural evolution of social behaviour.

PubMed

Molleman, Lucas; Pen, Ido; Weissing, Franz J

2013-01-01

Models of cultural evolution study how the distribution of cultural traits changes over time. The dynamics of cultural evolution strongly depends on the way these traits are transmitted between individuals by social learning. Two prominent forms of social learning are payoff-based learning (imitating others that have higher payoffs) and conformist learning (imitating locally common behaviours). How payoff-based and conformist learning affect the cultural evolution of cooperation is currently a matter of lively debate, but few studies systematically analyse the interplay of these forms of social learning. Here we perform such a study by investigating how the interaction of payoff-based and conformist learning affects the outcome of cultural evolution in three social contexts. First, we develop a simple argument that provides insights into how the outcome of cultural evolution will change when more and more conformist learning is added to payoff-based learning. In a social dilemma (e.g. a Prisoner's Dilemma), conformism can turn cooperation into a stable equilibrium; in an evasion game (e.g. a Hawk-Dove game or a Snowdrift game) conformism tends to destabilize the polymorphic equilibrium; and in a coordination game (e.g. a Stag Hunt game), conformism changes the basin of attraction of the two equilibria. Second, we analyse a stochastic event-based model, revealing that conformism increases the speed of cultural evolution towards pure equilibria. Individual-based simulations as well as the analysis of the diffusion approximation of the stochastic model by and large confirm our findings. Third, we investigate the effect of an increasing degree of conformism on cultural group selection in a group-structured population. We conclude that, in contrast to statements in the literature, conformism hinders rather than promotes the evolution of cooperation.

Mantle convection and the distribution of geochemical reservoirs in the silicate shell of the Earth

NASA Astrophysics Data System (ADS)

Walzer, Uwe; Hendel, Roland

2010-05-01

We present a dynamic 3-D spherical-shell model of mantle convection and the evolution of the chemical reservoirs of the Earth`s silicate shell. Chemical differentiation, convection, stirring and thermal evolution constitute an inseparable dynamic system. Our model is based on the solution of the balance equations of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs 238U-206Pb, 235U-207Pb, 232Th-208Pb, and 40K-40Ar. Similar to the present model, the continental crust of the real Earth was not produced entirely at the start of the evolution but developed episodically in batches [1-7]. The details of the continental distribution of the model are largely stochastic, but the spectral properties are quite similar to the present real Earth. The calculated Figures reveal that the modeled present-day mantle has no chemical stratification but we find a marble-cake structure. If we compare the observational results of the present-day proportion of depleted MORB mantle with the model then we find a similar order of magnitude. The MORB source dominates under the lithosphere. In our model, there are nowhere pure unblended reservoirs in the mantle. It is, however, remarkable that, in spite of 4500 Ma of solid-state mantle convection, certain strong concentrations of distributed chemical reservoirs continue to persist in certain volumes, although without sharp abundance boundaries. We deal with the question of predictable and stochastic portions of the phenomena. Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Rat , is relatively well predictable and the stochastic parts of the Rat(t)-curves are small. Regarding the juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution. Later on, the distribution of the continental-growth episodes is increasingly stochastic. Independently of the varying individual runs, our model shows that the total mass of the present-day continents is not generated in a single process at the beginning of the thermal evolution of the Earth but in episodically distributed processes in the course of geological time. This is in accord with observation. Finally, we present results regarding the numerical method, implementation, scalability and performance. References [1] Condie, K. C., Episodie continental growth models: Afterthoughts and extensions, Tectonophysics, 322 (2000), 153-162. [2] Davidson, J. P. and Arculus, R. J., The significance of Phanerozoic arc magmatism in generating continental crust, in Evolution and Differentiation of the Continental Crust, edited by M. Brown and T. Rushmer (2006), 135-172, Cambridge Univ. Press, Cambridge, UK. [3] Hofmann, A. W., Sampling mantle heterogeneity through oceanic basalts: Isotopes and trace elements, in Treatise on Geochemistry, Vol. 2: The Mantle and the Core, edited by R. W. Carlson (2003), 61-101, Elsevier, Amsterdam. [4] Rollinson, H., Crustal generation in the Archean, in Evolution and Differentiation of the Continental Crust, edited by M. Brown and T. Rushmer (2006), 173-230, Cambridge Univ. Press, Cambridge, UK: [5] Taylor, S. R. and McLennan, S. M., Planetary Crusts. Their Composition, Origin and Evolution. (2009), 1-378, Cambridge Univ. Press, Cambridge, UK. [6] Walzer, U. and Hendel, R., Mantle convection and evolution with growing continents. J. Geophys. Res. 113 (2008), B09405, doi: 10.1029/2007JB005459 [7] http://www.igw.uni-jena.de/geodyn

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

NASA Astrophysics Data System (ADS)

Spettl, A.; Wimmer, R.; Werz, T.; Heinze, M.; Odenbach, S.; Krill, C. E., III; Schmidt, V.

2015-09-01

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al-Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Stochastic simulation and analysis of biomolecular reaction networks

PubMed Central

Frazier, John M; Chushak, Yaroslav; Foy, Brent

2009-01-01

Background In recent years, several stochastic simulation algorithms have been developed to generate Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks. However, the effects of various stochastic simulation and data analysis conditions on the observed dynamics of complex biomolecular reaction networks have not recieved much attention. In order to investigate these issues, we employed a a software package developed in out group, called Biomolecular Network Simulator (BNS), to simulate and analyze the behavior of such systems. The behavior of a hypothetical two gene in vitro transcription-translation reaction network is investigated using the Gillespie exact stochastic algorithm to illustrate some of the factors that influence the analysis and interpretation of these data. Results Specific issues affecting the analysis and interpretation of simulation data are investigated, including: (1) the effect of time interval on data presentation and time-weighted averaging of molecule numbers, (2) effect of time averaging interval on reaction rate analysis, (3) effect of number of simulations on precision of model predictions, and (4) implications of stochastic simulations on optimization procedures. Conclusion The two main factors affecting the analysis of stochastic simulations are: (1) the selection of time intervals to compute or average state variables and (2) the number of simulations generated to evaluate the system behavior. PMID:19534796

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Modelling the evolution and diversity of cumulative culture

PubMed Central

Enquist, Magnus; Ghirlanda, Stefano; Eriksson, Kimmo

2011-01-01

Previous work on mathematical models of cultural evolution has mainly focused on the diffusion of simple cultural elements. However, a characteristic feature of human cultural evolution is the seemingly limitless appearance of new and increasingly complex cultural elements. Here, we develop a general modelling framework to study such cumulative processes, in which we assume that the appearance and disappearance of cultural elements are stochastic events that depend on the current state of culture. Five scenarios are explored: evolution of independent cultural elements, stepwise modification of elements, differentiation or combination of elements and systems of cultural elements. As one application of our framework, we study the evolution of cultural diversity (in time as well as between groups). PMID:21199845

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-06-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R}^d. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^-, ɛ > 0. Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+, where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^-. We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^-. Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^-. In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on {Γ}^+ associated with the averaged Markov birth-and-death operator {\\overline{L}} = \\int _{Γ}^- L^+(γ ^-)d μ _{inv}(γ ^-).

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-04-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R^d . Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^- , ɛ > 0 . Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+ , where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^- . We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^- . Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^- . In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on Γ^+ associated with the averaged Markov birth-and-death operator \\overline{L} = \\int _{Γ}^-}L^+(γ ^-)d μ _{inv}(γ ^-).

Concepts in solid tumor evolution.

PubMed

Sidow, Arend; Spies, Noah

2015-04-01

Evolutionary mechanisms in cancer progression give tumors their individuality. Cancer evolution is different from organismal evolution, however, and we discuss where concepts from evolutionary genetics are useful or limited in facilitating an understanding of cancer. Based on these concepts we construct and apply the simplest plausible model of tumor growth and progression. Simulations using this simple model illustrate the importance of stochastic events early in tumorigenesis, highlight the dominance of exponential growth over linear growth and differentiation, and explain the clonal substructure of tumors. Copyright © 2015 Elsevier Ltd. All rights reserved.

Neutral evolution in a biological population as diffusion in phenotype space: reproduction with local mutation but without selection.

PubMed

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-02

The process of "evolutionary diffusion," i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

Stochastic transformation of points in polygons according to the Voronoi tessellation: microstructural description.

PubMed

Di Vito, Alessia; Fanfoni, Massimo; Tomellini, Massimo

2010-12-01

Starting from a stochastic two-dimensional process we studied the transformation of points in disks and squares following a protocol according to which at any step the island size increases proportionally to the corresponding Voronoi tessera. Two interaction mechanisms among islands have been dealt with: coalescence and impingement. We studied the evolution of the island density and of the island size distribution functions, in dependence on island collision mechanisms for both Poissonian and correlated spatial distributions of points. The island size distribution functions have been found to be invariant with the fraction of transformed phase for a given stochastic process. The n(Θ) curve describing the island decay has been found to be independent of the shape (apart from high correlation degrees) and interaction mechanism.

Thermal and Driven Stochastic Growth of Langmuir Waves in the Solar Wind and Earth's Foreshock

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Robinson, P. A.; Anderson, R. R.

2000-01-01

Statistical distributions of Langmuir wave fields in the solar wind and the edge of Earth's foreshock are analyzed and compared with predictions for stochastic growth theory (SGT). SGT quantitatively explains the solar wind, edge, and deep foreshock data as pure thermal waves, driven thermal waves subject to net linear growth and stochastic effects, and as waves in a pure SGT state, respectively, plus radiation near the plasma frequency f(sub p). These changes are interpreted in terms of spatial variations in the beam instability's growth rate and evolution toward a pure SGT state. SGT analyses of field distributions are shown to provide a viable alternative to thermal noise spectroscopy for wave instruments with coarse frequency resolution, and to separate f(sub p) radiation from Langmuir waves.

Autoionizing states driven by stochastic electromagnetic fields

NASA Astrophysics Data System (ADS)

Mouloudakis, G.; Lambropoulos, P.

2018-01-01

We have examined the profile of an isolated autoionizing resonance driven by a pulse of short duration and moderately strong field. The analysis has been based on stochastic differential equations governing the time evolution of the density matrix under a stochastic field. Having focused our quantitative analysis on the 2{{s}}2{{p}}({}1{{P}}) resonance of helium, we have investigated the role of field fluctuations and of the duration of the pulse. We report surprisingly strong distortion of the profile, even for peak intensity below the strong field limit. Our results demonstrate the intricate connection between intensity and pulse duration, with the latter appearing to be the determining influence, even for a seemingly short pulse of 50 fs. Further effects that would arise under much shorter pulses are discussed.

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Extinction in neutrally stable stochastic Lotka-Volterra models

NASA Astrophysics Data System (ADS)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Extinction in neutrally stable stochastic Lotka-Volterra models.

PubMed

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Recent topographic evolution and erosion of the deglaciated Washington Cascades inferred from a stochastic landscape evolution model

NASA Astrophysics Data System (ADS)

Moon, S.; Shelef, E.; Hilley, G. E.

2013-12-01

The Washington Cascades is currently in topographic and erosional disequilibrium after deglaciation occurred around 11- 17 ka ago. The topography still shows the features inherited from prior alpine glacial processes (e.g., cirques, steep side-valleys, and flat valley bottoms), though postglacial processes are currently denuding this landscape. Our previous study in this area calculated the thousand-year-timescale denudation rates using cosmogenic 10Be concentration (CRN-denudation rates), and showed that they were ~ four times higher than million-year-timescale uplift rates. In addition, the spatial distribution of denudation rates showed a good correlation with a factor-of-ten variation in precipitation. We interpreted this correlation as reflecting the sensitivity of landslide triggering in over-steepened deglaciated topography to precipitation, which produced high denudation rates in wet areas that experienced frequent landsliding. We explored this interpretation using a model of postglacial surface processes that predicts the evolution of the topography and denudation rates within the deglaciated Washington Cascades. Specifically, we used the model to understand the controls on and timescales of landscape response to changes in the surface process regime after deglaciation. The postglacial adjustment of this landscape is modeled using a geomorphic-transport-law-based numerical model that includes processes of river incision, hillslope diffusion, and stochastic landslides. The surface lowering due to landslides is parameterized using a physically-based slope stability model coupled to a stochastic model of the generation of landslides. The model parameters of river incision and stochastic landslides are calibrated based on the rates and distribution of thousand-year-timescale denudation rates measured from cosmogenic 10Be isotopes. The probability distribution of model parameters required to fit the observed denudation rates shows comparable ranges from previous studies in similar rock types and climatic conditions. The calibrated parameters suggest that the dominant sediment source of river sediments originates from stochastic landslides. The magnitude of landslide denudation rates is determined by failure density (similar to landslide frequency), while their spatial distribution is largely controlled by precipitation and slope angles. Simulation results show that denudation rates decay over time and take approximately 130-180 ka to reach steady-state rates. This response timescale is longer than glacial/interglacial cycles, suggesting that frequent climatic perturbations during the Quaternary may prevent these types of landscapes from reaching a dynamic equilibrium with postglacial processes.

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Discrete stochastic simulation methods for chemically reacting systems.

PubMed

Cao, Yang; Samuels, David C

2009-01-01

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Ten reasons why a thermalized system cannot be described by a many-particle wave function

NASA Astrophysics Data System (ADS)

Drossel, Barbara

2017-05-01

It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of statistical mechanics. The usual attempts to resolve this conflict for instance by appealing to decoherence or eigenstate thermalization are riddled with problems. This paper considers theoretical physics of thermalized systems as it is done in practice and shows that all approaches to thermalized systems presuppose in some form limits to linear superposition and deterministic time evolution. These considerations include, among others, the classical limit, extensivity, the concepts of entropy and equilibrium, and symmetry breaking in phase transitions and quantum measurement. As a conclusion, the paper suggests that the irreversibility and stochasticity of statistical mechanics should be taken as a real property of nature. It follows that a gas of a macroscopic number N of atoms in thermal equilibrium is best represented by a collection of N wave packets of a size of the order of the thermal de Broglie wave length, which behave quantum mechanically below this scale but classically sufficiently far beyond this scale. In particular, these wave packets must localize again after scattering events, which requires stochasticity and indicates a connection to the measurement process.

COUPLED SPIN AND SHAPE EVOLUTION OF SMALL RUBBLE-PILE ASTEROIDS: SELF-LIMITATION OF THE YORP EFFECT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cotto-Figueroa, Desireé; Statler, Thomas S.; Richardson, Derek C.

2015-04-10

We present the first self-consistent simulations of the coupled spin-shape evolution of small gravitational aggregates under the influence of the YORP effect. Because of YORP’s sensitivity to surface topography, even small centrifugally driven reconfigurations of aggregates can alter the YORP torque dramatically, resulting in spin evolution that can differ qualitatively from the rigid-body prediction. One-third of our simulations follow a simple evolution described as a modified YORP cycle. Two-thirds exhibit one or more of three distinct behaviors—stochastic YORP, self-governed YORP, and stagnating YORP—which together result in YORP self-limitation. Self-limitation confines rotation rates of evolving aggregates to far narrower ranges thanmore » those expected in the classical YORP cycle, greatly prolonging the times over which objects can preserve their sense of rotation. Simulated objects are initially randomly packed, disordered aggregates of identical spheres in rotating equilibrium, with low internal angles of friction. Their shape evolution is characterized by rearrangement of the entire body, including the deep interior. They do not evolve to axisymmetric top shapes with equatorial ridges. Mass loss occurs in one-third of the simulations, typically in small amounts from the ends of a prolate-triaxial body. We conjecture that YORP self-limitation may inhibit formation of top-shapes, binaries, or both, by restricting the amount of angular momentum that can be imparted to a deformable body. Stochastic YORP, in particular, will affect the evolution of collisional families whose orbits drift apart under the influence of Yarkovsky forces, in observable ways.« less

Gravitational Instabilities in a Young Protoplanetary Disk with Embedded Objects

NASA Astrophysics Data System (ADS)

Desai, Karna M.

Gravitational Instabilities (GIs), a mechanism for angular momentum transport, are prominent during the early phases of protoplanetary disk evolution when the disk is relatively massive. In this dissertation, I analyze GIs by inserting different objects in a disk by employing 3D hydrodynamics simulations. GIs in a circumbinary disks are studied to determine how the presence of the companion affects the nature and strength of GIs in the disk. The circumbinary disk achieves a state of sustained marginal instability similar to an identical disk without the companion. A realistic evolution of the binary is detected. Planet and disk interactions play an important role in the evolution of planetary systems. To study this interaction during the early phases of planet formation, a migration study of Jovian planets in a GI-active disk is conducted. I find the migration timescales to be longer in a GI-active disk, when compared to laminar disks. The 3 MJupiter planet controls its own orbital evolution, while the migration of a 0.3 MJupiter planet is stochastic in nature. I define a 'critical mass' as the mass of an arm of the dominant two-armed spiral density wave within the planet's Hill diameter. Planets above this mass control their own destiny, and planets below this mass are scattered by the disk. This critical mass could provide a recipe for predicting the migration behavior of planets in GI-active disks. To understand the stochastic migration of low-mass planets, I perform a simulation of 240 zero-mass planet-tracers by inserting these at a range of locations in the disk. A Diffusion Coefficient is calculated to characterize the stochastic migration of low-mass objects. The eccentricity dispersion for the sample is also studied. I find that the diffusion of planets can be a slow process, resulting in the survival of small planetary cores.

Discrete and Continuum Approximations for Collective Cell Migration in a Scratch Assay with Cell Size Dynamics.

PubMed

Matsiaka, Oleksii M; Penington, Catherine J; Baker, Ruth E; Simpson, Matthew J

2018-04-01

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

Model reduction for slow–fast stochastic systems with metastable behaviour

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruna, Maria, E-mail: bruna@maths.ox.ac.uk; Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB; Chapman, S. Jonathan

2014-05-07

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediatedmore » chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system.« less

A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

Stochastic ice stream dynamics

PubMed Central

Bertagni, Matteo Bernard; Ridolfi, Luca

2016-01-01

Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution. PMID:27457960

Mesoscale Thermodynamically motivated Statistical Mechanics based Kinetic Model for Sintering monoliths

NASA Astrophysics Data System (ADS)

Mohan, Nisha

Modeling the evolution of microstructure during sintering is a persistent challenge in ceramics science, although needed as the microstructure impacts properties of an engineered material. Bridging the gap between microscopic and continuum models, kinetic Monte Carlo (kMC) methods provide a stochastic approach towards sintering and microstructure evolution. These kMC models work at the mesoscale, with length and time-scales between those of atomistic and continuum approaches. We develop a sintering/compacting model for the two-phase sintering of boron nitride ceramics and allotropes alike. Our formulation includes mechanisms for phase transformation between h-BN and c-BN and takes into account thermodynamics of pressure and temperature on interaction energies and mechanism rates. In addition to replicating the micro-structure evolution observed in experiments, it also captures the phase diagram of Boron Nitride materials. Results have been analyzed in terms of phase diagrams and crystal growth. It also serves with insights to guide the choice of additives and conditions for the sintering process.While detailed time and spatial resolutions are lost in any MC, the progression of stochastic events still captures plausible local energy minima and long-time temporal developments. DARPA.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

DOE PAGES

Duarte, Vinicius N.; Berk, H. L.; Gorelenkov, N. N.; ...

2017-03-17

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. Furthermore, the latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

NASA Astrophysics Data System (ADS)

Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N.; Heidbrink, W. W.; Kramer, G. J.; Nazikian, R.; Pace, D. C.; Podestà, M.; Tobias, B. J.; Van Zeeland, M. A.

2017-05-01

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time.

PubMed

Dhar, Amrit; Minin, Vladimir N

2017-05-01

Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

PubMed Central

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780

Northern Hemisphere glaciation and the evolution of Plio-Pleistocene climate noise

NASA Astrophysics Data System (ADS)

Meyers, Stephen R.; Hinnov, Linda A.

2010-08-01

Deterministic orbital controls on climate variability are commonly inferred to dominate across timescales of 104-106 years, although some studies have suggested that stochastic processes may be of equal or greater importance. Here we explicitly quantify changes in deterministic orbital processes (forcing and/or pacing) versus stochastic climate processes during the Plio-Pleistocene, via time-frequency analysis of two prominent foraminifera oxygen isotopic stacks. Our results indicate that development of the Northern Hemisphere ice sheet is paralleled by an overall amplification of both deterministic and stochastic climate energy, but their relative dominance is variable. The progression from a more stochastic early Pliocene to a strongly deterministic late Pleistocene is primarily accommodated during two transitory phases of Northern Hemisphere ice sheet growth. This long-term trend is punctuated by “stochastic events,” which we interpret as evidence for abrupt reorganization of the climate system at the initiation and termination of the mid-Pleistocene transition and at the onset of Northern Hemisphere glaciation. In addition to highlighting a complex interplay between deterministic and stochastic climate change during the Plio-Pleistocene, our results support an early onset for Northern Hemisphere glaciation (between 3.5 and 3.7 Ma) and reveal some new characteristics of the orbital signal response, such as the puzzling emergence of 100 ka and 400 ka cyclic climate variability during theoretical eccentricity nodes.

Stochastic volatility models and Kelvin waves

NASA Astrophysics Data System (ADS)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Neutral Evolution in a Biological Population as Diffusion in Phenotype Space: Reproduction with Local Mutation but without Selection

NASA Astrophysics Data System (ADS)

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-01

The process of “evolutionary diffusion,” i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

The evolution of wealth transmission in human populations: a stochastic model

NASA Astrophysics Data System (ADS)

Augustins, G.; Etienne, L.; Ferdy, J.-B.; Ferrer, R.; Godelle, B.; Pitard, E.; Rousset, F.

2014-03-01

Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is transmitted to children. Here we propose a model where we simulate both the dynamics of wealth in a population and the evolution of a trait that determines how wealth is transmitted from parents to offspring, in a darwinian context.

JavaGenes Molecular Evolution

NASA Technical Reports Server (NTRS)

Lohn, Jason; Smith, David; Frank, Jeremy; Globus, Al; Crawford, James

2007-01-01

JavaGenes is a general-purpose, evolutionary software system written in Java. It implements several versions of a genetic algorithm, simulated annealing, stochastic hill climbing, and other search techniques. This software has been used to evolve molecules, atomic force field parameters, digital circuits, Earth Observing Satellite schedules, and antennas. This version differs from version 0.7.28 in that it includes the molecule evolution code and other improvements. Except for the antenna code, JaveGenes is available for NASA Open Source distribution.

MEANS: python package for Moment Expansion Approximation, iNference and Simulation

PubMed Central

Fan, Sisi; Geissmann, Quentin; Lakatos, Eszter; Lukauskas, Saulius; Ale, Angelique; Babtie, Ann C.; Kirk, Paul D. W.; Stumpf, Michael P. H.

2016-01-01

Motivation: Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system’s moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. Results: We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. Availability and implementation: https://github.com/theosysbio/means Contacts: m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153663

MEANS: python package for Moment Expansion Approximation, iNference and Simulation.

PubMed

Fan, Sisi; Geissmann, Quentin; Lakatos, Eszter; Lukauskas, Saulius; Ale, Angelique; Babtie, Ann C; Kirk, Paul D W; Stumpf, Michael P H

2016-09-15

Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system's moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. https://github.com/theosysbio/means m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Effective long wavelength scalar dynamics in de Sitter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moss, Ian; Rigopoulos, Gerasimos, E-mail: ian.moss@newcastle.ac.uk, E-mail: gerasimos.rigopoulos@ncl.ac.uk

We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius k / a ∼ H can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales Δ t >> H {sup −1}, this results in the well-known Starobinsky stochastic evolution. However, our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place. Themore » long wavelength stochastic dynamical equations are now second order in time, incorporating temporal scales Δ t ∼ H {sup −1} and resulting in a Kramers equation for the probability distribution—more precisely the Wigner function—in contrast to the more usual Fokker-Planck equation. This feature allows us to non-perturbatively evaluate, within the stochastic formalism, not only expectation values of field correlators, but also the stress-energy tensor of φ.« less

The effects of self-interstitial clusters on cascade defect evolution beyond the primary damage state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinisch, H.L.

1997-04-01

The intracascade evolution of the defect distributions of cascades in copper is investigated using stochastic annealing simulations applied to cascades generated with molecular dynamics (MD). The temperature and energy dependencies of annihilation, clustering and free defect production are determined for individual cascades. The annealing simulation results illustrate the strong influence on intracascade evolution of the defect configuration existing in the primary damage state. Another factor significantly affecting the evolution of the defect distribution is the rapid one-dimensional diffusion of small, glissile interstitial loops produced directly in cascades. This phenomenon introduces a cascade energy dependence of defect evolution that is apparentmore » only beyond the primary damage state, amplifying the need for further study of the annealing phase of cascade evolution and for performing many more MD cascade simulations at higher energies.« less

Size Evolution and Stochastic Models: Explaining Ostracod Size through Probabilistic Distributions

NASA Astrophysics Data System (ADS)

Krawczyk, M.; Decker, S.; Heim, N. A.; Payne, J.

2014-12-01

The biovolume of animals has functioned as an important benchmark for measuring evolution throughout geologic time. In our project, we examined the observed average body size of ostracods over time in order to understand the mechanism of size evolution in these marine organisms. The body size of ostracods has varied since the beginning of the Ordovician, where the first true ostracods appeared. We created a stochastic branching model to create possible evolutionary trees of ostracod size. Using stratigraphic ranges for ostracods compiled from over 750 genera in the Treatise on Invertebrate Paleontology, we calculated overall speciation and extinction rates for our model. At each timestep in our model, new lineages can evolve or existing lineages can become extinct. Newly evolved lineages are assigned sizes based on their parent genera. We parameterized our model to generate neutral and directional changes in ostracod size to compare with the observed data. New sizes were chosen via a normal distribution, and the neutral model selected new sizes differentials centered on zero, allowing for an equal chance of larger or smaller ostracods at each speciation. Conversely, the directional model centered the distribution on a negative value, giving a larger chance of smaller ostracods. Our data strongly suggests that the overall direction of ostracod evolution has been following a model that directionally pushes mean ostracod size down, shying away from a neutral model. Our model was able to match the magnitude of size decrease. Our models had a constant linear decrease while the actual data had a much more rapid initial rate followed by a constant size. The nuance of the observed trends ultimately suggests a more complex method of size evolution. In conclusion, probabilistic methods can provide valuable insight into possible evolutionary mechanisms determining size evolution in ostracods.

Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

DOE PAGES

Woods, Benjamin J. Q.; Duarte, Vinicius N.; De-Gol, Anthony J.; ...

2018-01-23

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a 'hole' and 'clump'. Here in this paper, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto radial microturbulence via canonical toroidal momentummore » scattering, affecting hole and clump formation. While the mechanism allowing for the formation of the hole and clump is coherent, the lifetime of a hole and clump is shown to be highly sensitive to initial conditions, affecting the temporal profile of a single bursting event in mode amplitude.« less

Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, Benjamin J. Q.; Duarte, Vinicius N.; De-Gol, Anthony J.

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a 'hole' and 'clump'. Here in this paper, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto radial microturbulence via canonical toroidal momentummore » scattering, affecting hole and clump formation. While the mechanism allowing for the formation of the hole and clump is coherent, the lifetime of a hole and clump is shown to be highly sensitive to initial conditions, affecting the temporal profile of a single bursting event in mode amplitude.« less

Comparing reactive and memory-one strategies of direct reciprocity

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Jeong, Hyeong-Chai; Hilbe, Christian; Nowak, Martin A.

2016-05-01

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player’s previous move, and memory-one strategies, which take into account the own and the co-player’s previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.

Stochastic charging of dust grains in planetary rings: Diffusion rates and their effects on Lorentz resonances

NASA Technical Reports Server (NTRS)

Schaffer, L.; Burns, J. A.

1995-01-01

Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.

Comparing reactive and memory-one strategies of direct reciprocity

PubMed Central

Baek, Seung Ki; Jeong, Hyeong-Chai; Hilbe, Christian; Nowak, Martin A.

2016-01-01

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player’s previous move, and memory-one strategies, which take into account the own and the co-player’s previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation. PMID:27161141

Resonant activation of population extinctions

NASA Astrophysics Data System (ADS)

Spalding, Christopher; Doering, Charles R.; Flierl, Glenn R.

2017-10-01

Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's demographic stochasticity and environmental noise remain poorly understood. Here we model environmental forcing as a stochastic fluctuation between two states, one with a higher death rate than the other. We find that, in general, there exists a rate of fluctuations that minimizes the mean time to extinction, a phenomenon previously dubbed "resonant activation." We develop a heuristic description of the phenomenon, together with a criterion for the existence of resonant activation. Specifically, the minimum extinction time arises as a result of the system approaching a scenario wherein the severity of rare events is balanced by the time interval between them. We discuss our findings within the context of more general forms of environmental noise and suggest potential applications to evolutionary models.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Application of stochastic differential geometry to the term structure of interst rates in developed markets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taranenko, Y.; Barnes, C.

1996-12-31

This paper deals with further developments of the new theory that applies stochastic differential geometry (SDG) to dynamics of interest rates. We examine mathematical constraints on the evolution of interest rate volatilities that arise from stochastic differential calculus under assumptions of an arbitrage free evolution of zero coupon bonds and developed markets (i.e., none of the party/factor can drive the whole market). The resulting new theory incorporates the Heath-Jarrow-Morton (HJM) model of interest rates and provides new equations for volatilities which makes the system of equations for interest rates and volatilities complete and self consistent. It results in much smallermore » amount of volatility data that should be guessed for the SDG model as compared to the HJM model. Limited analysis of the market volatility data suggests that the assumption of the developed market is violated around maturity of two years. Such maturities where the assumptions of the SDG model are violated are suggested to serve as boundaries at which volatilities should be specified independently from the model. Our numerical example with two boundaries (two years and five years) qualitatively resembles the market behavior. Under some conditions solutions of the SDG model become singular that may indicate market crashes. More detail comparison with the data is needed before the theory can be established or refuted.« less

Planetary Rings

NASA Astrophysics Data System (ADS)

Esposito, Larry W.

2011-07-01

Preface; 1. Introduction: the allure of ringed planets; 2. Studies of planetary rings 1610-2004; 3. Diversity of planetary rings; 4. Individual ring particles and their collisions; 5. Large-scale ring evolution; 6. Moons confine and sculpt rings; 7. Explaining ring phenomena; 8. N-Body simulations; 9. Stochastic models; 10. Age and evolution of rings; 11. Saturn's mysterious F ring; 12. Neptune's partial rings; 13. Jupiter's ring-moon system after Galileo; 14. Ring photometry; 15. Dusty rings; 16. Cassini observations; 17. Summary: the big questions; Glossary; References; Index.

Pathogen-mediated selection in free-ranging elk populations infected by chronic wasting disease

USDA-ARS?s Scientific Manuscript database

Pathogens can exert a large influence on the evolution of hosts via selection for alleles or genotypes that moderate pathogen virulence. Inconsistent interactions between parasites and the host genome, such as those resulting from genetic linkages and environmental stochasticity, have largely preven...

The Economics of Has-Beens

ERIC Educational Resources Information Center

MacDonald, Glenn; Weisbach, Michael S.

2004-01-01

The evolution of technology causes human capital to become obsolete. We study this phenomenon in an overlapping generations setting, assuming that technology evolves stochastically and that older workers find updating uneconomic. Experience and learning by doing may offer the old some income protection, but technology advance always turns them…

On the Radio-emitting Particles of the Crab Nebula: Stochastic Acceleration Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tanaka, Shuta J.; Asano, Katsuaki, E-mail: sjtanaka@center.konan-u.ac.jp

The broadband emission of pulsar wind nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model to include themore » energy diffusion, i.e., the stochastic acceleration, and apply the model to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration timescale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock-accelerated particles comparable.« less

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.

2007-01-01

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Effects of stochastic noise on dynamical decoupling procedures

NASA Astrophysics Data System (ADS)

Bernád, J. Z.; Frydrych, H.

2014-06-01

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

Stochastic effects in hybrid inflation

NASA Astrophysics Data System (ADS)

Martin, Jérôme; Vennin, Vincent

2012-02-01

Hybrid inflation is a two-field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in particular, the question of how the quantum diffusion can affect the observable predictions of hybrid inflation.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Cultural evolution: The case of babies’ first names

NASA Astrophysics Data System (ADS)

Xi, Ning; Zhang, Zi-Ke; Zhang, Yi-Cheng; Ge, Zehui; She, Li; Zhang, Kui

2014-07-01

In social sciences, there is currently rare consensus on the underlying mechanism for cultural evolution, partially due to lack of suitable data. The evolution of first names of newborn babies offers a remarkable example for such researches. In this paper, we employ the historical data on baby names from the United States to investigate the evolutionary process of culture, in particular focusing on how inequality among baby names changes over time. Then we propose a stochastic model where individual choice is determined by both individual preference and social influence, and show that the decrease in the strength of social influence can account for all the observed empirical features. Therefore, we claim that the weakening of social influence drives cultural evolution.

Evolution of a plastic quantitative trait in an age-structured population in a fluctuating environment.

PubMed

Engen, Steinar; Lande, Russell; Saether, Bernt-Erik

2011-10-01

We analyze weak fluctuating selection on a quantitative character in an age-structured population not subject to density regulation. We assume that early in the first year of life before selection, during a critical state of development, environments exert a plastic effect on the phenotype, which remains constant throughout the life of an individual. Age-specific selection on the character affects survival and fecundity, which have intermediate optima subject to temporal environmental fluctuations with directional selection in some age classes as special cases. Weighting individuals by their reproductive value, as suggested by Fisher, we show that the expected response per year in the weighted mean character has the same form as for models with no age structure. Environmental stochasticity generates stochastic fluctuations in the weighted mean character following a first-order autoregressive model with a temporally autocorrelated noise term and stationary variance depending on the amount of phenotypic plasticity. The parameters of the process are simple weighted averages of parameters used to describe age-specific survival and fecundity. The "age-specific selective weights" are related to the stable distribution of reproductive values among age classes. This allows partitioning of the change in the weighted mean character into age-specific components. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

LIDT-DD: A new hybrid model to understand debris discs observations - The case of massive collisions.

NASA Astrophysics Data System (ADS)

Kral, Q.; Thébault, P.; Augereau, J.-C.; Boccaletti, A.; Charnoz, S.

2014-12-01

LIDT-DD is a new hybrid model coupling the collisional and dynamical evolution in debris discs in a self-consistent way. It has been developed in a way that allows to treat a large number of different astrophysical cases where collisions and dynamics have an important role. This interplay was often totally neglected in previous studies whereas, even for the simplest configurations, the real physics of debris discs imposes strong constraints and interactions between dynamics and collisions. After presenting the LIDT-DD model, we will describe the evolution of violent stochastic collisional events with this model. These massive impacts have been invoked as a possible explanation for some debris discs displaying pronounced azimuthal asymmetries or having a luminosity excess exceeding that expected for systems at collisional steady-state. So far, no thorough modelling of the consequences of such stochastic events has been carried out, mainly because of the extreme numerical challenge of coupling the dynamical and collisional evolution of the released dust. We follow the collisional and dynamical evolution of dust released after the breakup of a Ceres-sized body at 6 AU from its central star. We investigate the duration, magnitude and spatial structure of the signature left by such a violent event, as well as its observational detectability. We use the GRaTer package to estimate the system's luminosity at different wavelengths and derive synthetic images for the SPHERE/VLT and MIRI/JWST instruments.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Improved Upper Limits on the Stochastic Gravitational-Wave Background from 2009-2010 LIGO and Virgo Data

NASA Astrophysics Data System (ADS)

Aasi, J.; Abbott, B. P.; Abbott, R.; Abbott, T.; Abernathy, M. R.; Accadia, T.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Affeldt, C.; Agathos, M.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Alemic, A.; Allen, B.; Allocca, A.; Amariutei, D.; Andersen, M.; Anderson, R.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C.; Areeda, J.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Austin, L.; Aylott, B. E.; Babak, S.; Baker, P. T.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barbet, M.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barton, M. A.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Bauchrowitz, J.; Bauer, Th. S.; Behnke, B.; Bejger, M.; Beker, M. G.; Belczynski, C.; Bell, A. S.; Bell, C.; Bergmann, G.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Beyersdorf, P. T.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Biscans, S.; Bitossi, M.; Bizouard, M. A.; Black, E.; Blackburn, J. K.; Blackburn, L.; Blair, D.; Bloemen, S.; Blom, M.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bond, C.; Bondu, F.; Bonelli, L.; Bonnand, R.; Bork, R.; Born, M.; Boschi, V.; Bose, Sukanta; Bosi, L.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Bridges, D. O.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brückner, F.; Buchman, S.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Burman, R.; Buskulic, D.; Buy, C.; Cadonati, L.; Cagnoli, G.; Bustillo, J. Calderón; Calloni, E.; Camp, J. B.; Campsie, P.; Cannon, K. C.; Canuel, B.; Cao, J.; Capano, C. D.; Carbognani, F.; Carbone, L.; Caride, S.; Castiglia, A.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Celerier, C.; Cella, G.; Cepeda, C.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, X.; Chen, Y.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Chow, J.; Christensen, N.; Chu, Q.; Chua, S. S. Y.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C.; Colombini, M.; Cominsky, L.; Constancio, M.; Conte, A.; Cook, D.; Corbitt, T. R.; Cordier, M.; Cornish, N.; Corpuz, A.; Corsi, A.; Costa, C. A.; Coughlin, M. W.; Coughlin, S.; Coulon, J.-P.; Countryman, S.; Couvares, P.; Coward, D. M.; Cowart, M.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dahl, K.; Canton, T. Dal; Damjanic, M.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dattilo, V.; Daveloza, H.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; Dayanga, T.; Debreczeni, G.; Degallaix, J.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Dhurandhar, S.; Díaz, M.; Di Fiore, L.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Donath, A.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dossa, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Dwyer, S.; Eberle, T.; Edo, T.; Edwards, M.; Effler, A.; Eggenstein, H.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Endrőczi, G.; Essick, R.; Etzel, T.; Evans, M.; Evans, T.; Factourovich, M.; Fafone, V.; Fairhurst, S.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fehrmann, H.; Fejer, M. M.; Feldbaum, D.; Feroz, F.; Ferrante, I.; Ferrini, F.; Fidecaro, F.; Finn, L. S.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frede, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gair, J.; Gammaitoni, L.; Gaonkar, S.; Garufi, F.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, C.; Gleason, J.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gordon, N.; Gorodetsky, M. L.; Gossan, S.; Goßler, S.; Gouaty, R.; Gräf, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greenhalgh, R. J. S.; Gretarsson, A. M.; Groot, P.; Grote, H.; Grover, K.; Grunewald, S.; Guidi, G. M.; Guido, C.; Gushwa, K.; Gustafson, E. K.; Gustafson, R.; Hammer, D.; Hammond, G.; Hanke, M.; Hanks, J.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G. M.; Harry, I. W.; Harstad, E. D.; Hart, M.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Heptonstall, A. W.; Heurs, M.; Hewitson, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Holt, K.; Hooper, S.; Hopkins, P.; Hosken, D. J.; Hough, J.; Howell, E. J.; Hu, Y.; Huerta, E.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh, M.; Huynh-Dinh, T.; Ingram, D. R.; Inta, R.; Isogai, T.; Ivanov, A.; Iyer, B. R.; Izumi, K.; Jacobson, M.; James, E.; Jang, H.; Jaranowski, P.; Ji, Y.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Haris, K.; Kalmus, P.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karlen, J.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, H.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Keiser, G. M.; Keitel, D.; Kelley, D. B.; Kells, W.; Khalaidovski, A.; Khalili, F. Y.; Khazanov, E. A.; Kim, C.; Kim, K.; Kim, N.; Kim, N. G.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kline, J.; Koehlenbeck, S.; Kokeyama, K.; Kondrashov, V.; Koranda, S.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kremin, A.; Kringel, V.; Królak, A.; Kuehn, G.; Kumar, A.; Kumar, P.; Kumar, R.; Kuo, L.; Kutynia, A.; Kwee, P.; Landry, M.; Lantz, B.; Larson, S.; Lasky, P. D.; Lawrie, C.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C.-H.; Lee, H. K.; Lee, H. M.; Lee, J.; Leonardi, M.; Leong, J. R.; Le Roux, A.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B.; Lewis, J.; Li, T. G. F.; Libbrecht, K.; Libson, A.; Lin, A. C.; Littenberg, T. B.; Litvine, V.; Lockerbie, N. A.; Lockett, V.; Lodhia, D.; Loew, K.; Logue, J.; Lombardi, A. L.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J.; Lubinski, M. J.; Lück, H.; Luijten, E.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macarthur, J.; Macdonald, E. P.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magana-Sandoval, F.; Mageswaran, M.; Maglione, C.; Mailand, K.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Manca, G. M.; Mandel, I.; Mandic, V.; Mangano, V.; Mangini, N.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A.; Maros, E.; Marque, J.; Martelli, F.; Martin, I. W.; Martin, R. M.; Martinelli, L.; Martynov, D.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Matichard, F.; Matone, L.; Matzner, R. A.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McIntyre, G.; McIver, J.; McLin, K.; Meacher, D.; Meadors, G. D.; Mehmet, M.; Meidam, J.; Meinders, M.; Melatos, A.; Mendell, G.; Mercer, R. A.; Meshkov, S.; Messenger, C.; Meyers, P.; Miao, H.; Michel, C.; Mikhailov, E. E.; Milano, L.; Milde, S.; Miller, J.; Minenkov, Y.; Mingarelli, C. M. F.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moe, B.; Moesta, P.; Mohan, M.; Mohapatra, S. R. P.; Moraru, D.; Moreno, G.; Morgado, N.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D.; Murray, P. G.; Mytidis, A.; Nagy, M. F.; Kumar, D. Nanda; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nelemans, G.; Neri, I.; Neri, M.; Newton, G.; Nguyen, T.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Ochsner, E.; O'Dell, J.; Oelker, E.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oppermann, P.; O'Reilly, B.; O'Shaughnessy, R.; Osthelder, C.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Padilla, C.; Pai, A.; Palashov, O.; Palomba, C.; Pan, H.; Pan, Y.; Pankow, C.; Paoletti, F.; Paoletti, R.; Paris, H.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Pedraza, M.; Penn, S.; Perreca, A.; Phelps, M.; Pichot, M.; Pickenpack, M.; Piergiovanni, F.; Pierro, V.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poeld, J.; Poggiani, R.; Poteomkin, A.; Powell, J.; Prasad, J.; Premachandra, S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Qin, J.; Quetschke, V.; Quintero, E.; Quiroga, G.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Rácz, I.; Radkins, H.; Raffai, P.; Raja, S.; Rajalakshmi, G.; Rakhmanov, M.; Ramet, C.; Ramirez, K.; Rapagnani, P.; Raymond, V.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Reid, S.; Reitze, D. H.; Rhoades, E.; Ricci, F.; Riles, K.; Robertson, N. A.; Robinet, F.; Rocchi, A.; Rodruck, M.; Rolland, L.; Rollins, J. G.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Salemi, F.; Sammut, L.; Sandberg, V.; Sanders, J. R.; Sannibale, V.; Santiago-Prieto, I.; Saracco, E.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Savage, R.; Scheuer, J.; Schilling, R.; Schnabel, R.; Schofield, R. M. S.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Shaddock, D.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shapiro, B.; Shawhan, P.; Shoemaker, D. H.; Sidery, T. L.; Siellez, K.; Siemens, X.; Sigg, D.; Simakov, D.; Singer, A.; Singer, L.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Slutsky, J.; Smith, J. R.; Smith, M.; Smith, R. J. E.; Smith-Lefebvre, N. D.; Son, E. J.; Sorazu, B.; Souradeep, T.; Sperandio, L.; Staley, A.; Stebbins, J.; Steinlechner, J.; Steinlechner, S.; Stephens, B. C.; Steplewski, S.; Stevenson, S.; Stone, R.; Stops, D.; Strain, K. A.; Straniero, N.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Susmithan, S.; Sutton, P. J.; Swinkels, B.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tarabrin, S. P.; Taylor, R.; ter Braack, A. P. M.; Thirugnanasambandam, M. P.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Toncelli, A.; Tonelli, M.; Torre, O.; Torres, C. V.; Torrie, C. I.; Travasso, F.; Traylor, G.; Tse, M.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Urbanek, K.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van den Brand, J. F. J.; Van Den Broeck, C.; van der Putten, S.; van der Sluys, M. V.; van Heijningen, J.; van Veggel, A. A.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Verma, S. S.; Vetrano, F.; Viceré, A.; Vincent-Finley, R.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyachanin, S. P.; Wade, A.; Wade, L.; Wade, M.; Walker, M.; Wallace, L.; Wang, M.; Wang, X.; Ward, R. L.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Wessels, P.; West, M.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Wiesner, K.; Wilkinson, C.; Williams, K.; Williams, L.; Williams, R.; Williams, T.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M.; Winkler, W.; Wipf, C. C.; Wiseman, A. G.; Wittel, H.; Woan, G.; Worden, J.; Yablon, J.; Yakushin, I.; Yamamoto, H.; Yancey, C. C.; Yang, H.; Yang, Z.; Yoshida, S.; Yvert, M.; ZadroŻny, A.; Zanolin, M.; Zendri, J.-P.; Zhang, Fan; Zhang, L.; Zhao, C.; Zhu, X. J.; Zucker, M. E.; Zuraw, S.; Zweizig, J.; LIGO; Virgo Collaboration

2014-12-01

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of ΩGW(f )=Ωα(f/fref ) α , we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral index of α =0 , we constrain the energy density of the stochastic background to be ΩGW(f )<5.6 ×1 0-6 . For the 600-1000 Hz band, ΩGW(f )<0.14 (f /900 Hz )3 , a factor of 2.5 lower than the best previously reported upper limits. We find ΩGW(f )<1.8 ×1 0-4 using a spectral index of zero for 170-600 Hz and ΩGW(f )<1.0 (f /1300 Hz )3 for 1000-1726 Hz, bands in which no previous direct limits have been placed. The limits in these four bands are the lowest direct measurements to date on the stochastic background. We discuss the implications of these results in light of the recent claim by the BICEP2 experiment of the possible evidence for inflationary gravitational waves.

Improved upper limits on the stochastic gravitational-wave background from 2009-2010 LIGO and Virgo data.

PubMed

Aasi, J; Abbott, B P; Abbott, R; Abbott, T; Abernathy, M R; Accadia, T; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Affeldt, C; Agathos, M; Aggarwal, N; Aguiar, O D; Ain, A; Ajith, P; Alemic, A; Allen, B; Allocca, A; Amariutei, D; Andersen, M; Anderson, R; Anderson, S B; Anderson, W G; Arai, K; Araya, M C; Arceneaux, C; Areeda, J; Aston, S M; Astone, P; Aufmuth, P; Aulbert, C; Austin, L; Aylott, B E; Babak, S; Baker, P T; Ballardin, G; Ballmer, S W; Barayoga, J C; Barbet, M; Barish, B C; Barker, D; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barton, M A; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Bauchrowitz, J; Bauer, Th S; Behnke, B; Bejger, M; Beker, M G; Belczynski, C; Bell, A S; Bell, C; Bergmann, G; Bersanetti, D; Bertolini, A; Betzwieser, J; Beyersdorf, P T; Bilenko, I A; Billingsley, G; Birch, J; Biscans, S; Bitossi, M; Bizouard, M A; Black, E; Blackburn, J K; Blackburn, L; Blair, D; Bloemen, S; Blom, M; Bock, O; Bodiya, T P; Boer, M; Bogaert, G; Bogan, C; Bond, C; Bondu, F; Bonelli, L; Bonnand, R; Bork, R; Born, M; Boschi, V; Bose, Sukanta; Bosi, L; Bradaschia, C; Brady, P R; Braginsky, V B; Branchesi, M; Brau, J E; Briant, T; Bridges, D O; Brillet, A; Brinkmann, M; Brisson, V; Brooks, A F; Brown, D A; Brown, D D; Brückner, F; Buchman, S; Bulik, T; Bulten, H J; Buonanno, A; Burman, R; Buskulic, D; Buy, C; Cadonati, L; Cagnoli, G; Bustillo, J Calderón; Calloni, E; Camp, J B; Campsie, P; Cannon, K C; Canuel, B; Cao, J; Capano, C D; Carbognani, F; Carbone, L; Caride, S; Castiglia, A; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Celerier, C; Cella, G; Cepeda, C; Cesarini, E; Chakraborty, R; Chalermsongsak, T; Chamberlin, S J; Chao, S; Charlton, P; Chassande-Mottin, E; Chen, X; Chen, Y; Chincarini, A; Chiummo, A; Cho, H S; Chow, J; Christensen, N; Chu, Q; Chua, S S Y; Chung, S; Ciani, G; Clara, F; Clark, J A; Cleva, F; Coccia, E; Cohadon, P-F; Colla, A; Collette, C; Colombini, M; Cominsky, L; Constancio, M; Conte, A; Cook, D; Corbitt, T R; Cordier, M; Cornish, N; Corpuz, A; Corsi, A; Costa, C A; Coughlin, M W; Coughlin, S; Coulon, J-P; Countryman, S; Couvares, P; Coward, D M; Cowart, M; Coyne, D C; Coyne, R; Craig, K; Creighton, J D E; Crowder, S G; Cumming, A; Cunningham, L; Cuoco, E; Dahl, K; Canton, T Dal; Damjanic, M; Danilishin, S L; D'Antonio, S; Danzmann, K; Dattilo, V; Daveloza, H; Davier, M; Davies, G S; Daw, E J; Day, R; Dayanga, T; Debreczeni, G; Degallaix, J; Deléglise, S; Del Pozzo, W; Denker, T; Dent, T; Dereli, H; Dergachev, V; De Rosa, R; DeRosa, R T; DeSalvo, R; Dhurandhar, S; Díaz, M; Di Fiore, L; Di Lieto, A; Di Palma, I; Di Virgilio, A; Donath, A; Donovan, F; Dooley, K L; Doravari, S; Dossa, S; Douglas, R; Downes, T P; Drago, M; Drever, R W P; Driggers, J C; Du, Z; Dwyer, S; Eberle, T; Edo, T; Edwards, M; Effler, A; Eggenstein, H; Ehrens, P; Eichholz, J; Eikenberry, S S; Endrőczi, G; Essick, R; Etzel, T; Evans, M; Evans, T; Factourovich, M; Fafone, V; Fairhurst, S; Fang, Q; Farinon, S; Farr, B; Farr, W M; Favata, M; Fehrmann, H; Fejer, M M; Feldbaum, D; Feroz, F; Ferrante, I; Ferrini, F; Fidecaro, F; Finn, L S; Fiori, I; Fisher, R P; Flaminio, R; Fournier, J-D; Franco, S; Frasca, S; Frasconi, F; Frede, M; Frei, Z; Freise, A; Frey, R; Fricke, T T; Fritschel, P; Frolov, V V; Fulda, P; Fyffe, M; Gair, J; Gammaitoni, L; Gaonkar, S; Garufi, F; Gehrels, N; Gemme, G; Genin, E; Gennai, A; Ghosh, S; Giaime, J A; Giardina, K D; Giazotto, A; Gill, C; Gleason, J; Goetz, E; Goetz, R; Gondan, L; González, G; Gordon, N; Gorodetsky, M L; Gossan, S; Gossler, S; Gouaty, R; Gräf, C; Graff, P B; Granata, M; Grant, A; Gras, S; Gray, C; Greenhalgh, R J S; Gretarsson, A M; Groot, P; Grote, H; Grover, K; Grunewald, S; Guidi, G M; Guido, C; Gushwa, K; Gustafson, E K; Gustafson, R; Hammer, D; Hammond, G; Hanke, M; Hanks, J; Hanna, C; Hanson, J; Harms, J; Harry, G M; Harry, I W; Harstad, E D; Hart, M; Hartman, M T; Haster, C-J; Haughian, K; Heidmann, A; Heintze, M; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Heptonstall, A W; Heurs, M; Hewitson, M; Hild, S; Hoak, D; Hodge, K A; Holt, K; Hooper, S; Hopkins, P; Hosken, D J; Hough, J; Howell, E J; Hu, Y; Huerta, E; Hughey, B; Husa, S; Huttner, S H; Huynh, M; Huynh-Dinh, T; Ingram, D R; Inta, R; Isogai, T; Ivanov, A; Iyer, B R; Izumi, K; Jacobson, M; James, E; Jang, H; Jaranowski, P; Ji, Y; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; K, Haris; Kalmus, P; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karlen, J; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, H; Kawabe, K; Kawazoe, F; Kéfélian, F; Keiser, G M; Keitel, D; Kelley, D B; Kells, W; Khalaidovski, A; Khalili, F Y; Khazanov, E A; Kim, C; Kim, K; Kim, N; Kim, N G; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Klimenko, S; Kline, J; Koehlenbeck, S; Kokeyama, K; Kondrashov, V; Koranda, S; Korth, W Z; Kowalska, I; Kozak, D B; Kremin, A; Kringel, V; Królak, A; Kuehn, G; Kumar, A; Kumar, P; Kumar, R; Kuo, L; Kutynia, A; Kwee, P; Landry, M; Lantz, B; Larson, S; Lasky, P D; Lawrie, C; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E O; Lee, C-H; Lee, H K; Lee, H M; Lee, J; Leonardi, M; Leong, J R; Le Roux, A; Leroy, N; Letendre, N; Levin, Y; Levine, B; Lewis, J; Li, T G F; Libbrecht, K; Libson, A; Lin, A C; Littenberg, T B; Litvine, V; Lockerbie, N A; Lockett, V; Lodhia, D; Loew, K; Logue, J; Lombardi, A L; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J; Lubinski, M J; Lück, H; Luijten, E; Lundgren, A P; Lynch, R; Ma, Y; Macarthur, J; Macdonald, E P; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magana-Sandoval, F; Mageswaran, M; Maglione, C; Mailand, K; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Manca, G M; Mandel, I; Mandic, V; Mangano, V; Mangini, N; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A; Maros, E; Marque, J; Martelli, F; Martin, I W; Martin, R M; Martinelli, L; Martynov, D; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Matichard, F; Matone, L; Matzner, R A; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McGuire, S C; McIntyre, G; McIver, J; McLin, K; Meacher, D; Meadors, G D; Mehmet, M; Meidam, J; Meinders, M; Melatos, A; Mendell, G; Mercer, R A; Meshkov, S; Messenger, C; Meyers, P; Miao, H; Michel, C; Mikhailov, E E; Milano, L; Milde, S; Miller, J; Minenkov, Y; Mingarelli, C M F; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moe, B; Moesta, P; Mohan, M; Mohapatra, S R P; Moraru, D; Moreno, G; Morgado, N; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Mukherjee, S; Mullavey, A; Munch, J; Murphy, D; Murray, P G; Mytidis, A; Nagy, M F; Kumar, D Nanda; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nelemans, G; Neri, I; Neri, M; Newton, G; Nguyen, T; Nitz, A; Nocera, F; Nolting, D; Normandin, M E N; Nuttall, L K; Ochsner, E; O'Dell, J; Oelker, E; Oh, J J; Oh, S H; Ohme, F; Oppermann, P; O'Reilly, B; O'Shaughnessy, R; Osthelder, C; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Padilla, C; Pai, A; Palashov, O; Palomba, C; Pan, H; Pan, Y; Pankow, C; Paoletti, F; Paoletti, R; Paris, H; Pasqualetti, A; Passaquieti, R; Passuello, D; Pedraza, M; Penn, S; Perreca, A; Phelps, M; Pichot, M; Pickenpack, M; Piergiovanni, F; Pierro, V; Pinard, L; Pinto, I M; Pitkin, M; Poeld, J; Poggiani, R; Poteomkin, A; Powell, J; Prasad, J; Premachandra, S; Prestegard, T; Price, L R; Prijatelj, M; Privitera, S; Prodi, G A; Prokhorov, L; Puncken, O; Punturo, M; Puppo, P; Qin, J; Quetschke, V; Quintero, E; Quiroga, G; Quitzow-James, R; Raab, F J; Rabeling, D S; Rácz, I; Radkins, H; Raffai, P; Raja, S; Rajalakshmi, G; Rakhmanov, M; Ramet, C; Ramirez, K; Rapagnani, P; Raymond, V; Re, V; Read, J; Reed, C M; Regimbau, T; Reid, S; Reitze, D H; Rhoades, E; Ricci, F; Riles, K; Robertson, N A; Robinet, F; Rocchi, A; Rodruck, M; Rolland, L; Rollins, J G; Romano, J D; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Salemi, F; Sammut, L; Sandberg, V; Sanders, J R; Sannibale, V; Santiago-Prieto, I; Saracco, E; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Savage, R; Scheuer, J; Schilling, R; Schnabel, R; Schofield, R M S; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sengupta, A S; Sentenac, D; Sequino, V; Sergeev, A; Shaddock, D; Shah, S; Shahriar, M S; Shaltev, M; Shapiro, B; Shawhan, P; Shoemaker, D H; Sidery, T L; Siellez, K; Siemens, X; Sigg, D; Simakov, D; Singer, A; Singer, L; Singh, R; Sintes, A M; Slagmolen, B J J; Slutsky, J; Smith, J R; Smith, M; Smith, R J E; Smith-Lefebvre, N D; Son, E J; Sorazu, B; Souradeep, T; Sperandio, L; Staley, A; Stebbins, J; Steinlechner, J; Steinlechner, S; Stephens, B C; Steplewski, S; Stevenson, S; Stone, R; Stops, D; Strain, K A; Straniero, N; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Susmithan, S; Sutton, P J; Swinkels, B; Tacca, M; Talukder, D; Tanner, D B; Tarabrin, S P; Taylor, R; Ter Braack, A P M; Thirugnanasambandam, M P; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, V; Tokmakov, K V; Tomlinson, C; Toncelli, A; Tonelli, M; Torre, O; Torres, C V; Torrie, C I; Travasso, F; Traylor, G; Tse, M; Ugolini, D; Unnikrishnan, C S; Urban, A L; Urbanek, K; Vahlbruch, H; Vajente, G; Valdes, G; Vallisneri, M; van den Brand, J F J; Van Den Broeck, C; van der Putten, S; van der Sluys, M V; van Heijningen, J; van Veggel, A A; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Verma, S S; Vetrano, F; Viceré, A; Vincent-Finley, R; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Vousden, W D; Vyachanin, S P; Wade, A; Wade, L; Wade, M; Walker, M; Wallace, L; Wang, M; Wang, X; Ward, R L; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Wessels, P; West, M; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Wiesner, K; Wilkinson, C; Williams, K; Williams, L; Williams, R; Williams, T; Williamson, A R; Willis, J L; Willke, B; Wimmer, M; Winkler, W; Wipf, C C; Wiseman, A G; Wittel, H; Woan, G; Worden, J; Yablon, J; Yakushin, I; Yamamoto, H; Yancey, C C; Yang, H; Yang, Z; Yoshida, S; Yvert, M; Zadrożny, A; Zanolin, M; Zendri, J-P; Zhang, Fan; Zhang, L; Zhao, C; Zhu, X J; Zucker, M E; Zuraw, S; Zweizig, J

2014-12-05

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of Ω_{GW}(f)=Ω_{α}(f/f_{ref})^{α}, we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral index of α=0, we constrain the energy density of the stochastic background to be Ω_{GW}(f)<5.6×10^{-6}. For the 600-1000 Hz band, Ω_{GW}(f)<0.14(f/900  Hz)^{3}, a factor of 2.5 lower than the best previously reported upper limits. We find Ω_{GW}(f)<1.8×10^{-4} using a spectral index of zero for 170-600 Hz and Ω_{GW}(f)<1.0(f/1300  Hz)^{3} for 1000-1726 Hz, bands in which no previous direct limits have been placed. The limits in these four bands are the lowest direct measurements to date on the stochastic background. We discuss the implications of these results in light of the recent claim by the BICEP2 experiment of the possible evidence for inflationary gravitational waves.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu

2016-12-10

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imagingmore » come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.« less

Stochastic Mixing Model with Power Law Decay of Variance

NASA Technical Reports Server (NTRS)

Fedotov, S.; Ihme, M.; Pitsch, H.

2003-01-01

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

Stochastic collective dynamics of charged-particle beams in the stability regime

NASA Astrophysics Data System (ADS)

Petroni, Nicola Cufaro; de Martino, Salvatore; de Siena, Silvio; Illuminati, Fabrizio

2001-01-01

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by λcN, where N is the number of particles in the beam and λc the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called ``quantum-like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

Clinical Applications of Stochastic Dynamic Models of the Brain, Part I: A Primer.

PubMed

Roberts, James A; Friston, Karl J; Breakspear, Michael

2017-04-01

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior. Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Effects of Extrinsic Mortality on the Evolution of Aging: A Stochastic Modeling Approach

PubMed Central

Shokhirev, Maxim Nikolaievich; Johnson, Adiv Adam

2014-01-01

The evolutionary theories of aging are useful for gaining insights into the complex mechanisms underlying senescence. Classical theories argue that high levels of extrinsic mortality should select for the evolution of shorter lifespans and earlier peak fertility. Non-classical theories, in contrast, posit that an increase in extrinsic mortality could select for the evolution of longer lifespans. Although numerous studies support the classical paradigm, recent data challenge classical predictions, finding that high extrinsic mortality can select for the evolution of longer lifespans. To further elucidate the role of extrinsic mortality in the evolution of aging, we implemented a stochastic, agent-based, computational model. We used a simulated annealing optimization approach to predict which model parameters predispose populations to evolve longer or shorter lifespans in response to increased levels of predation. We report that longer lifespans evolved in the presence of rising predation if the cost of mating is relatively high and if energy is available in excess. Conversely, we found that dramatically shorter lifespans evolved when mating costs were relatively low and food was relatively scarce. We also analyzed the effects of increased predation on various parameters related to density dependence and energy allocation. Longer and shorter lifespans were accompanied by increased and decreased investments of energy into somatic maintenance, respectively. Similarly, earlier and later maturation ages were accompanied by increased and decreased energetic investments into early fecundity, respectively. Higher predation significantly decreased the total population size, enlarged the shared resource pool, and redistributed energy reserves for mature individuals. These results both corroborate and refine classical predictions, demonstrating a population-level trade-off between longevity and fecundity and identifying conditions that produce both classical and non-classical lifespan effects. PMID:24466165

Modeling the lake eutrophication stochastic ecosystem and the research of its stability.

PubMed

Wang, Bo; Qi, Qianqian

2018-06-01

In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e., nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0,  0.388644) and (0.66003825,  1.0), there only exists a stable equilibrium state and the additive noise intensity could not change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be capable of effectively explaining the regime shift theory and agreed with the realistic analyze. These conclusions also confirms the two paths for the system to move from one stable state to another proposed by Beisner et al. [3], which may help understand the occurrence mechanism related to the lake eutrophication from the view point of the stochastic model and mathematical analysis. Copyright © 2018 Elsevier Inc. All rights reserved.

Etiology and treatment of hematological neoplasms: stochastic mathematical models.

PubMed

Radivoyevitch, Tomas; Li, Huamin; Sachs, Rainer K

2014-01-01

Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.

Planetary Rings

NASA Astrophysics Data System (ADS)

Esposito, Larry

2014-03-01

Preface: a personal view of planetary rings; 1. Introduction: the allure of the ringed planets; 2. Studies of planetary rings 1610-2013; 3. Diversity of planetary rings; 4. Individual ring particles and their collisions; 5. Large-scale ring evolution; 6. Moons confine and sculpt rings; 7. Explaining ring phenomena; 8. N-body simulations; 9. Stochastic models; 10. Age and evolution of rings; 11. Saturn's mysterious F ring; 12. Uranus' rings and moons; 13. Neptune's partial rings; 14. Jupiter's ring-moon system after Galileo and New Horizons; 15. Ring photometry; 16. Dusty rings; 17. Concluding remarks; Afterword; Glossary; References; Index.

On spatial mutation-selection models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE PAGES

Hagos, Samson; Feng, Zhe; Plant, Robert S.; ...

2018-02-20

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

NASA Astrophysics Data System (ADS)

Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

2018-02-01

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

PubMed

Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

2016-01-01

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

External noise-induced transitions in a current-biased Josephson junction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Qiongwei; Xue, Changfeng, E-mail: cfxue@163.com; Tang, Jiashi

We investigate noise-induced transitions in a current-biased and weakly damped Josephson junction in the presence of multiplicative noise. By using the stochastic averaging procedure, the averaged amplitude equation describing dynamic evolution near a constant phase difference is derived. Numerical results show that a stochastic Hopf bifurcation between an absorbing and an oscillatory state occurs. This means the external controllable noise triggers a transition into the non-zero junction voltage state. With the increase of noise intensity, the stationary probability distribution peak shifts and is characterised by increased width and reduced height. And the different transition rates are shown for large andmore » small bias currents.« less

Long-term strength and damage accumulation in laminates

NASA Astrophysics Data System (ADS)

Dzenis, Yuris A.; Joshi, Shiv P.

1993-04-01

A modified version of the probabilistic model developed by authors for damage evolution analysis of laminates subjected to random loading is utilized to predict long-term strength of laminates. The model assumes that each ply in a laminate consists of a large number of mesovolumes. Probabilistic variation functions for mesovolumes stiffnesses as well as strengths are used in the analysis. Stochastic strains are calculated using the lamination theory and random function theory. Deterioration of ply stiffnesses is calculated on the basis of the probabilities of mesovolumes failures using the theory of excursions of random process beyond the limits. Long-term strength and damage accumulation in a Kevlar/epoxy laminate under tension and complex in-plane loading are investigated. Effects of the mean level and stochastic deviation of loading on damage evolution and time-to-failure of laminate are discussed. Long-term cumulative damage at the time of the final failure at low loading levels is more than at high loading levels. The effect of the deviation in loading is more pronounced at lower mean loading levels.

Evolution of fairness and coalition formation in three-person ultimatum games.

PubMed

Nishimura, Takeshi; Okada, Akira; Shirata, Yasuhiro

2017-05-07

We consider the evolution of fairness and coalition formation in a three-person ultimatum game in which the coalition value depends on its size. Traditional game theory, which assumes selfish and rational players, predicts the largest and efficient coalition with a proposer exploiting most of the total value. In a stochastic evolutionary model (the frequency-dependent Moran process with mutations) where players make errors in estimating the payoffs and strategies of others, evolutionary selection favors the formation of a two-person subcoalition under weak selection and in the low mutation limit if and only if its coalition value exceeds a high proportion (0.7) of that of the largest coalition. Proposers offer 30-35% of the subcoalition value to a coalition member, excluding a non-member. Multilateral bargaining is critically different from the bilateral one. Coalition-forming behavior may cause economic inefficiency and social exclusion. Stochastic evolutionary game theory thus provides theoretical support to explain the behavior of human subjects in economic experiments of a three-person ultimatum game. Copyright © 2017 Elsevier Ltd. All rights reserved.

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

NASA Astrophysics Data System (ADS)

Cook, Robert L.; Riofrío, Carlos A.; Deutsch, Ivan H.

2014-09-01

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a non-negligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem: state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal generalized measurement. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

A self-adaptive memeplexes robust search scheme for solving stochastic demands vehicle routing problem

NASA Astrophysics Data System (ADS)

Chen, Xianshun; Feng, Liang; Ong, Yew Soon

2012-07-01

In this article, we proposed a self-adaptive memeplex robust search (SAMRS) for finding robust and reliable solutions that are less sensitive to stochastic behaviours of customer demands and have low probability of route failures, respectively, in vehicle routing problem with stochastic demands (VRPSD). In particular, the contribution of this article is three-fold. First, the proposed SAMRS employs the robust solution search scheme (RS 3) as an approximation of the computationally intensive Monte Carlo simulation, thus reducing the computation cost of fitness evaluation in VRPSD, while directing the search towards robust and reliable solutions. Furthermore, a self-adaptive individual learning based on the conceptual modelling of memeplex is introduced in the SAMRS. Finally, SAMRS incorporates a gene-meme co-evolution model with genetic and memetic representation to effectively manage the search for solutions in VRPSD. Extensive experimental results are then presented for benchmark problems to demonstrate that the proposed SAMRS serves as an efficable means of generating high-quality robust and reliable solutions in VRPSD.

Time-Frequency Approach for Stochastic Signal Detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish

2011-10-20

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Villemore » Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.« less

Time-Frequency Approach for Stochastic Signal Detection

NASA Astrophysics Data System (ADS)

Ghosh, Ripul; Akula, Aparna; Kumar, Satish; Sardana, H. K.

2011-10-01

The detection of events in a stochastic signal has been a subject of great interest. One of the oldest signal processing technique, Fourier Transform of a signal contains information regarding frequency content, but it cannot resolve the exact onset of changes in the frequency, all temporal information is contained in the phase of the transform. On the other hand, Spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Therefore, time-frequency representations are considered for energetic characterisation of the non-stationary signals. Wigner Ville Distribution (WVD) is the most prominent quadratic time-frequency signal representation and used for analysing frequency variations in signals.WVD allows for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. This paper through simulations describes the way time frequency models are applied for the detection of event in a stochastic signal.

Rogue waves and entropy consumption

NASA Astrophysics Data System (ADS)

Hadjihoseini, Ali; Lind, Pedro G.; Mori, Nobuhito; Hoffmann, Norbert P.; Peinke, Joachim

2017-11-01

Based on data from the Sea of Japan and the North Sea the occurrence of rogue waves is analyzed by a scale-dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stochastic cascade process, which provides information of the general multipoint statistics. Furthermore the evolution of single trajectories in scale, which characterize wave height fluctuations in the surroundings of a chosen location, can be determined. The explicit knowledge of the stochastic process enables to assign entropy values to all wave events. We show that for these entropies the integral fluctuation theorem, a basic law of non-equilibrium thermodynamics, is valid. This implies that positive and negative entropy events must occur. Extreme events like rogue waves are characterized as negative entropy events. The statistics of these entropy fluctuations changes with the wave state, thus for the Sea of Japan the statistics of the entropies has a more pronounced tail for negative entropy values, indicating a higher probability of rogue waves.

Modified parton branching model for multi-particle production in hadronic collisions: Application to SUSY particle branching

NASA Astrophysics Data System (ADS)

Yuanyuan, Zhang

The stochastic branching model of multi-particle productions in high energy collision has theoretical basis in perturbative QCD, and also successfully describes the experimental data for a wide energy range. However, over the years, little attention has been put on the branching model for supersymmetric (SUSY) particles. In this thesis, a stochastic branching model has been built to describe the pure supersymmetric particle jets evolution. This model is a modified two-phase stochastic branching process, or more precisely a two phase Simple Birth Process plus Poisson Process. The general case that the jets contain both ordinary particle jets and supersymmetric particle jets has also been investigated. We get the multiplicity distribution of the general case, which contains a Hypergeometric function in its expression. We apply this new multiplicity distribution to the current experimental data of pp collision at center of mass energy √s = 0.9, 2.36, 7 TeV. The fitting shows the supersymmetric particles haven't participate branching at current collision energy.

Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

NASA Astrophysics Data System (ADS)

Lin, Lifeng; Wang, Huiqi; Huang, Xipei; Wen, Yongxian

2018-03-01

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro-Loginov formula and generalized fractional Shapiro-Loginov formula are derived. Then, by using the generalized (fractional) Shapiro-Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

Political model of social evolution

PubMed Central

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-01-01

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved. PMID:22198760

Political model of social evolution.

PubMed

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-12-27

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padgett, Jill M. A.; Ilie, Silvana, E-mail: silvana@ryerson.ca

2016-03-15

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating themore » solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.« less

A unified model of the hierarchical and stochastic theories of gastric cancer

PubMed Central

Song, Yanjing; Wang, Yao; Tong, Chuan; Xi, Hongqing; Zhao, Xudong; Wang, Yi; Chen, Lin

2017-01-01

Gastric cancer (GC) is a life-threatening disease worldwide. Despite remarkable advances in treatments for GC, it is still fatal to many patients due to cancer progression, recurrence and metastasis. Regarding the development of novel therapeutic techniques, many studies have focused on the biological mechanisms that initiate tumours and cause treatment resistance. Tumours have traditionally been considered to result from somatic mutations, either via clonal evolution or through a stochastic model. However, emerging evidence has characterised tumours using a hierarchical organisational structure, with cancer stem cells (CSCs) at the apex. Both stochastic and hierarchical models are reasonable systems that have been hypothesised to describe tumour heterogeneity. Although each model alone inadequately explains tumour diversity, the two models can be integrated to provide a more comprehensive explanation. In this review, we discuss existing evidence supporting a unified model of gastric CSCs, including the regulatory mechanisms of this unified model in addition to the current status of stemness-related targeted therapy in GC patients. PMID:28301871

Biological signatures of dynamic river networks from a coupled landscape evolution and neutral community model

NASA Astrophysics Data System (ADS)

Stokes, M.; Perron, J. T.

2017-12-01

Freshwater systems host exceptionally species-rich communities whose spatial structure is dictated by the topology of the river networks they inhabit. Over geologic time, river networks are dynamic; drainage basins shrink and grow, and river capture establishes new connections between previously separated regions. It has been hypothesized that these changes in river network structure influence the evolution of life by exchanging and isolating species, perhaps boosting biodiversity in the process. However, no general model exists to predict the evolutionary consequences of landscape change. We couple a neutral community model of freshwater organisms to a landscape evolution model in which the river network undergoes drainage divide migration and repeated river capture. Neutral community models are macro-ecological models that include stochastic speciation and dispersal to produce realistic patterns of biodiversity. We explore the consequences of three modes of speciation - point mutation, time-protracted, and vicariant (geographic) speciation - by tracking patterns of diversity in time and comparing the final result to an equilibrium solution of the neutral model on the final landscape. Under point mutation, a simple model of stochastic and instantaneous speciation, the results are identical to the equilibrium solution and indicate the dominance of the species-area relationship in forming patterns of diversity. The number of species in a basin is proportional to its area, and regional species richness reaches its maximum when drainage area is evenly distributed among sub-basins. Time-protracted speciation is also modeled as a stochastic process, but in order to produce more realistic rates of diversification, speciation is not assumed to be instantaneous. Rather, each new species must persist for a certain amount of time before it is considered to be established. When vicariance (geographic speciation) is included, there is a transient signature of increased regional diversity after river capture. The results indicate that the mode of speciation and the rate of speciation relative to the rate of divide migration determine the evolutionary signature of river capture.

Conditional Stochastic Models in Reduced Space: Towards Efficient Simulation of Tropical Cyclone Precipitation Patterns

NASA Astrophysics Data System (ADS)

Dodov, B.

2017-12-01

Stochastic simulation of realistic and statistically robust patterns of Tropical Cyclone (TC) induced precipitation is a challenging task. It is even more challenging in a catastrophe modeling context, where tens of thousands of typhoon seasons need to be simulated in order to provide a complete view of flood risk. Ultimately, one could run a coupled global climate model and regional Numerical Weather Prediction (NWP) model, but this approach is not feasible in the catastrophe modeling context and, most importantly, may not provide TC track patterns consistent with observations. Rather, we propose to leverage NWP output for the observed TC precipitation patterns (in terms of downscaled reanalysis 1979-2015) collected on a Lagrangian frame along the historical TC tracks and reduced to the leading spatial principal components of the data. The reduced data from all TCs is then grouped according to timing, storm evolution stage (developing, mature, dissipating, ETC transitioning) and central pressure and used to build a dictionary of stationary (within a group) and non-stationary (for transitions between groups) covariance models. Provided that the stochastic storm tracks with all the parameters describing the TC evolution are already simulated, a sequence of conditional samples from the covariance models chosen according to the TC characteristics at a given moment in time are concatenated, producing a continuous non-stationary precipitation pattern in a Lagrangian framework. The simulated precipitation for each event is finally distributed along the stochastic TC track and blended with a non-TC background precipitation using a data assimilation technique. The proposed framework provides means of efficient simulation (10000 seasons simulated in a couple of days) and robust typhoon precipitation patterns consistent with observed regional climate and visually undistinguishable from high resolution NWP output. The framework is used to simulate a catalog of 10000 typhoon seasons implemented in a flood risk model for Japan.

The Role of Breccia Lenses in Regolith Generation From the Formation of Small, Simple Craters: Application to the Apollo 15 Landing Site

NASA Astrophysics Data System (ADS)

Hirabayashi, M.; Howl, B. A.; Fassett, C. I.; Soderblom, J. M.; Minton, D. A.; Melosh, H. J.

2018-02-01

Impact cratering is likely a primary agent of regolith generation on airless bodies. Regolith production via impact cratering has long been a key topic of study since the Apollo era. The evolution of regolith due to impact cratering, however, is not well understood. A better formulation is needed to help quantify the formation mechanism and timescale of regolith evolution. Here we propose an analytically derived stochastic model that describes the evolution of regolith generated by small, simple craters. We account for ejecta blanketing as well as regolith infilling of the transient crater cavity. Our results show that the regolith infilling plays a key role in producing regolith. Our model demonstrates that because of the stochastic nature of impact cratering, the regolith thickness varies laterally, which is consistent with earlier work. We apply this analytical model to the regolith evolution at the Apollo 15 site. The regolith thickness is computed considering the observed crater size-frequency distribution of small, simple lunar craters (< 381 m in radius for ejecta blanketing and <100 m in radius for the regolith infilling). Allowing for some amount of regolith coming from the outside of the area, our result is consistent with an empirical result from the Apollo 15 seismic experiment. Finally, we find that the timescale of regolith growth is longer than that of crater equilibrium, implying that even if crater equilibrium is observed on a cratered surface, it is likely that the regolith thickness is still evolving due to additional impact craters.

Residual Viremia in Treated HIV+ Individuals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conway, Jessica M.; Perelson, Alan S.

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. Furthermore, the source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Our observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. The phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived frommore » activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.« less

Residual Viremia in Treated HIV+ Individuals

DOE PAGES

Conway, Jessica M.; Perelson, Alan S.

2016-01-06

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. Furthermore, the source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Our observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. The phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived frommore » activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.« less

Evolution of Life and SETI (Evo-SETI)

NASA Astrophysics Data System (ADS)

Maccone, Claudio

When SETI scientists will be able to discover a signal or just some signs of an Extra-Terrestrial (ET) Civilization, those ETs should turn out to be technologically advanced at least as much as Humans, if not more, or much more so. Comparing the technological level of two different Civilizations is then a key issue in SETI. But at the moment we only know about the development of life on Earth over the last 3.5 billion years. We thus need to mathematically model the evolution of life on Earth (RNA to Humans) and then apply our results to other extra-solar planets to find out “where they stand” along their evolution of life. In a series of recent papers and in a book (refs. [1] through [4]) this author introduced a new statistical model embracing SETI, Darwinian Evolution and Human History into a unified statistical picture and concisely called Evo-SETI (Evolution & SETI). The relevant mathematical instruments are: 1) The statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. Assuming that each input variable in the Drake equation was a random variable, rather than just a pure number, N was shown to follow the lognormal probability distribution having as mean value the sum of the input mean values, and as variance the sum of the input variances (ref. [1]). 2) Geometric Brownian Motion (GBM), the stochastic process representing Evolution as the stochastic increase of the number of Species living on Earth over the last 3.5 billion years. This GBM is well-known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing, or, more rarely (as in the Mass Extinctions of the past) a decreasing exponential of the time. 3) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (this is the so-called “Peak-Locus Theorem”). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to identify with Cladistics (refs. [2], [3], [4]). 4) The (Shannon) Entropy of such b-lognormals is then seen to represent the “degree of progress” reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, Human History may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller “chaos”), and have their peaks located on the increasing GBM exponential. This exponential is thus the “trend of progress” in Human History. 5) But our most striking new result is about the well-known “Molecular Clock of Evolution”, namely the “constant rate of Evolution at the molecular level” as shown by Kimura’s Neutral Theory of Molecular Evolution. We showed that that the Molecular Clock identifies with Entropy in our Evo-SETI model because they both grew linearly in time since the origin of life. 6) Furthermore, we applid our Evo-SETI model to lognormal stochastic processes other then the GBMs. For instance, we showed that the Markov-Korotayev (2007-2008, refs. [5], [6]) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the lognormal stochastic process is a cubic (third degree polynomial) function of the time. In conclusion: we have provided a vast mathematical model capable of embracing Molecular Evolution, SETI and Entropy into a simple set of statistical equations based upon b-lognormals pdfs and lognormal stochastic processes Keywords: Molecular Clock, Darwinian evolution, statistical Drake equation, lognormal probability densities, geometric Brownian motion, entropy. REFERENCES [1] Maccone, C. (2008), “The Statistical Drake Equation”, paper #IAC-08-A4.1.4 presented on October 1st, 2008, at the 59th International Astronautical Congress (IAC) held in Glasgow, Scotland, UK, September 29th thru October 3rd, 2008, later published in Acta Astronautica, Vol. 67 (2010), pages 1366-1383. [2] Maccone, C. (2011, b), “A Mathematical Model for Evolution and SETI”, Origins of Life and Evolutionary Biospheres (OLEB), Vol. 41, pages 609-619, available online December 3rd, 2011. [3] Maccone, C. (2012), “Mathematical SETI”, a 724-pages book published by Praxis-Springer in the fall of 2012. ISBN, ISBN-10: 3642274366 | ISBN-13: 978-3642274367 | Edition: 2012 [4] Maccone, C., (2013), “SETI, Evolution and Human History merged into a Mathematical Model”, International Journal of Astrobiology, Vol. 12, issue 3 (2013), pages 218-245. Available online since April 23, 2013. [5] Markov A., Korotayev A., “Phanerozoic marine biodiversity follows a hyperbolic trend”, Paleoworld, Volume 16, Issue 4, December 2007, Pages 311-318. [6] Markov A., Korotayev A., “Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution”, Journal of General Biology. Volume 69, 2008, N. 3, pp. 175-194.

Stochastic tools hidden behind the empirical dielectric relaxation laws

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2017-03-01

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of ‘structures with variations’ (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools—by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.

Transient ensemble dynamics in time-independent galactic potentials

NASA Astrophysics Data System (ADS)

Mahon, M. Elaine; Abernathy, Robert A.; Bradley, Brendan O.; Kandrup, Henry E.

1995-07-01

This paper summarizes a numerical investigation of the short-time, possibly transient, behaviour of ensembles of stochastic orbits evolving in fixed non-integrable potentials, with the aim of deriving insights into the structure and evolution of galaxies. The simulations involved three different two-dimensional potentials, quite different in appearance. However, despite these differences, ensembles in all three potentials exhibit similar behaviour. This suggests that the conclusions inferred from the simulations are robust, relying only on basic topological properties, e.g., the existence of KAM tori and cantori. Generic ensembles of initial conditions, corresponding to stochastic orbits, exhibit a rapid coarse-grained approach towards a near-invariant distribution on a time-scale <>t_H, although various irregularities associated with external and/or internal irregularities can drastically accelerate this process. A principal tool in the analysis is the notion of a local Liapounov exponent, which provides a statistical characterization of the overall instability of stochastic orbits over finite time intervals. In particular, there is a precise sense in which confined stochastic orbits are less unstable, with smaller local Liapounov exponents, than are unconfined stochastic orbits.

Mathematical Modeling of the Origins of Life

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.

The Ising Decision Maker: a binary stochastic network for choice response time.

PubMed

Verdonck, Stijn; Tuerlinckx, Francis

2014-07-01

The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.

Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system

NASA Astrophysics Data System (ADS)

Woillez, E.; Bouchet, F.

2017-11-01

Over timescales much longer than an orbital period, the solar system exhibits large-scale chaotic behavior and can thus be viewed as a stochastic dynamical system. The aim of the present paper is to compare different sources of stochasticity in the solar system. More precisely we studied the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects of asteroids on planets is similar to a white noise process, when those effects are considered on a timescale much larger than the correlation time τϕ ≃ 104 yr of asteroid trajectories. We computed the timescale τe after which the effects of the stochastic evolution of the asteroids lead to a loss of information for the initial conditions of the perturbed Laplace-Lagrange secular dynamics. The order of magnitude of this timescale is precisely determined by theoretical argument, and we find that τe ≃ 104 Myr. Although comparable to the full main-sequence lifetime of the sun, this timescale is considerably longer than the Lyapunov time τI ≃ 10 Myr of the solar system without asteroids. This shows that the external sources of chaos arise as a small perturbation in the stochastic secular behavior of the solar system, rather due to intrinsic chaos.

Coastal zone management with stochastic multi-criteria analysis.

PubMed

Félix, A; Baquerizo, A; Santiago, J M; Losada, M A

2012-12-15

The methodology for coastal management proposed in this study takes into account the physical processes of the coastal system and the stochastic nature of forcing agents. Simulation techniques are used to assess the uncertainty in the performance of a set of predefined management strategies based on different criteria representing the main concerns of interest groups. This statistical information as well as the distribution function that characterizes the uncertainty regarding the preferences of the decision makers is fed into a stochastic multi-criteria acceptability analysis that provides the probability of alternatives obtaining certain ranks and also calculates the preferences of a typical decision maker who supports an alternative. This methodology was applied as a management solution for Playa Granada in the Guadalfeo River Delta (Granada, Spain), where the construction of a dam in the river basin is causing severe erosion. The analysis of shoreline evolution took into account the coupled action of atmosphere, ocean, and land agents and their intrinsic stochastic character. This study considered five different management strategies. The criteria selected for the analysis were the economic benefits for three interest groups: (i) indirect beneficiaries of tourist activities; (ii) beach homeowners; and (iii) the administration. The strategies were ranked according to their effectiveness, and the relative importance given to each criterion was obtained. Copyright © 2012 Elsevier Ltd. All rights reserved.

Exact lower and upper bounds on stationary moments in stochastic biochemical systems

NASA Astrophysics Data System (ADS)

Ghusinga, Khem Raj; Vargas-Garcia, Cesar A.; Lamperski, Andrew; Singh, Abhyudai

2017-08-01

In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to find exact lower and upper bounds on stationary moments for a given arbitrary system of biochemical reactions. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints that are compactly represented through the positive semidefiniteness of moment matrices. Our analysis shows that solving moment equations at steady state in conjunction with constraints on moment matrices provides exact lower and upper bounds on the moments. These results are illustrated by three different examples—the commonly used logistic growth model, stochastic gene expression with auto-regulation and an activator-repressor gene network motif. Interestingly, in all cases the accuracy of the bounds is shown to improve as moment equations are expanded to include higher-order moments. Our results provide avenues for development of approximation methods that provide explicit bounds on moments for nonlinear stochastic systems that are otherwise analytically intractable.

Distribution and regulation of stochasticity and plasticity in Saccharomyces cerevisiae

DOE PAGES

Dar, R. D.; Karig, D. K.; Cooke, J. F.; ...

2010-09-01

Stochasticity is an inherent feature of complex systems with nanoscale structure. In such systems information is represented by small collections of elements (e.g. a few electrons on a quantum dot), and small variations in the populations of these elements may lead to big uncertainties in the information. Unfortunately, little is known about how to work within this inherently noisy environment to design robust functionality into complex nanoscale systems. Here, we look to the biological cell as an intriguing model system where evolution has mediated the trade-offs between fluctuations and function, and in particular we look at the relationships and trade-offsmore » between stochastic and deterministic responses in the gene expression of budding yeast (Saccharomyces cerevisiae). We find gene regulatory arrangements that control the stochastic and deterministic components of expression, and show that genes that have evolved to respond to stimuli (stress) in the most strongly deterministic way exhibit the most noise in the absence of the stimuli. We show that this relationship is consistent with a bursty 2-state model of gene expression, and demonstrate that this regulatory motif generates the most uncertainty in gene expression when there is the greatest uncertainty in the optimal level of gene expression.« less

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Mass fluctuation kinetics: Capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations

NASA Astrophysics Data System (ADS)

Gómez-Uribe, Carlos A.; Verghese, George C.

2007-01-01

The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system.

Topographic signatures of deep-seated landslides and a general landscape evolution model

NASA Astrophysics Data System (ADS)

Booth, A. M.; Roering, J. J.; Rempel, A. W.

2012-12-01

A fundamental goal of studying earth surface processes is to disentangle the complex web of interactions among baselevel, climate, and rock properties that generate characteristic landforms. Mechanistic geomorphic transport laws can quantitatively address this goal, but no widely accepted law for landslides exists. Here, we propose a transport law for deep-seated landslides and demonstrate its utility using a two-dimensional numerical landscape evolution model informed by study areas in the Waipaoa catchment, New Zealand and the Eel River catchment, California. We define a non-dimensional landslide number, which is the ratio of uplift to landslide flow time scales, that predicts three distinct landscape types. The first is dominated by stochastic landsliding, whereby discrete landslide events episodically erode material at rates far exceeding the long term uplift rate. The second is characterized by steady landsliding, in which the landslide flux at any location remains constant through time and is largest at the steepest locations in the catchment. The third is not significantly affected by landsliding. In both the "stochastic landsliding" and "steady landsliding" regimes, increases in the non-dimensional landslide number systematically reduce catchment relief and widen valley spacing, producing long, quasi-planar, low angle hillslopes despite high uplift rates. The stochastic landsliding regime best captures the frequent observation that deep-seated landslides produce a large sediment flux from a small aerial extent while being active only a fraction of the time. We suggest that this model is adaptable to a wide range of geologic settings and may be useful for interpreting climate-driven changes in landslide behavior.

Topographic signatures and a general transport law for deep-seated landslides in a landscape evolution model

NASA Astrophysics Data System (ADS)

Booth, Adam M.; Roering, Josh J.; Rempel, Alan W.

2013-06-01

A fundamental goal of studying earth surface processes is to disentangle the complex web of interactions among baselevel, tectonics, climate, and rock properties that generate characteristic landforms. Mechanistic geomorphic transport laws can quantitatively address this goal, but no widely accepted law for landslides exists. Here we propose a transport law for deep-seated landslides in weathered bedrock and demonstrate its utility using a two-dimensional numerical landscape evolution model informed by study areas in the Waipaoa catchment, New Zealand, and the Eel River catchment, California. We define a non-dimensional landslide number, which is the ratio of the horizontal landslide flux to the vertical tectonic flux, that characterizes three distinct landscape types. One is dominated by stochastic landsliding, whereby discrete landslide events episodically erode material at rates exceeding the long-term uplift rate. Another is characterized by steady landsliding, in which the landslide flux at any location remains constant through time and is greatest at the steepest locations in the catchment. The third is not significantly affected by landsliding. In both the "stochastic landsliding" and "steady landsliding" regimes, increases in the non-dimensional landslide number systematically reduce catchment relief and widen valley spacing, producing long, low angle hillslopes despite high uplift rates. The stochastic landsliding regime captures the frequent observation that deep-seated landslides produce large sediment fluxes from small areal extents while being active only a fraction of the time. We suggest that this model is adaptable to a wide range of geologic settings and is useful for interpreting climate-driven changes in landslide behavior.

Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition.

PubMed

Alemani, Davide; Pappalardo, Francesco; Pennisi, Marzio; Motta, Santo; Brusic, Vladimir

2012-02-28

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. Copyright © 2011 Elsevier B.V. All rights reserved.

Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories

USGS Publications Warehouse

Miller, David A.; Clark, W.R.; Arnold, S.J.; Bronikowski, A.M.

2011-01-01

Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (??s) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on ?? s. The magnitude of variation in the proportion of gravid females and its effect on ??s was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on ??s was 4- 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life-history traits in the two ecotypes, which, in turn, affect population dynamics. M-slow populations have evolved life-history traits that buffer fitness against direct effects of variation in reproduction and that spread lifetime reproduction across a greater number of reproductive bouts. These results highlight the importance of long-term demographic and environmental monitoring and of incorporating temporal dynamics into empirical studies of life-history evolution. ?? 2011 by the Ecological Society of America.

Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories.

PubMed

Miller, David A; Clark, William R; Arnold, Stevan J; Bronikowski, Anne M

2011-08-01

Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life-history traits in the two ecotypes, which, in turn, affect population dynamics. M-slow populations have evolved life-history traits that buffer fitness against direct effects of variation in reproduction and that spread lifetime reproduction across a greater number of reproductive bouts. These results highlight the importance of long-term demographic and environmental monitoring and of incorporating temporal dynamics into empirical studies of life-history evolution.

MONALISA for stochastic simulations of Petri net models of biochemical systems.

PubMed

Balazki, Pavel; Lindauer, Klaus; Einloft, Jens; Ackermann, Jörg; Koch, Ina

2015-07-10

The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0.

Evolution of regulatory networks towards adaptability and stability in a changing environment

NASA Astrophysics Data System (ADS)

Lee, Deok-Sun

2014-11-01

Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which evolve by selectively rewiring links towards enhancing adaptability to a changing environment and stability against dynamical perturbations. We find that sparse and heterogeneous connectivity patterns emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks. The characteristic scaling behavior of stability reflects the balance between robustness and flexibility. The scaling of fluctuation in the perturbation spread shows a dynamic crossover, which is analyzed by investigating separately the stochasticity of internal dynamics and the network structure differences depending on the evolution pathways. Our study delineates how the ambivalent pressure of evolution shapes biological networks, which can be helpful for studying general complex systems interacting with environments.

Studies of concentration and temperature dependences of precipitation kinetics in iron-copper alloys using kinetic Monte Carlo and stochastic statistical simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khromov, K. Yu.; Vaks, V. G., E-mail: vaks@mbslab.kiae.ru; Zhuravlev, I. A.

2013-02-15

The previously developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using an improved version of the previously suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependences of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM usually describes the precipitation kinetics in good agreement with the KMCM, and using the SSM in conjunction withmore » the KMCM allows extending the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of simulation results with experiments for some multicomponent Fe-Cu-based alloys allows making certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.« less

Modeling and optimization of the multiobjective stochastic joint replenishment and delivery problem under supply chain environment.

PubMed

Wang, Lin; Qu, Hui; Liu, Shan; Dun, Cai-xia

2013-01-01

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted.

A novel procedure for the identification of chaos in complex biological systems

NASA Astrophysics Data System (ADS)

Bazeia, D.; Pereira, M. B. P. N.; Brito, A. V.; Oliveira, B. F. De; Ramos, J. G. G. S.

2017-03-01

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.

Study of selected phenotype switching strategies in time varying environment

NASA Astrophysics Data System (ADS)

Horvath, Denis; Brutovsky, Branislav

2016-03-01

Population heterogeneity plays an important role across many research, as well as the real-world, problems. The population heterogeneity relates to the ability of a population to cope with an environment change (or uncertainty) preventing its extinction. However, this ability is not always desirable as can be exemplified by an intratumor heterogeneity which positively correlates with the development of resistance to therapy. Causation of population heterogeneity is therefore in biology and medicine an intensively studied topic. In this paper the evolution of a specific strategy of population diversification, the phenotype switching, is studied at a conceptual level. The presented simulation model studies evolution of a large population of asexual organisms in a time-varying environment represented by a stochastic Markov process. Each organism disposes with a stochastic or nonlinear deterministic switching strategy realized by discrete-time models with evolvable parameters. We demonstrate that under rapidly varying exogenous conditions organisms operate in the vicinity of the bet-hedging strategy, while the deterministic patterns become relevant as the environmental variations are less frequent. Statistical characterization of the steady state regimes of the populations is done using the Hellinger and Kullback-Leibler functional distances and the Hamming distance.

Modeling and Optimization of the Multiobjective Stochastic Joint Replenishment and Delivery Problem under Supply Chain Environment

PubMed Central

Dun, Cai-xia

2013-01-01

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted. PMID:24302880

Particle Swarm Optimization algorithms for geophysical inversion, practical hints

NASA Astrophysics Data System (ADS)

Garcia Gonzalo, E.; Fernandez Martinez, J.; Fernandez Alvarez, J.; Kuzma, H.; Menendez Perez, C.

2008-12-01

PSO is a stochastic optimization technique that has been successfully used in many different engineering fields. PSO algorithm can be physically interpreted as a stochastic damped mass-spring system (Fernandez Martinez and Garcia Gonzalo 2008). Based on this analogy we present a whole family of PSO algorithms and their respective first order and second order stability regions. Their performance is also checked using synthetic functions (Rosenbrock and Griewank) showing a degree of ill-posedness similar to that found in many geophysical inverse problems. Finally, we present the application of these algorithms to the analysis of a Vertical Electrical Sounding inverse problem associated to a seawater intrusion in a coastal aquifer in South Spain. We analyze the role of PSO parameters (inertia, local and global accelerations and discretization step), both in convergence curves and in the a posteriori sampling of the depth of an intrusion. Comparison is made with binary genetic algorithms and simulated annealing. As result of this analysis, practical hints are given to select the correct algorithm and to tune the corresponding PSO parameters. Fernandez Martinez, J.L., Garcia Gonzalo, E., 2008a. The generalized PSO: a new door to PSO evolution. Journal of Artificial Evolution and Applications. DOI:10.1155/2008/861275.

Exploring Quantum Dynamics of Continuous Measurement with a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Jadbabaie, Arian; Forouzani, Neda; Tan, Dian; Murch, Kater

Weak measurements obtain partial information about a quantum state with minimal backaction. This enables state tracking without immediate collapse to eigenstates, of interest to both experimental and theoretical physics. State tomography and continuous weak measurements may be used to reconstruct the evolution of a single system, known as a quantum trajectory. We examine experimental trajectories of a two-level system at varied measurement strengths with constant unitary drive. Our analysis is applied to a transmon qubit dispersively coupled to a 3D microwave cavity in the circuit QED architecture. The weakly coupled cavity acts as pointer system for QND measurements in the qubit's energy basis. Our results indicate a marked difference in state purity between two approaches for trajectory reconstruction: the Bayesian and Stochastic Master Equation (SME) formalisms. Further, we observe the transition from diffusive to jump-like trajectories, state purity evolution, and a novel, tilted form of the Quantum Zeno effect. This work provides new insight into quantum behavior and prompts further comparison of SME and Bayesian formalisms to understand the nature of quantum systems. Our results are applicable to a variety of fields, from stochastic thermodynamics to quantum control.

Continuously growing rodent molars result from a predictable quantitative evolutionary change over 50 million years

PubMed Central

Mushegyan, Vagan; Eronen, Jussi T.; Lawing, A. Michelle; Sharir, Amnon; Janis, Christine; Jernvall, Jukka; Klein, Ophir D.

2015-01-01

Summary The fossil record is widely informative about evolution, but fossils are not systematically used to study the evolution of stem cell-driven renewal. Here, we examined evolution of the continuous growth (hypselodonty) of rodent molar teeth, which is fuelled by the presence of dental stem cells. We studied occurrences of 3500 North American rodent fossils, ranging from 50 million years ago (mya) to 2 mya. We examined changes in molar height to determine if evolution of hypselodonty shows distinct patterns in the fossil record, and we found that hypselodont taxa emerged through intermediate forms of increasing crown height. Next, we designed a Markov simulation model, which replicated molar height increases throughout the Cenozoic, and, moreover, evolution of hypselodonty. Thus, by extension, the retention of the adult stem-cell niche appears to be a predictable quantitative rather than a stochastic qualitative process. Our analyses predict that hypselodonty will eventually become the dominant phenotype. PMID:25921530

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

The role of phase dynamics in a stochastic model of a passively advected scalar

NASA Astrophysics Data System (ADS)

Moradi, Sara; Anderson, Johan

2016-05-01

Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form -βk/1 +k2 , where β is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of β, where we find that the energy spectrum follows a k-7 /2 scaling. Whereas for lower β there is a significant difference between a-synchronised and synchronised phase states, one could expect the formation of coherent modulations in the latter case.

Modelling stock order flows with non-homogeneous intensities from high-frequency data

NASA Astrophysics Data System (ADS)

Gorshenin, Andrey K.; Korolev, Victor Yu.; Zeifman, Alexander I.; Shorgin, Sergey Ya.; Chertok, Andrey V.; Evstafyev, Artem I.; Korchagin, Alexander Yu.

2013-10-01

A micro-scale model is proposed for the evolution of such information system as the limit order book in financial markets. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of buy and sell orders that determine the price discovery mechanism. The proposed multiplicative model of stochastic intensities makes it possible to analyze the characteristics of the order flows as well as the instantaneous proportion of the forces of buyers and sellers, that is, the imbalance process, without modelling the external information background. The proposed model gives the opportunity to link the micro-scale (high-frequency) dynamics of the limit order book with the macro-scale models of stock price processes of the form of subordinated Wiener processes by means of limit theorems of probability theory and hence, to use the normal variance-mean mixture models of the corresponding heavy-tailed distributions. The approach can be useful in different areas with similar properties (e.g., in plasma physics).

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

Burstiness in Viral Bursts: How Stochasticity Affects Spatial Patterns in Virus-Microbe Dynamics

NASA Astrophysics Data System (ADS)

Lin, Yu-Hui; Taylor, Bradford P.; Weitz, Joshua S.

Spatial patterns emerge in living systems at the scale of microbes to metazoans. These patterns can be driven, in part, by the stochasticity inherent to the birth and death of individuals. For microbe-virus systems, infection and lysis of hosts by viruses results in both mortality of hosts and production of viral progeny. Here, we study how variation in the number of viral progeny per lysis event affects the spatial clustering of both viruses and microbes. Each viral ''burst'' is initially localized at a near-cellular scale. The number of progeny in a single lysis event can vary in magnitude between tens and thousands. These perturbations are not accounted for in mean-field models. Here we developed individual-based models to investigate how stochasticity affects spatial patterns in virus-microbe systems. We measured the spatial clustering of individuals using pair correlation functions. We found that increasing the burst size of viruses while maintaining the same production rate led to enhanced clustering. In this poster we also report on preliminary analysis on the evolution of the burstiness of viral bursts given a spatially distributed host community.

Most Colorful Example of Genetic Assimilation? Exploring the Evolutionary Destiny of Recurrent Phenotypic Accommodation.

PubMed

Badyaev, Alexander V; Potticary, Ahva L; Morrison, Erin S

2017-08-01

Evolution of adaptation requires both generation of novel phenotypic variation and retention of a locally beneficial subset of this variation. Such retention can be facilitated by genetic assimilation, the accumulation of genetic and molecular mechanisms that stabilize induced phenotypes and assume progressively greater control over their reliable production. A particularly strong inference into genetic assimilation as an evolutionary process requires a system where it is possible to directly evaluate the extent to which an induced phenotype is progressively incorporated into preexisting developmental pathways. Evolution of diet-dependent pigmentation in birds-where external carotenoids are coopted into internal metabolism to a variable degree before being integrated with a feather's developmental processes-provides such an opportunity. Here we combine a metabolic network view of carotenoid evolution with detailed empirical study of feather modifications to show that the effect of physical properties of carotenoids on feather structure depends on their metabolic modification, their environmental recurrence, and biochemical redundancy, as predicted by the genetic assimilation hypothesis. Metabolized carotenoids caused less stochastic variation in feather structure and were more closely integrated with feather growth than were dietary carotenoids of the same molecular weight. These patterns were driven by the recurrence of organism-carotenoid associations: commonly used dietary carotenoids and biochemically redundant derived carotenoids caused less stochastic variation in feather structure than did rarely used or biochemically unique compounds. We discuss implications of genetic assimilation processes for the evolutionary diversification of diet-dependent animal coloration.

Stochastic, adaptive sampling of information by microvilli in fly photoreceptors.

PubMed

Song, Zhuoyi; Postma, Marten; Billings, Stephen A; Coca, Daniel; Hardie, Roger C; Juusola, Mikko

2012-08-07

In fly photoreceptors, light is focused onto a photosensitive waveguide, the rhabdomere, consisting of tens of thousands of microvilli. Each microvillus is capable of generating elementary responses, quantum bumps, in response to single photons using a stochastically operating phototransduction cascade. Whereas much is known about the cascade reactions, less is known about how the concerted action of the microvilli population encodes light changes into neural information and how the ultrastructure and biochemical machinery of photoreceptors of flies and other insects evolved in relation to the information sampling and processing they perform. We generated biophysically realistic fly photoreceptor models, which accurately simulate the encoding of visual information. By comparing stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how adaptive sampling by 30,000 microvilli captures the temporal structure of natural contrast changes. Following each bump, individual microvilli are rendered briefly (~100-200 ms) refractory, thereby reducing quantum efficiency with increasing intensity. The refractory period opposes saturation, dynamically and stochastically adjusting availability of microvilli (bump production rate: sample rate), whereas intracellular calcium and voltage adapt bump amplitude and waveform (sample size). These adapting sampling principles result in robust encoding of natural light changes, which both approximates perceptual contrast constancy and enhances novel events under different light conditions, and predict information processing across a range of species with different visual ecologies. These results clarify why fly photoreceptors are structured the way they are and function as they do, linking sensory information to sensory evolution and revealing benefits of stochasticity for neural information processing. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stochastic, Adaptive Sampling of Information by Microvilli in Fly Photoreceptors

PubMed Central

Song, Zhuoyi; Postma, Marten; Billings, Stephen A.; Coca, Daniel; Hardie, Roger C.; Juusola, Mikko

2012-01-01

Summary Background In fly photoreceptors, light is focused onto a photosensitive waveguide, the rhabdomere, consisting of tens of thousands of microvilli. Each microvillus is capable of generating elementary responses, quantum bumps, in response to single photons using a stochastically operating phototransduction cascade. Whereas much is known about the cascade reactions, less is known about how the concerted action of the microvilli population encodes light changes into neural information and how the ultrastructure and biochemical machinery of photoreceptors of flies and other insects evolved in relation to the information sampling and processing they perform. Results We generated biophysically realistic fly photoreceptor models, which accurately simulate the encoding of visual information. By comparing stochastic simulations with single cell recordings from Drosophila photoreceptors, we show how adaptive sampling by 30,000 microvilli captures the temporal structure of natural contrast changes. Following each bump, individual microvilli are rendered briefly (∼100–200 ms) refractory, thereby reducing quantum efficiency with increasing intensity. The refractory period opposes saturation, dynamically and stochastically adjusting availability of microvilli (bump production rate: sample rate), whereas intracellular calcium and voltage adapt bump amplitude and waveform (sample size). These adapting sampling principles result in robust encoding of natural light changes, which both approximates perceptual contrast constancy and enhances novel events under different light conditions, and predict information processing across a range of species with different visual ecologies. Conclusions These results clarify why fly photoreceptors are structured the way they are and function as they do, linking sensory information to sensory evolution and revealing benefits of stochasticity for neural information processing. PMID:22704990

Emergence, reductionism and landscape response to climate change

NASA Astrophysics Data System (ADS)

Harrison, Stephan; Mighall, Tim

2010-05-01

Predicting landscape response to external forcing is hampered by the non-linear, stochastic and contingent (ie dominated by historical accidents) forcings inherent in landscape evolution. Using examples from research carried out in southwest Ireland we suggest that non-linearity in landform evolution is likely to be a strong control making regional predictions of landscape response to climate change very difficult. While uncertainties in GCM projections have been widely explored in climate science much less attention has been directed by geomorphologists to the uncertainties in landform evolution under conditions of climate change and this problem may be viewed within the context of philosophical approaches to reductionsim and emergence. Understanding the present and future trajectory of landform change may also guide us to provide an enhanced appreciation of how landforms evolved in the past.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Amini, Hadis, E-mail: nhamini@stanford.edu

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, whichmore » extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.« less

Emergent Lévy behavior in single-cell stochastic gene expression

NASA Astrophysics Data System (ADS)

Jia, Chen; Zhang, Michael Q.; Qian, Hong

2017-10-01

Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the Lévy limit provides a theoretical foundation for an empirical equation proposed in N. Friedman et al., Phys. Rev. Lett. 97, 168302 (2006), 10.1103/PhysRevLett.97.168302. Furthermore, we clarify the biochemical implications and ranges of applicability for various macroscopic limits and calculate a comprehensive analytic expression for the protein concentration distribution in autoregulatory gene networks. The relationship between our work and modern population genetics is discussed.

Weighted Flow Algorithms (WFA) for stochastic particle coagulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

DeVille, R.E.L., E-mail: rdeville@illinois.edu; Riemer, N., E-mail: nriemer@illinois.edu; West, M., E-mail: mwest@illinois.edu

2011-09-20

Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangianmore » trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications.« less

Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leonard, T.; Lander, B.; Seifert, U.

2013-11-28

We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example, simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstrate that even if coarse-grained dynamics and density functional do not match, the fluctuation relations for themore » work still hold albeit for a different, apparent, change of free energy.« less

Inversion method based on stochastic optimization for particle sizing.

PubMed

Sánchez-Escobar, Juan Jaime; Barbosa-Santillán, Liliana Ibeth; Vargas-Ubera, Javier; Aguilar-Valdés, Félix

2016-08-01

A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem.

Weighted Flow Algorithms (WFA) for stochastic particle coagulation

NASA Astrophysics Data System (ADS)

DeVille, R. E. L.; Riemer, N.; West, M.

2011-09-01

Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangian trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications.

Historical and contingent factors affect re-evolution of a complex feature lost during mass extinction in communities of digital organisms.

PubMed

Yedid, G; Ofria, C A; Lenski, R E

2008-09-01

Re-evolution of complex biological features following the extinction of taxa bearing them remains one of evolution's most interesting phenomena, but is not amenable to study in fossil taxa. We used communities of digital organisms (computer programs that self-replicate, mutate and evolve), subjected to periods of low resource availability, to study the evolution, loss and re-evolution of a complex computational trait, the function EQU (bit-wise logical equals). We focused our analysis on cases where the pre-extinction EQU clade had surviving descendents at the end of the extinction episode. To see if these clades retained the capacity to re-evolve EQU, we seeded one set of multiple subreplicate 'replay' populations using the most abundant survivor of the pre-extinction EQU clade, and another set with the actual end-extinction ancestor of the organism in which EQU re-evolved following the extinction episode. Our results demonstrate that stochastic, historical, genomic and ecological factors can lead to constraints on further adaptation, and facilitate or hinder re-evolution of a complex feature.

Stochastic Lotka-Volterra equations: A model of lagged diffusion of technology in an interconnected world

NASA Astrophysics Data System (ADS)

Chakrabarti, Anindya S.

2016-01-01

We present a model of technological evolution due to interaction between multiple countries and the resultant effects on the corresponding macro variables. The world consists of a set of economies where some countries are leaders and some are followers in the technology ladder. All of them potentially gain from technological breakthroughs. Applying Lotka-Volterra (LV) equations to model evolution of the technology frontier, we show that the way technology diffuses creates repercussions in the partner economies. This process captures the spill-over effects on major macro variables seen in the current highly globalized world due to trickle-down effects of technology.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Stochastic Coastal/Regional Uncertainty Modelling: a Copernicus marine research project in the framework of Service Evolution

NASA Astrophysics Data System (ADS)

Vervatis, Vassilios; De Mey, Pierre; Ayoub, Nadia; Kailas, Marios; Sofianos, Sarantis

2017-04-01

The project entitled Stochastic Coastal/Regional Uncertainty Modelling (SCRUM) aims at strengthening CMEMS in the areas of ocean uncertainty quantification, ensemble consistency verification and ensemble data assimilation. The project has been initiated by the University of Athens and LEGOS/CNRS research teams, in the framework of CMEMS Service Evolution. The work is based on stochastic modelling of ocean physics and biogeochemistry in the Bay of Biscay, on an identical sub-grid configuration of the IBI-MFC system in its latest CMEMS operational version V2. In a first step, we use a perturbed tendencies scheme to generate ensembles describing uncertainties in open ocean and on the shelf, focusing on upper ocean processes. In a second step, we introduce two methodologies (i.e. rank histograms and array modes) aimed at checking the consistency of the above ensembles with respect to TAC data and arrays. Preliminary results highlight that wind uncertainties dominate all other atmosphere-ocean sources of model errors. The ensemble spread in medium-range ensembles is approximately 0.01 m for SSH and 0.15 °C for SST, though these values vary depending on season and cross shelf regions. Ecosystem model uncertainties emerging from perturbations in physics appear to be moderately larger than those perturbing the concentration of the biogeochemical compartments, resulting in total chlorophyll spread at about 0.01 mg.m-3. First consistency results show that the model ensemble and the pseudo-ensemble of OSTIA (L4) observation SSTs appear to exhibit nonzero joint probabilities with each other since error vicinities overlap. Rank histograms show that the model ensemble is initially under-dispersive, though results improve in the context of seasonal-range ensembles.

On the modeling of epidemics under the influence of risk perception

NASA Astrophysics Data System (ADS)

de Lillo, S.; Fioriti, G.; Prioriello, M. L.

An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

Dynamics of Markets

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2009-09-01

Preface; 1. Econophysics: why and what; 2. Neo-classical economic theory; 3. Probability and stochastic processes; 4. Introduction to financial economics; 5. Introduction to portfolio selection theory; 6. Scaling, pair correlations, and conditional densities; 7. Statistical ensembles: deducing dynamics from time series; 8. Martingale option pricing; 9. FX market globalization: evolution of the dollar to worldwide reserve currency; 10. Macroeconomics and econometrics: regression models vs. empirically based modeling; 11. Complexity; Index.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

A continuum dislocation dynamics framework for plasticity of polycrystalline materials

NASA Astrophysics Data System (ADS)

Askari, Hesam Aldin

The objective of this research is to investigate the mechanical response of polycrystals in different settings to identify the mechanisms that give rise to specific response observed in the deformation process. Particularly the large deformation of magnesium alloys and yield properties of copper in small scales are investigated. We develop a continuum dislocation dynamics framework based on dislocation mechanisms and interaction laws and implement this formulation in a viscoplastic self-consistent scheme to obtain the mechanical response in a polycrystalline system. The versatility of this method allows various applications in the study of problems involving large deformation, study of microstructure and its evolution, superplasticity, study of size effect in polycrystals and stochastic plasticity. The findings from the numerical solution are compared to the experimental results to validate the simulation results. We apply this framework to study the deformation mechanisms in magnesium alloys at moderate to fast strain rates and room temperature to 450 °C. Experiments for the same range of strain rates and temperatures were carried out to obtain the mechanical and material properties, and to compare with the numerical results. The numerical approach for magnesium is divided into four main steps; 1) room temperature unidirectional loading 2) high temperature deformation without grain boundary sliding 3) high temperature with grain boundary sliding mechanism 4) room temperature cyclic loading. We demonstrate the capability of our modeling approach in prediction of mechanical properties and texture evolution and discuss the improvement obtained by using the continuum dislocation dynamics method. The framework was also applied to nano-sized copper polycrystals to study the yield properties at small scales and address the observed yield scatter. By combining our developed method with a Monte Carlo simulation approach, the stochastic plasticity at small length scales was studied and the sources of the uncertainty in the polycrystalline structure are discussed. Our results suggest that the stochastic response is mainly because of a) stochastic plasticity due to dislocation substructure inside crystals and b) the microstructure of the polycrystalline material. The extent of the uncertainty is correlated to the "effective cell length" in the sampling procedure whether using simulations and experimental approach.

The Star-Forming Main Sequence as a Natural Consequence of the Central Limit Theorem

NASA Astrophysics Data System (ADS)

Kelson, Daniel David

2015-08-01

Star-formation rates (SFR) of disk galaxies correlate with stellar mass, with a small dispersion in SSFR at fixed mass, sigma~0.3 dex. With such scatter this star-formation main sequence (SFMS) has been interpreted as deterministic and fundamental. Here I demonstrate that such a correlation arises naturally from the central limit theorem. The derivation begins by approximating in situ stellar mass growth as a stochastic process, much like a random walk, where the expectation of SFR at any time is equal to the SFR at the previous time. The SFRs of real galaxies, however, do not experience wholly random stochastic changes over time, but change in a highly correlated fashion due to the long reach of gravity and the correlation of structure in the universe. We therefore generalize the results for star-formation as a stochastic process that has random correlations over random and potentially infinite timescales. For unbiased samples of (disk) galaxies we derive expectation values for SSFR and its scatter, such that =2/T, and Sig[SFR/M]=. Note that this relative scatter is independent of mass and time. This derived correlation between SFR and stellar mass, and its evolution, matches published data to z=10 with sufficient accuracy to constrain cosmological parameters from the data. This statistical approach to the diversity of star-formation histories reproduces several important observables, including: the scatter in SSFR at fixed mass; the forms of SFHs of nearby dwarf galaxies and the Milky Way. At least one additional process beyond a single one responsible for in situ stellar mass growth will be required to match the evolution of the stellar mass function, and we discuss ways to generalize the framework. The implied dispersion in SFHs, and the SFMS's insensitivity to timescales of stochasticity, thus substantially limits the ability to connect massive galaxies to their progenitors over long cosmic baselines. Such analytical work shows promise for statisically modeling distributions of galaxies over cosmic time, in a manner particularly indpendent of the thorny uncertainties in sub-grid astrophysics of modern cosmological simulations.

Slowly switching between environments facilitates reverse evolution in small populations.

PubMed

Tan, Longzhi; Gore, Jeff

2012-10-01

Natural populations must constantly adapt to ever-changing environmental conditions. A particularly interesting question is whether such adaptations can be reversed by returning the population to an ancestral environment. Such evolutionary reversals have been observed in both natural and laboratory populations. However, the factors that determine the reversibility of evolution are still under debate. The time scales of environmental change vary over a wide range, but little is known about how the rate of environmental change influences the reversibility of evolution. Here, we demonstrate computationally that slowly switching between environments increases the reversibility of evolution for small populations that are subject to only modest clonal interference. For small populations, slow switching reduces the mean number of mutations acquired in a new environment and also increases the probability of reverse evolution at each of these "genetic distances." As the population size increases, slow switching no longer reduces the genetic distance, thus decreasing the evolutionary reversibility. We confirm this effect using both a phenomenological model of clonal interference and also a Wright-Fisher stochastic simulation that incorporates genetic diversity. Our results suggest that the rate of environmental change is a key determinant of the reversibility of evolution, and provides testable hypotheses for experimental evolution. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.

A case study in evolutionary contingency.

PubMed

Blount, Zachary D

2016-08-01

Biological evolution is a fundamentally historical phenomenon in which intertwined stochastic and deterministic processes shape lineages with long, continuous histories that exist in a changing world that has a history of its own. The degree to which these characteristics render evolution historically contingent, and evolutionary outcomes thereby unpredictably sensitive to history has been the subject of considerable debate in recent decades. Microbial evolution experiments have proven among the most fruitful means of empirically investigating the issue of historical contingency in evolution. One such experiment is the Escherichia coli Long-Term Evolution Experiment (LTEE), in which twelve populations founded from the same clone of E. coli have evolved in parallel under identical conditions. Aerobic growth on citrate (Cit(+)), a novel trait for E. coli, evolved in one of these populations after more than 30,000 generations. Experimental replays of this population's evolution from various points in its history showed that the Cit(+) trait was historically contingent upon earlier mutations that potentiated the trait by rendering it mutationally accessible. Here I review this case of evolutionary contingency and discuss what it implies about the importance of historical contingency arising from the core processes of evolution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Molecular logic behind the three-way stochastic choices that expand butterfly colour vision.

PubMed

Perry, Michael; Kinoshita, Michiyo; Saldi, Giuseppe; Huo, Lucy; Arikawa, Kentaro; Desplan, Claude

2016-07-14

Butterflies rely extensively on colour vision to adapt to the natural world. Most species express a broad range of colour-sensitive Rhodopsin proteins in three types of ommatidia (unit eyes), which are distributed stochastically across the retina. The retinas of Drosophila melanogaster use just two main types, in which fate is controlled by the binary stochastic decision to express the transcription factor Spineless in R7 photoreceptors. We investigated how butterflies instead generate three stochastically distributed ommatidial types, resulting in a more diverse retinal mosaic that provides the basis for additional colour comparisons and an expanded range of colour vision. We show that the Japanese yellow swallowtail (Papilio xuthus, Papilionidae) and the painted lady (Vanessa cardui, Nymphalidae) butterflies have a second R7-like photoreceptor in each ommatidium. Independent stochastic expression of Spineless in each R7-like cell results in expression of a blue-sensitive (Spineless(ON)) or an ultraviolet (UV)-sensitive (Spineless(OFF)) Rhodopsin. In P. xuthus these choices of blue/blue, blue/UV or UV/UV sensitivity in the two R7 cells are coordinated with expression of additional Rhodopsin proteins in the remaining photoreceptors, and together define the three types of ommatidia. Knocking out spineless using CRISPR/Cas9 (refs 5, 6) leads to the loss of the blue-sensitive fate in R7-like cells and transforms retinas into homogeneous fields of UV/UV-type ommatidia, with corresponding changes in other coordinated features of ommatidial type. Hence, the three possible outcomes of Spineless expression define the three ommatidial types in butterflies. This developmental strategy allowed the deployment of an additional red-sensitive Rhodopsin in P. xuthus, allowing for the evolution of expanded colour vision with a greater variety of receptors. This surprisingly simple mechanism that makes use of two binary stochastic decisions coupled with local coordination may prove to be a general means of generating an increased diversity of developmental outcomes.

Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

PubMed

Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

2016-10-21

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Scaling and efficiency determine the irreversible evolution of a market

PubMed Central

Baldovin, F.; Stella, A. L.

2007-01-01

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. In addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model.

Evolution of specialization under non-equilibrium population dynamics.

PubMed

Nurmi, Tuomas; Parvinen, Kalle

2013-03-21

We analyze the evolution of specialization in resource utilization in a mechanistically underpinned discrete-time model using the adaptive dynamics approach. We assume two nutritionally equivalent resources that in the absence of consumers grow sigmoidally towards a resource-specific carrying capacity. The consumers use resources according to the law of mass-action with rates involving trade-off. The resulting discrete-time model for the consumer population has over-compensatory dynamics. We illuminate the way non-equilibrium population dynamics affect the evolutionary dynamics of the resource consumption rates, and show that evolution to the trimorphic coexistence of a generalist and two specialists is possible due to asynchronous non-equilibrium population dynamics of the specialists. In addition, various forms of cyclic evolutionary dynamics are possible. Furthermore, evolutionary suicide may occur even without Allee effects and demographic stochasticity. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stochastic dynamics of dengue epidemics.

PubMed

de Souza, David R; Tomé, Tânia; Pinho, Suani T R; Barreto, Florisneide R; de Oliveira, Mário J

2013-01-01

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

The propagator of stochastic electrodynamics

NASA Astrophysics Data System (ADS)

Cavalleri, G.

1981-01-01

The "elementary propagator" for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density ~ω3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to ψψ* where ψ is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics.

Intrinsic noise analysis and stochastic simulation on transforming growth factor beta signal pathway

NASA Astrophysics Data System (ADS)

Wang, Lu; Ouyang, Qi

2010-10-01

A typical biological cell lives in a small volume at room temperature; the noise effect on the cell signal transduction pathway may play an important role in its dynamics. Here, using the transforming growth factor-β signal transduction pathway as an example, we report our stochastic simulations of the dynamics of the pathway and introduce a linear noise approximation method to calculate the transient intrinsic noise of pathway components. We compare the numerical solutions of the linear noise approximation with the statistic results of chemical Langevin equations, and find that they are quantitatively in agreement with the other. When transforming growth factor-β dose decreases to a low level, the time evolution of noise fluctuation of nuclear Smad2—Smad4 complex indicates the abnormal enhancement in the transient signal activation process.

What does convergent evolution mean? The interpretation of convergence and its implications in the search for limits to evolution

PubMed Central

Stayton, C. Tristan

2015-01-01

Convergent evolution is central to the study of life's evolutionary history. Researchers have documented the ubiquity of convergence and have used this ubiquity to make inferences about the nature of limits on evolution. However, these inferences are compromised by unrecognized inconsistencies in the definitions, measures, significance tests and inferred causes of convergent evolution. I review these inconsistencies and provide recommendations for standardizing studies of convergence. A fundamental dichotomy exists between definitions that describe convergence as a pattern and those that describe it as a pattern caused by a particular process. When this distinction is not acknowledged it becomes easy to assume that a pattern of convergence indicates that a particular process has been active, leading researchers away from alternative explanations. Convergence is not necessarily caused by limits to evolution, either adaptation or constraint; even substantial amounts of convergent evolution can be generated by a purely stochastic process. In the absence of null models, long lists of examples of convergent events do not necessarily indicate that convergence or any evolutionary process is ubiquitous throughout the history of life. Pattern-based definitions of convergence, coupled with quantitative measures and null models, must be applied before drawing inferences regarding large-scale limits to evolution. PMID:26640646

Chaos and the (un)predictability of evolution in a changing environment.

PubMed

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-02-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Stochastic orbital migration of small bodies in Saturn's rings

NASA Astrophysics Data System (ADS)

Rein, H.; Papaloizou, J. C. B.

2010-12-01

Many small moonlets that create propeller structures have been found in Saturn's rings by the Cassini spacecraft. We study the dynamical evolution of such 20-50 m sized bodies, which are embedded in Saturn's rings. We estimate the importance of various interaction processes with the ring particles on the moonlet's eccentricity and semi-major axis analytically. For low ring surface densities, the main effects on the evolution of the eccentricity and the semi-major axis are found to be caused by collisions and the gravitational interaction with particles in the vicinity of the moonlet. For high surface densities, the gravitational interaction with self-gravity wakes becomes important. We also perform realistic three-dimensional, collisional N-body simulations with up to a quarter of a million particles. A new set of pseudo shear periodic boundary conditions is used, which reduces the computational costs by an order of magnitude compared to previous studies. Our analytic estimates are confirmed to within a factor of two. On short timescales the evolution is always dominated by stochastic effects caused by collisions and gravitational interaction with self-gravitating ring particles. These result in a random walk of the moonlet's semi-major axis. The eccentricity of the moonlet quickly reaches an equilibrium value owing to collisional damping. The average change in semi-major axis of the moonlet after 100 orbital periods is 10-100m. This translates to an offset in the azimuthal direction of several hundred kilometres. We expect that such a shift is easily observable. Two movies are only available in electronic form at http://www.aanda.org

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

On swinging spring chaotic oscillations

NASA Astrophysics Data System (ADS)

Aldoshin, Gennady T.; Yakovlev, Sergey P.

2018-05-01

In this work, chaotic modes of Swinging spring oscillations, their appearing conditions and probable scenario of evolution are studied. Swinging spring two-dimensional potential has (under certain conditions) local maximum. It can lead to stochastic attractor appearing. The system instability reason is inner (auto-parametric) resonance with frequencies ratio 2:1, which allows us to conclude that attractor could evolve according to the period doubling scenario, which was predicted by Feigenbaum in 1978.

Widening Disparity and its Suppression in a Stochastic Replicator Model

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu

2016-04-01

Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all elements are statistically equivalent. A lognormal distribution describes well the nonstationary time evolution. If a nonlinear load corresponding to progressive taxation is introduced, a stationary distribution is obtained and disparity widening is suppressed.

Dynamic Trust Models between Users over Social Networks

DTIC Science & Technology

2016-03-30

SUPPLEMENTARY NOTES 14. ABSTRACT In this project, by focusing on a number of word -of- mouth communication websites, we attempted to...analyzed evolution of trust networks in social media sites from a perspective of mediators. To this end, we proposed two stochastic models that...focusing on a number of word -of- mouth communication websites, we first attempt to construct dynamic trust models between users that enable to explain trust

Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2012-09-01

It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are "locked" inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.

Drift-Induced Selection Between Male and Female Heterogamety.

PubMed

Veller, Carl; Muralidhar, Pavitra; Constable, George W A; Nowak, Martin A

2017-10-01

Evolutionary transitions between male and female heterogamety are common in both vertebrates and invertebrates. Theoretical studies of these transitions have found that, when all genotypes are equally fit, continuous paths of intermediate equilibria link the two sex chromosome systems. This observation has led to a belief that neutral evolution along these paths can drive transitions, and that arbitrarily small fitness differences among sex chromosome genotypes can determine the system to which evolution leads. Here, we study stochastic evolutionary dynamics along these equilibrium paths. We find non-neutrality, both in transitions retaining the ancestral pair of sex chromosomes, and in those creating a new pair. In fact, substitution rates are biased in favor of dominant sex determining chromosomes, which fix with higher probabilities than mutations of no effect. Using diffusion approximations, we show that this non-neutrality is a result of "drift-induced selection" operating at every point along the equilibrium paths: stochastic jumps off the paths return with, on average, a directional bias in favor of the dominant segregating sex chromosome. Our results offer a novel explanation for the observed preponderance of dominant sex determining genes, and hint that drift-induced selection may be a common force in standard population genetic systems. Copyright © 2017 by the Genetics Society of America.

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

NASA Astrophysics Data System (ADS)

Pizzolato, N.; Persano Adorno, D.; Valenti, D.; Spagnolo, B.

2016-05-01

Front line therapy for the treatment of patients affected by chronic myeloid leukemia (CML) is based on the administration of tyrosine kinase inhibitors, namely imatinib or, more recently, axitinib. Although imatinib is highly effective and represents an example of a successful molecular targeted therapy, the appearance of resistance is observed in a proportion of patients, especially those in advanced stages. In this work, we investigate the appearance of resistance in patients affected by CML, by modeling the evolutionary dynamics of cancerous cell populations in a simulated patient treated by an intermittent targeted therapy. We simulate, with the Monte Carlo method, the stochastic evolution of initially healthy cells to leukemic clones, due to genetic mutations and changes in their reproductive behavior. We first present the model and its validation with experimental data by considering a continuous therapy. Then, we investigate how fluctuations in the number of leukemic cells affect patient response to the therapy when the drug is administered with an intermittent time scheduling. Here we show that an intermittent therapy (IT) represents a valid choice in patients with high risk of toxicity, despite an associated delay to the complete restoration of healthy cells. Moreover, a suitably tuned IT can reduce the probability of developing resistance.

COMMUNICATION: Stochastic resonance and the evolution of Daphnia foraging strategy

NASA Astrophysics Data System (ADS)

Dees, Nathan D.; Bahar, Sonya; Moss, Frank

2008-12-01

Search strategies are currently of great interest, with reports on foraging ranging from albatrosses and spider monkeys to microzooplankton. Here, we investigate the role of noise in optimizing search strategies. We focus on the zooplankton Daphnia, which move in successive sequences consisting of a hop, a pause and a turn through an angle. Recent experiments have shown that their turning angle distributions (TADs) and underlying noise intensities are similar across species and age groups, suggesting an evolutionary origin of this internal noise. We explore this hypothesis further with a digital simulation (EVO) based solely on the three central Darwinian themes: inheritability, variability and survivability. Separate simulations utilizing stochastic resonance (SR) indicate that foraging success, and hence fitness, is maximized at an optimum TAD noise intensity, which is represented by the distribution's characteristic width, σ. In both the EVO and SR simulations, foraging success is the criterion, and the results are the predicted characteristic widths of the TADs that maximize success. Our results are twofold: (1) the evolving characteristic widths achieve stasis after many generations; (2) as a hop length parameter is changed, variations in the evolved widths generated by EVO parallel those predicted by SR. These findings provide support for the hypotheses that (1) σ is an evolved quantity and that (2) SR plays a role in evolution.

Influence of Microphysical Variability on Stochastic Condensation in Turbulent Clouds

NASA Astrophysics Data System (ADS)

Desai, N.; Chandrakar, K. K.; Chang, K.; Glienke, S.; Cantrell, W. H.; Fugal, J. P.; Shaw, R. A.

2017-12-01

We investigate the influence of variability in droplet number concentration and radius on the evolution of cloud droplet size distributions. Measurements are made on the centimeter scale using digitial inline holography, both in a controlled laboratory setting and in the field using HOLODEC measurements from CSET. We created steady state cloud conditions in the laboratory Pi Chamber, in which a turbulent cloud can be sustained for long periods of time. Using holographic imaging, we directly observe the variations in local number concentration and droplet size distribution and, thereby, the integral radius. We interpret the measurements in the context of stochastic condensation theory to determine how fluctuations in integral radius contribute to droplet growth. We find that the variability in integral radius is primarily driven by variations in the droplet number concentration and not the droplet radius. This variability does not contribute significantly to the mean droplet growth rate, but contributes significantly to the rate of increase of the size distribution width. We compare these results with in-situ measurements and find evidence for microphysical signatures of stochastic condensation. The results suggest that supersaturation fluctuations lead to broader size distributions and allow droplets to reach the collision-coalescence stage.

Stochastic hyperfine interactions modeling library-Version 2

NASA Astrophysics Data System (ADS)

Zacate, Matthew O.; Evenson, William E.

2016-02-01

The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized. The original version of SHIML constructed and solved Blume matrices for methods that measure hyperfine interactions of nuclear probes in a single spin state. Version 2 provides additional support for methods that measure interactions on two different spin states such as Mössbauer spectroscopy and nuclear resonant scattering of synchrotron radiation. Example codes are provided to illustrate the use of SHIML to (1) generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A22 can be neglected and (2) generate Mössbauer spectra for polycrystalline samples for pure dipole or pure quadrupole transitions.

What can we learn from the stochastic gravitational wave background produced by oscillons?

NASA Astrophysics Data System (ADS)

Antusch, Stefan; Cefalà, Francesco; Orani, Stefano

2018-03-01

The stochastic gravitational wave (GW) background provides a fascinating window to the physics of the very early universe. Beyond the nearly scale-invariant primordial GW spectrum produced during inflation, a spectrum with a much richer structure is typically generated during the preheating phase after inflation (or after some other phase transition at lower energies). This raises the question of what one can learn from a future observation of the stochastic gravitational wave background spectrum about the underlying physics during preheating. Recently, it has been shown that during preheating non-perturbative quasi-stable objects like oscillons can act as strong sources for GW, leading to characteristic features such as distinct peaks in the spectrum. In this paper, we study the GW production from oscillons using semi-analytical techniques. In particular, we discuss how the GW spectrum is affected by the parameters that characterise a given oscillon system, e.g. by the background cosmology, the asymmetry of the oscillons and the evolution of the number density of the oscillons. We compare our semi-analytic results with numerical lattice simulations for a hilltop inflation model and a KKLT scenario, which differ strongly in some of these characteristics, and find very good agreement.

Stochastic acceleration of electrons. I - Effects of collisions in solar flares

NASA Technical Reports Server (NTRS)

Hamilton, Russell J.; Petrosian, Vahe

1992-01-01

Stochastic acceleration of thermal electrons to nonrelativistic energies is studied under solar flare conditions. We show that, in turbulent regions, electron-whistler wave interactions can result in the acceleration of electrons in times comparable to or shorter than the Coulomb collision time. The kinetic equation describing the evolution of the electron energy distribution including stochastic acceleration by whistlers and energy loss via Coulomb interactions is solved for an initial thermal electron energy spectrum. In general, the shape of the resulting electron distributions are characterized by the energy E(c) where systematic energy gain by turbulence equals energy loss due to Coulomb collisions. For energies less than E(c), the spectra are steep (quasi-thermal) whereas above E(c), the spectra are power laws. We find that hard X-ray spectra computed using the electron distributions obtained from our numerical simulations are able to explain the complex spectral shapes and variations observed in impulsive hard X-ray bursts. In particular, we show that the gradual steepening observed by Lin et al. (1981) could be due to a systematic increase in the density of the plasma (due to evaporation) and the increasing importance of collisions instead of the appearance of a superhot thermal component.

Evolutionary fields can explain patterns of high-dimensional complexity in ecology

NASA Astrophysics Data System (ADS)

Wilsenach, James; Landi, Pietro; Hui, Cang

2017-04-01

One of the properties that make ecological systems so unique is the range of complex behavioral patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to stochastic factors that have very high-degrees of freedom. Orthodox study of the evolution of these simple networks has generally been limited in its ability to explain complexity, since it restricts evolutionary adaptation to an inertia-free process with few degrees of freedom in which only gradual, moderately complex behaviors are possible. We propose a model inspired by particle-mediated field phenomena in classical physics in combination with fundamental concepts in adaptation, which suggests that small but high-dimensional chaotic dynamics near to the adaptive trait optimum could help explain complex properties shared by most ecological datasets, such as aperiodicity and pink, fractal noise spectra. By examining a simple predator-prey model and appealing to real ecological data, we show that this type of complexity could be easily confused for or confounded by stochasticity, especially when spurred on or amplified by stochastic factors that share variational and spectral properties with the underlying dynamics.

A Vision for Co-optimized T&D System Interaction with Renewables and Demand Response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, Lindsay; Zéphyr, Luckny; Cardell, Judith B.

The evolution of the power system to the reliable, efficient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. The use of demand response to counterbalance the intermittency of renewable generation brings the consumer into the spotlight. Though individual consumers are interconnected at the low-voltage distribution system, these resources are typically modeled as variables at the transmission network level. In this paper, a vision for cooptimized interaction of distribution systems, or microgrids, with the high-voltage transmission system is described. In this framework, microgrids encompass consumers, distributed renewables and storage. The energy managementmore » system of the microgrid can also sell (buy) excess (necessary) energy from the transmission system. Preliminary work explores price mechanisms to manage the microgrid and its interactions with the transmission system. Wholesale market operations are addressed through the development of scalable stochastic optimization methods that provide the ability to co-optimize interactions between the transmission and distribution systems. Modeling challenges of the co-optimization are addressed via solution methods for large-scale stochastic optimization, including decomposition and stochastic dual dynamic programming.« less

A Vision for Co-optimized T&D System Interaction with Renewables and Demand Response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, C. Lindsay; Zéphyr, Luckny; Liu, Jialin

The evolution of the power system to the reliable, effi- cient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. The use of demand response to counterbalance the intermittency of re- newable generation brings the consumer into the spotlight. Though individual consumers are interconnected at the low-voltage distri- bution system, these resources are typically modeled as variables at the transmission network level. In this paper, a vision for co- optimized interaction of distribution systems, or microgrids, with the high-voltage transmission system is described. In this frame- work, microgrids encompass consumers, distributed renewablesmore » and storage. The energy management system of the microgrid can also sell (buy) excess (necessary) energy from the transmission system. Preliminary work explores price mechanisms to manage the microgrid and its interactions with the transmission system. Wholesale market operations are addressed through the devel- opment of scalable stochastic optimization methods that provide the ability to co-optimize interactions between the transmission and distribution systems. Modeling challenges of the co-optimization are addressed via solution methods for large-scale stochastic op- timization, including decomposition and stochastic dual dynamic programming.« less

Intimate Partner Violence: A Stochastic Model.

PubMed

Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco

2017-01-01

Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

Stress-Induced Mutagenesis: Implications in Cancer and Drug Resistance.

PubMed

Fitzgerald, Devon M; Hastings, P J; Rosenberg, Susan M

2017-03-01

Genomic instability underlies many cancers and generates genetic variation that drives cancer initiation, progression, and therapy resistance. In contrast with classical assumptions that mutations occur purely stochastically at constant, gradual rates, microbes, plants, flies, and human cancer cells possess mechanisms of mutagenesis that are upregulated by stress responses. These generate transient, genetic-diversity bursts that can propel evolution, specifically when cells are poorly adapted to their environments-that is, when stressed. We review molecular mechanisms of stress-response-dependent (stress-induced) mutagenesis that occur from bacteria to cancer, and are activated by starvation, drugs, hypoxia, and other stressors. We discuss mutagenic DNA break repair in Escherichia coli as a model for mechanisms in cancers. The temporal regulation of mutagenesis by stress responses and spatial restriction in genomes are common themes across the tree of life. Both can accelerate evolution, including the evolution of cancers. We discuss possible anti-evolvability drugs, aimed at targeting mutagenesis and other variation generators, that could be used to delay the evolution of cancer progression and therapy resistance.

Stress-Induced Mutagenesis: Implications in Cancer and Drug Resistance

PubMed Central

Fitzgerald, Devon M.; Hastings, P.J.; Rosenberg, Susan M.

2017-01-01

Genomic instability underlies many cancers and generates genetic variation that drives cancer initiation, progression, and therapy resistance. In contrast with classical assumptions that mutations occur purely stochastically at constant, gradual rates, microbes, plants, flies, and human cancer cells possess mechanisms of mutagenesis that are upregulated by stress responses. These generate transient, genetic-diversity bursts that can propel evolution, specifically when cells are poorly adapted to their environments—that is, when stressed. We review molecular mechanisms of stress-response-dependent (stress-induced) mutagenesis that occur from bacteria to cancer, and are activated by starvation, drugs, hypoxia, and other stressors. We discuss mutagenic DNA break repair in Escherichia coli as a model for mechanisms in cancers. The temporal regulation of mutagenesis by stress responses and spatial restriction in genomes are common themes across the tree of life. Both can accelerate evolution, including the evolution of cancers. We discuss possible anti-evolvability drugs, aimed at targeting mutagenesis and other variation generators, that could be used to delay the evolution of cancer progression and therapy resistance. PMID:29399660

Emergent Irreversibility and Entanglement Spectrum Statistics

NASA Astrophysics Data System (ADS)

Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo R.

2014-06-01

We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wave-function level and offers an alternative route to study quantum chaos and quantum integrability.

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

The contribution of statistical physics to evolutionary biology.

PubMed

de Vladar, Harold P; Barton, Nicholas H

2011-08-01

Evolutionary biology shares many concepts with statistical physics: both deal with populations, whether of molecules or organisms, and both seek to simplify evolution in very many dimensions. Often, methodologies have undergone parallel and independent development, as with stochastic methods in population genetics. Here, we discuss aspects of population genetics that have embraced methods from physics: non-equilibrium statistical mechanics, travelling waves and Monte-Carlo methods, among others, have been used to study polygenic evolution, rates of adaptation and range expansions. These applications indicate that evolutionary biology can further benefit from interactions with other areas of statistical physics; for example, by following the distribution of paths taken by a population through time. Copyright © 2011 Elsevier Ltd. All rights reserved.

Effect of Inherited Genetic Information on Stochastic Predator-Prey Model

NASA Astrophysics Data System (ADS)

Duda, Artur; Dyś, Paweł; Nowicka, Alekandra; Dudek, Mirosław R.

We discuss the Lotka-Volterra dynamics of two populations, preys and predators, in the case when the predators posses a genetic information. The genetic information is inherited according to the rules of the Penna model of genetic evolution. Each individual of the predator population is uniquely determined by sex, genotype and phenotype. In our case, the genes are represented by 8-bit integers and the phenotypes are defined with the help of the 8-state Potts model Hamiltonian. We showed that during time evolution, the population of the predators can experience a series of dynamical phase transitions which are connected with the different types of the dominant phenotypes present in the population.

CellTrans: An R Package to Quantify Stochastic Cell State Transitions.

PubMed

Buder, Thomas; Deutsch, Andreas; Seifert, Michael; Voss-Böhme, Anja

2017-01-01

Many normal and cancerous cell lines exhibit a stable composition of cells in distinct states which can, e.g., be defined on the basis of cell surface markers. There is evidence that such an equilibrium is associated with stochastic transitions between distinct states. Quantifying these transitions has the potential to better understand cell lineage compositions. We introduce CellTrans, an R package to quantify stochastic cell state transitions from cell state proportion data from fluorescence-activated cell sorting and flow cytometry experiments. The R package is based on a mathematical model in which cell state alterations occur due to stochastic transitions between distinct cell states whose rates only depend on the current state of a cell. CellTrans is an automated tool for estimating the underlying transition probabilities from appropriately prepared data. We point out potential analytical challenges in the quantification of these cell transitions and explain how CellTrans handles them. The applicability of CellTrans is demonstrated on publicly available data on the evolution of cell state compositions in cancer cell lines. We show that CellTrans can be used to (1) infer the transition probabilities between different cell states, (2) predict cell line compositions at a certain time, (3) predict equilibrium cell state compositions, and (4) estimate the time needed to reach this equilibrium. We provide an implementation of CellTrans in R, freely available via GitHub (https://github.com/tbuder/CellTrans).

Chaos and the (un)predictability of evolution in a changing environment

PubMed Central

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-01-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. PMID:29235104

Was the Watchmaker Blind? Or Was She One-Eyed?

PubMed Central

Noble, Raymond; Noble, Denis

2017-01-01

The question whether evolution is blind is usually presented as a choice between no goals at all (‘the blind watchmaker’) and long-term goals which would be external to the organism, for example in the form of special creation or intelligent design. The arguments either way do not address the question whether there are short-term goals within rather than external to organisms. Organisms and their interacting populations have evolved mechanisms by which they can harness blind stochasticity and so generate rapid functional responses to environmental challenges. They can achieve this by re-organising their genomes and/or their regulatory networks. Epigenetic as well as DNA changes are involved. Evolution may have no foresight, but it is at least partially directed by organisms themselves and by the populations of which they form part. Similar arguments support partial direction in the evolution of behavior. PMID:29261138

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Constructive neutral evolution: exploring evolutionary theory's curious disconnect.

PubMed

Stoltzfus, Arlin

2012-10-13

Constructive neutral evolution (CNE) suggests that neutral evolution may follow a stepwise path to extravagance. Whether or not CNE is common, the mere possibility raises provocative questions about causation: in classical neo-Darwinian thinking, selection is the sole source of creativity and direction, the only force that can cause trends or build complex features. However, much of contemporary evolutionary genetics departs from the conception of evolution underlying neo-Darwinism, resulting in a widening gap between what formal models allow, and what the prevailing view of the causes of evolution suggests. In particular, a mutationist conception of evolution as a 2-step origin-fixation process has been a source of theoretical innovation for 40 years, appearing not only in the Neutral Theory, but also in recent breakthroughs in modeling adaptation (the "mutational landscape" model), and in practical software for sequence analysis. In this conception, mutation is not a source of raw materials, but an agent that introduces novelty, while selection is not an agent that shapes features, but a stochastic sieve. This view, which now lays claim to important theoretical, experimental, and practical results, demands our attention. CNE provides a way to explore its most significant implications about the role of variation in evolution. Alex Kondrashov, Eugene Koonin and Johann Peter Gogarten reviewed this article.

Constructive neutral evolution: exploring evolutionary theory’s curious disconnect

PubMed Central

2012-01-01

Abstract Constructive neutral evolution (CNE) suggests that neutral evolution may follow a stepwise path to extravagance. Whether or not CNE is common, the mere possibility raises provocative questions about causation: in classical neo-Darwinian thinking, selection is the sole source of creativity and direction, the only force that can cause trends or build complex features. However, much of contemporary evolutionary genetics departs from the conception of evolution underlying neo-Darwinism, resulting in a widening gap between what formal models allow, and what the prevailing view of the causes of evolution suggests. In particular, a mutationist conception of evolution as a 2-step origin-fixation process has been a source of theoretical innovation for 40 years, appearing not only in the Neutral Theory, but also in recent breakthroughs in modeling adaptation (the “mutational landscape” model), and in practical software for sequence analysis. In this conception, mutation is not a source of raw materials, but an agent that introduces novelty, while selection is not an agent that shapes features, but a stochastic sieve. This view, which now lays claim to important theoretical, experimental, and practical results, demands our attention. CNE provides a way to explore its most significant implications about the role of variation in evolution. Reviewers Alex Kondrashov, Eugene Koonin and Johann Peter Gogarten reviewed this article. PMID:23062217

Stochastic Forecasting of Algae Blooms in Lakes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Peng; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

We consider the development of harmful algae blooms (HABs) in a lake with uncertain nutrients inflow. Two general frameworks, Fokker-Planck equation and the PDF methods, are developed to quantify the resultant concentration uncertainty of various algae groups, via deriving a deterministic equation of their joint probability density function (PDF). A computational example is examined to study the evolution of cyanobacteria (the blue-green algae) and the impacts of initial concentration and inflow-outflow ratio.

The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks.

PubMed

Sainudiin, Raazesh; Welch, David

2016-12-07

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network - three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of "meme" evolution in online social media networks through transmission events that can be distilled from observable actions such as "likes", "mentions", "retweets" and "+1s" along with any concomitant comments. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

Baldovin-Stella stochastic volatility process and Wiener process mixtures

NASA Astrophysics Data System (ADS)

Peirano, P. P.; Challet, D.

2012-08-01

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distributions and show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.

Steady-state helices of the actin homolog MreB inside bacteria: dynamics without motors.

PubMed

Allard, Jun F; Rutenberg, Andrew D

2007-09-01

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasistatic evolution of the helical pitch with cell growth, as well as time scales of helix turnover and de novo establishment. We find that while the body of a polarized MreB helix treadmills toward its slow-growing end, the fast-growing tips of laterally associated protofilaments move toward the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.

Steady-state helices of the actin homolog MreB inside bacteria: Dynamics without motors

NASA Astrophysics Data System (ADS)

Allard, Jun F.; Rutenberg, Andrew D.

2007-09-01

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasistatic evolution of the helical pitch with cell growth, as well as time scales of helix turnover and de novo establishment. We find that while the body of a polarized MreB helix treadmills toward its slow-growing end, the fast-growing tips of laterally associated protofilaments move toward the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.

Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory

NASA Astrophysics Data System (ADS)

Helbing, Dirk

1993-03-01

In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distinguished: Avoidance processes, compromising processes, and imitative processes. Computational results are presented for a special case of imitative processes: the competition of two equivalent strategies. They show a phase transition that describes the self-organization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmann-like equations. Special cases of Boltzmann-like equations do not obey the H-theorem and have oscillatory or even chaotic solutions. A suitable Taylor approximation leads to the so-called game dynamical equations (also known as selection-mutation equations in the theory of evolution).

Stochastic analysis of a pulse-type prey-predator model

NASA Astrophysics Data System (ADS)

Wu, Y.; Zhu, W. Q.

2008-04-01

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity

NASA Astrophysics Data System (ADS)

Ispánovity, Péter Dusán; Tüzes, Dániel; Szabó, Péter; Zaiser, Michael; Groma, István

2017-02-01

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where details of the microstructure evolution are statistically represented in terms of a fluctuating local yield threshold. In the present paper we propose a method for determining the corresponding yield stress distribution for the case of crystal plasticity from lower scale discrete dislocation dynamics simulations which we combine with weakest link arguments. The success of scale linking is demonstrated by comparing stress-strain curves obtained from the resulting mesoscopic and the underlying discrete dislocation models in the microplastic regime. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable to different microstructures and also to amorphous materials.

Stochastic analysis of a pulse-type prey-predator model.

PubMed

Wu, Y; Zhu, W Q

2008-04-01

A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.

Stochastic algorithm for simulating gas transport coefficients

NASA Astrophysics Data System (ADS)

Rudyak, V. Ya.; Lezhnev, E. V.

2018-02-01

The aim of this paper is to create a molecular algorithm for modeling the transport processes in gases that will be more efficient than molecular dynamics method. To this end, the dynamics of molecules are modeled stochastically. In a rarefied gas, it is sufficient to consider the evolution of molecules only in the velocity space, whereas for a dense gas it is necessary to model the dynamics of molecules also in the physical space. Adequate integral characteristics of the studied system are obtained by averaging over a sufficiently large number of independent phase trajectories. The efficiency of the proposed algorithm was demonstrated by modeling the coefficients of self-diffusion and the viscosity of several gases. It was shown that the accuracy comparable to the experimental one can be obtained on a relatively small number of molecules. The modeling accuracy increases with the growth of used number of molecules and phase trajectories.

Analytical approach to Eigen-emittance evolution in storage rings

NASA Astrophysics Data System (ADS)

Nash, Boaz

This dissertation develops the subject of beam evolution in storage rings with nearly uncoupled symplectic linear dynamics. Linear coupling and dissipative/diffusive processes are treated perturbatively. The beam distribution is assumed Gaussian and a function of the invariants. The development requires two pieces: the global invariants and the local stochastic processes which change the emittances, or averages of the invariants. A map based perturbation theory is described, providing explicit expressions for the invariants near each linear resonance, where small perturbations can have a large effect. Emittance evolution is determined by the damping and diffusion coefficients. The discussion is divided into the cases of uniform and non-uniform stochasticity, synchrotron radiation an example of the former and intrabeam scattering the latter. For the uniform case, the beam dynamics is captured by a global diffusion coefficent and damping decrement for each eigen-invariant. Explicit expressions for these quantities near coupling resonances are given. In many cases, they are simply related to the uncoupled values. Near a sum resonance, it is found that one of the damping decrements becomes negative, indicating an anti-damping instability. The formalism is applied to a number of examples, including synchrobetatron coupling caused by a crab cavity, a case of current interest where there is concern about operation near half integer betatron tune. In the non-uniform case, the moment evolution is computed directly, which is illustrated through the example of intrabeam scattering. Our approach to intrabeam scattering damping and diffusion has the advantage of not requiring a loosely-defined Coulomb Logarithm. It is found that in some situations there is a small difference between our results and the standard approaches such as Bjorken-Mtingwa, which is illustrated by comparison of the two approaches and with a measurement of Au evolution in RHIC. Finally, in combining IBS with the global invariants some general statements about IBS equilibrium can be made. Specifically, it is emphasized that no such equilibrium is possible in a non-smooth lattice, even below transition. Near enough to a synchrobetatron coupling resonance, it is found that even for a smooth ring, no IBS equilibrium occurs.

Hybrid deterministic/stochastic simulation of complex biochemical systems.

PubMed

Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina

2017-11-21

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.

Virulence evolution at the front line of spreading epidemics.

PubMed

Griette, Quentin; Raoul, Gaël; Gandon, Sylvain

2015-11-01

Understanding and predicting the spatial spread of emerging pathogens is a major challenge for the public health management of infectious diseases. Theoretical epidemiology shows that the speed of an epidemic is governed by the life-history characteristics of the pathogen and its ability to disperse. Rapid evolution of these traits during the invasion may thus affect the speed of epidemics. Here we study the influence of virulence evolution on the spatial spread of an epidemic. At the edge of the invasion front, we show that more virulent and transmissible genotypes are expected to win the competition with other pathogens. Behind the front line, however, more prudent exploitation strategies outcompete virulent pathogens. Crucially, even when the presence of the virulent mutant is limited to the edge of the front, the invasion speed can be dramatically altered by pathogen evolution. We support our analysis with individual-based simulations and we discuss the additional effects of demographic stochasticity taking place at the front line on virulence evolution. We confirm that an increase of virulence can occur at the front, but only if the carrying capacity of the invading pathogen is large enough. These results are discussed in the light of recent empirical studies examining virulence evolution at the edge of spreading epidemics. © 2015 The Author(s). Evolution © 2015 The Society for the Study of Evolution.

Gene family evolution: an in-depth theoretical and simulation analysis of non-linear birth-death-innovation models.

PubMed

Karev, Georgy P; Wolf, Yuri I; Berezovskaya, Faina S; Koonin, Eugene V

2004-09-09

The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution. In this work, we extend our previous analysis of stochastic BDIMs. In addition to the previously examined rational BDIMs, we introduce potentially more realistic logistic BDIMs, in which birth/death rates are limited for the largest families, and show that their properties are similar to those of models that include no such limitation. We show that the mean time required for the formation of the largest gene families detected in eukaryotic genomes is limited by the mean number of duplications per gene and does not increase indefinitely with the model degree. Instead, this time reaches a minimum value, which corresponds to a non-linear rational BDIM with the degree of approximately 2.7. Even for this BDIM, the mean time of the largest family formation is orders of magnitude greater than any realistic estimates based on the timescale of life's evolution. We employed the embedding chains technique to estimate the expected number of elementary evolutionary events (gene duplications and deletions) preceding the formation of gene families of the observed size and found that the mean number of events exceeds the family size by orders of magnitude, suggesting a highly dynamic process of genome evolution. The variance of the time required for the formation of the largest families was found to be extremely large, with the coefficient of variation > 1. This indicates that some gene families might grow much faster than the mean rate such that the minimal time required for family formation is more relevant for a realistic representation of genome evolution than the mean time. We determined this minimal time using Monte Carlo simulations of family growth from an ensemble of simultaneously evolving singletons. In these simulations, the time elapsed before the formation of the largest family was much shorter than the estimated mean time and was compatible with the timescale of evolution of eukaryotes. The analysis of stochastic BDIMs presented here shows that non-linear versions of such models can well approximate not only the size distribution of gene families but also the dynamics of their formation during genome evolution. The fact that only higher degree BDIMs are compatible with the observed characteristics of genome evolution suggests that the growth of gene families is self-accelerating, which might reflect differential selective pressure acting on different genes.

Post-Newtonian evolution of massive black hole triplets in galactic nuclei - III. A robust lower limit to the nHz stochastic background of gravitational waves

NASA Astrophysics Data System (ADS)

Bonetti, Matteo; Sesana, Alberto; Barausse, Enrico; Haardt, Francesco

2018-06-01

Inspiraling massive black hole binaries (MBHBs) forming in the aftermath of galaxy mergers are expected to be the loudest gravitational-wave (GW) sources relevant for pulsar-timing arrays (PTAs) at nHz frequencies. The incoherent overlap of signals from a cosmic population of MBHBs gives rise to a stochastic GW background (GWB) with characteristic strain around hc ˜ 10-15 at a reference frequency of 1 yr-1, although uncertainties around this value are large. Current PTAs are piercing into the GW amplitude range predicted by MBHB-population models, but no detection has been reported so far. To assess the future success prospects of PTA experiments, it is therefore important to estimate the minimum GWB level consistent with our current understanding of the formation and evolution of galaxies and massive black holes (MBHs). To this purpose, we couple a semi-analytic model of galaxy evolution and an extensive study of the statistical outcome of triple MBH interactions. We show that even in the most pessimistic scenario where all MBHBs stall before entering the GW-dominated regime, triple interactions resulting from subsequent galaxy mergers inevitably drive a considerable fraction of the MBHB population to coalescence. At frequencies relevant for PTA, the resulting GWB is only a factor of 2-3 suppressed compared to a fiducial model where binaries are allowed to merge over Gyr time-scales . Coupled with current estimates of the expected GWB amplitude range, our findings suggest that the minimum GWB from cosmic MBHBs is unlikely to be lower than hc ˜ 10-16 (at f = 1 yr-1), well within the expected sensitivity of projected PTAs based on future observations with FAST, MeerKAT, and SKA.

Using Nonlinear Stochastic Evolutionary Game Strategy to Model an Evolutionary Biological Network of Organ Carcinogenesis Under a Natural Selection Scheme

PubMed Central

Chen, Bor-Sen; Tsai, Kun-Wei; Li, Cheng-Wei

2015-01-01

Molecular biologists have long recognized carcinogenesis as an evolutionary process that involves natural selection. Cancer is driven by the somatic evolution of cell lineages. In this study, the evolution of somatic cancer cell lineages during carcinogenesis was modeled as an equilibrium point (ie, phenotype of attractor) shifting, the process of a nonlinear stochastic evolutionary biological network. This process is subject to intrinsic random fluctuations because of somatic genetic and epigenetic variations, as well as extrinsic disturbances because of carcinogens and stressors. In order to maintain the normal function (ie, phenotype) of an evolutionary biological network subjected to random intrinsic fluctuations and extrinsic disturbances, a network robustness scheme that incorporates natural selection needs to be developed. This can be accomplished by selecting certain genetic and epigenetic variations to modify the network structure to attenuate intrinsic fluctuations efficiently and to resist extrinsic disturbances in order to maintain the phenotype of the evolutionary biological network at an equilibrium point (attractor). However, during carcinogenesis, the remaining (or neutral) genetic and epigenetic variations accumulate, and the extrinsic disturbances become too large to maintain the normal phenotype at the desired equilibrium point for the nonlinear evolutionary biological network. Thus, the network is shifted to a cancer phenotype at a new equilibrium point that begins a new evolutionary process. In this study, the natural selection scheme of an evolutionary biological network of carcinogenesis was derived from a robust negative feedback scheme based on the nonlinear stochastic Nash game strategy. The evolvability and phenotypic robustness criteria of the evolutionary cancer network were also estimated by solving a Hamilton–Jacobi inequality – constrained optimization problem. The simulation revealed that the phenotypic shift of the lung cancer-associated cell network takes 54.5 years from a normal state to stage I cancer, 1.5 years from stage I to stage II cancer, and 2.5 years from stage II to stage III cancer, with a reasonable match for the statistical result of the average age of lung cancer. These results suggest that a robust negative feedback scheme, based on a stochastic evolutionary game strategy, plays a critical role in an evolutionary biological network of carcinogenesis under a natural selection scheme. PMID:26244004

Gravitational Instabilities in a Young Protoplanetary Disk with Embedded Objects

NASA Astrophysics Data System (ADS)

Desai, Karna M.; Steiman-Cameron, Thomas Y.; Durisen, Richard H.

2018-01-01

Gravitational Instabilities (GIs), a mechanism for angular momentum transport, are more prominent during the early phases of protoplanetary disk evolution when the disk is relatively massive. In my dissertation work, I performed radiative 3D hydrodynamics simulations (by employing the code, CHYMERA) and extensively studied GIs by inserting different objects in the ‘control disk’ (a 0.14 M⊙ protoplanetary disk around a 1 M⊙ star).Studying planetary migration helps us better constrain planet formation models. To study the migration of Jovian planets, in 9 separate simulations, each of the 0.3 MJ, 1 MJ, and 3 MJ planets was inserted near the Inner and Outer Lindblad Resonances and the Corotation Radius (CR) of the dominant GI-induced two-armed spiral density wave in the disk. I found the migration timescales to be longer in a GI-active disk when compared to laminar disks. The 3 MJ planet controls its own orbital evolution, while the migration of a 0.3 MJ planet is stochastic in nature. I defined a ‘critical mass’ as the mass of an arm of the dominant two-armed spiral density wave within the planet’s Hill diameter. Planets above this mass control their own destiny, and planets below this mass are scattered by the disk. This critical mass could provide a recipe for predicting the migration behavior of planets in GI-active disks.To understand the stochastic migration of low-mass planets, I performed a simulation of 240 zero-mass planet-tracers (hereafter, planets) by inserting these at a range of locations in the control disk (an equivalent of 240 simulations of Saturn-mass or lower-mass objects). I calculated a Diffusion Coefficient (3.6 AU2/ 1000 yr) to characterize the stochastic migration of planets. I analyzed the increase in the eccentricity dispersion and compared it with the observed exoplanet eccentricities. The diffusion of planets can be a slow process, resulting in the survival of small planetary cores. Stochastic migration of planets is dynamically similar to the radial migration of stars in the Milky Way (MW). In MW, the CR of transient spiral arms can cause radial migration of stars.Also, to determine the effects of a companion, I studied GIs in a circumbinary disk with a 0.2 M⊙ brown dwarf companion.

Stochastic annealing simulations of defect interactions among subcascades

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinisch, H.L.; Singh, B.N.

1997-04-01

The effects of the subcascade structure of high energy cascades on the temperature dependencies of annihilation, clustering and free defect production are investigated. The subcascade structure is simulated by closely spaced groups of lower energy MD cascades. The simulation results illustrate the strong influence of the defect configuration existing in the primary damage state on subsequent intracascade evolution. Other significant factors affecting the evolution of the defect distribution are the large differences in mobility and stability of vacancy and interstitial defects and the rapid one-dimensional diffusion of small, glissile interstitial loops produced directly in cascades. Annealing simulations are also performedmore » on high-energy, subcascade-producing cascades generated with the binary collision approximation and calibrated to MD results.« less

Black-Scholes model under subordination

NASA Astrophysics Data System (ADS)

Stanislavsky, A. A.

2003-02-01

In this paper, we consider a new mathematical extension of the Black-Scholes (BS) model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly α-stable process. The subordinated process represents the Brownian motion indexed by an independent, continuous and increasing process. This allows us to introduce the long-term memory effects in the classical BS model.

In situ stress conditions at IODP Site C0002 reflecting the tectonic evolution of the sedimentary system near the seaward edge of the Kumano basin, offshore from SW Japan

NASA Astrophysics Data System (ADS)

Song, Insun; Chang, Chandong

2017-05-01

This paper presents a complete set of in situ stress calculations for depths of 200-1400 meters below seafloor at Integrated Ocean Drilling Program (IODP) Site C0002, near the seaward margin of the Kumano fore-arc basin, offshore from southwest Japan. The vertical stress component was obtained by integrating bulk density calculations from moisture and density logging data, and the two horizontal components were stochastically optimized by minimizing misfits between a probabilistic model and measured breakout widths for every 30 m vertical segment of the wellbore. Our stochastic optimization process reveals that the in situ stress regime is decoupled across an unconformity between an accretionary complex and the overlying Kumano fore-arc basin. The stress condition above the unconformity is close to the critical condition for normal faulting, while below the unconformity the geologic system is stable in a normal to strike-slip fault stress regime. The critical state of stress demonstrates that the tectonic evolution of the sedimentary system has been achieved mainly by the regionally continuous action of a major out-of-sequence thrust fault during sedimentation in the fore-arc basin. The stable stress condition in the accretionary prism is interpreted to have resulted from mechanical decoupling by the accommodation of large displacement along the megasplay fault.

A stochastic, evolutionary model for range shifts and richness on tropical elevational gradients under Quaternary glacial cycles

PubMed Central

Colwell, Robert K.; Rangel, Thiago F.

2010-01-01

Quaternary glacial–interglacial cycles repeatedly forced thermal zones up and down the slopes of mountains, at all latitudes. Although no one doubts that these temperature cycles have left their signature on contemporary patterns of geography and phylogeny, the relative roles of ecology and evolution are not well understood, especially for the tropics. To explore key mechanisms and their interactions in the context of chance events, we constructed a geographical range-based, stochastic simulation model that incorporates speciation, anagenetic evolution, niche conservatism, range shifts and extinctions under late Quaternary temperature cycles along tropical elevational gradients. In the model, elevational patterns of species richness arise from the differential survival of founder lineages, consolidated by speciation and the inheritance of thermal niche characteristics. The model yields a surprisingly rich variety of realistic patterns of phylogeny and biogeography, including close matches to a variety of contemporary elevational richness profiles from an elevational transect in Costa Rica. Mountaintop extinctions during interglacials and lowland extinctions at glacial maxima favour mid-elevation lineages, especially under the constraints of niche conservatism. Asymmetry in temperature (greater duration of glacial than of interglacial episodes) and in lateral area (greater land area at low than at high elevations) have opposing effects on lowland extinctions and the elevational pattern of species richness in the model—and perhaps in nature, as well. PMID:20980317

Infinite Systems of Interacting Chains with Memory of Variable Length—A Stochastic Model for Biological Neural Nets

NASA Astrophysics Data System (ADS)

Galves, A.; Löcherbach, E.

2013-06-01

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as follows. For each component, the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component. This class of systems extends in a non trivial way both the interacting particle systems, which are Markovian (Spitzer in Adv. Math. 5:246-290, 1970) and the stochastic chains with memory of variable length which have finite state space (Rissanen in IEEE Trans. Inf. Theory 29(5):656-664, 1983). These features make it suitable to describe the time evolution of biological neural systems. We construct a stationary version of the process by using a probabilistic tool which is a Kalikow-type decomposition either in random environment or in space-time. This construction implies uniqueness of the stationary process. Finally we consider the case where the interactions between components are given by a critical directed Erdös-Rényi-type random graph with a large but finite number of components. In this framework we obtain an explicit upper-bound for the correlation between successive inter-spike intervals which is compatible with previous empirical findings.

A continuous stochastic model for non-equilibrium dense gases

NASA Astrophysics Data System (ADS)

Sadr, M.; Gorji, M. H.

2017-12-01

While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are compared with respect to benchmark simulations, where good agreement is found for the flow field along with the transport properties.

Biology-Culture Co-evolution in Finite Populations.

PubMed

de Boer, Bart; Thompson, Bill

2018-01-19

Language is the result of two concurrent evolutionary processes: biological and cultural inheritance. An influential evolutionary hypothesis known as the moving target problem implies inherent limitations on the interactions between our two inheritance streams that result from a difference in pace: the speed of cultural evolution is thought to rule out cognitive adaptation to culturally evolving aspects of language. We examine this hypothesis formally by casting it as as a problem of adaptation in time-varying environments. We present a mathematical model of biology-culture co-evolution in finite populations: a generalisation of the Moran process, treating co-evolution as coupled non-independent Markov processes, providing a general formulation of the moving target hypothesis in precise probabilistic terms. Rapidly varying culture decreases the probability of biological adaptation. However, we show that this effect declines with population size and with stronger links between biology and culture: in realistically sized finite populations, stochastic effects can carry cognitive specialisations to fixation in the face of variable culture, especially if the effects of those specialisations are amplified through cultural evolution. These results support the view that language arises from interactions between our two major inheritance streams, rather than from one primary evolutionary process that dominates another.

Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance

NASA Astrophysics Data System (ADS)

De Jong, Maxwell G.; Wood, Kevin B.

2018-06-01

Spatial heterogeneity plays an important role in the evolution of drug resistance. While recent studies have indicated that spatial gradients of selection pressure can accelerate resistance evolution, much less is known about evolution in more complex spatial profiles. Here we use a stochastic toy model of drug resistance to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. Interestingly, there exists an intermediate regime—characterized by comparable rates of migration and mutation—in which the rate of fixation can be either accelerated or decelerated depending on the spatial profile, even when spatially averaged selection pressure remains constant. Finally, we demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Our results may lay the groundwork for optimized, spatially resolved drug dosing strategies for mitigating the effects of drug resistance.

Stochastic and epigenetic changes of gene expression in Arabidopsis polyploids.

PubMed

Wang, Jianlin; Tian, Lu; Madlung, Andreas; Lee, Hyeon-Se; Chen, Meng; Lee, Jinsuk J; Watson, Brian; Kagochi, Trevor; Comai, Luca; Chen, Z Jeffrey

2004-08-01

Polyploidization is an abrupt speciation mechanism for eukaryotes and is especially common in plants. However, little is known about patterns and mechanisms of gene regulation during early stages of polyploid formation. Here we analyzed differential expression patterns of the progenitors' genes among successive selfing generations and independent lineages. The synthetic Arabidopsis allotetraploid lines were produced by a genetic cross between A. thaliana and A. arenosa autotetraploids. We found that some progenitors' genes are differentially expressed in early generations, whereas other genes are silenced in late generations or among different siblings within a selfing generation, suggesting that the silencing of progenitors' genes is rapidly and/or stochastically established. Moreover, a subset of genes is affected in autotetraploid and multiple independent allotetraploid lines and in A. suecica, a natural allotetraploid derived from A. thaliana and A. arenosa, indicating locus-specific susceptibility to ploidy-dependent gene regulation. The role of DNA methylation in silencing progenitors' genes is tested in DNA-hypomethylation transgenic lines of A. suecica using RNA interference (RNAi). Two silenced genes are reactivated in both ddm1- and met1-RNAi lines, consistent with the demethylation of centromeric repeats and gene-specific regions in the genome. A rapid and stochastic process of differential gene expression is reinforced by epigenetic regulation during polyploid formation and evolution. Copyright 2004 Genetics Society of America

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

Stochastic population dynamics under resource constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gavane, Ajinkya S., E-mail: ajinkyagavane@gmail.com; Nigam, Rahul, E-mail: rahul.nigam@hyderabad.bits-pilani.ac.in

This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations formore » such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.« less

Pattern activation/recognition theory of mind

PubMed Central

du Castel, Bertrand

2015-01-01

In his 2012 book How to Create a Mind, Ray Kurzweil defines a “Pattern Recognition Theory of Mind” that states that the brain uses millions of pattern recognizers, plus modules to check, organize, and augment them. In this article, I further the theory to go beyond pattern recognition and include also pattern activation, thus encompassing both sensory and motor functions. In addition, I treat checking, organizing, and augmentation as patterns of patterns instead of separate modules, therefore handling them the same as patterns in general. Henceforth I put forward a unified theory I call “Pattern Activation/Recognition Theory of Mind.” While the original theory was based on hierarchical hidden Markov models, this evolution is based on their precursor: stochastic grammars. I demonstrate that a class of self-describing stochastic grammars allows for unifying pattern activation, recognition, organization, consistency checking, metaphor, and learning, into a single theory that expresses patterns throughout. I have implemented the model as a probabilistic programming language specialized in activation/recognition grammatical and neural operations. I use this prototype to compute and present diagrams for each stochastic grammar and corresponding neural circuit. I then discuss the theory as it relates to artificial network developments, common coding, neural reuse, and unity of mind, concluding by proposing potential paths to validation. PMID:26236228

Optimal regeneration planning for old-growth forest: addressing scientific uncertainty in endangered species recovery through adaptive management

USGS Publications Warehouse

Moore, C.T.; Conroy, M.J.

2006-01-01

Stochastic and structural uncertainties about forest dynamics present challenges in the management of ephemeral habitat conditions for endangered forest species. Maintaining critical foraging and breeding habitat for the endangered red-cockaded woodpecker (Picoides borealis) requires an uninterrupted supply of old-growth forest. We constructed and optimized a dynamic forest growth model for the Piedmont National Wildlife Refuge (Georgia, USA) with the objective of perpetuating a maximum stream of old-growth forest habitat. Our model accommodates stochastic disturbances and hardwood succession rates, and uncertainty about model structure. We produced a regeneration policy that was indexed by current forest state and by current weight of evidence among alternative model forms. We used adaptive stochastic dynamic programming, which anticipates that model probabilities, as well as forest states, may change through time, with consequent evolution of the optimal decision for any given forest state. In light of considerable uncertainty about forest dynamics, we analyzed a set of competing models incorporating extreme, but plausible, parameter values. Under any of these models, forest silviculture practices currently recommended for the creation of woodpecker habitat are suboptimal. We endorse fully adaptive approaches to the management of endangered species habitats in which predictive modeling, monitoring, and assessment are tightly linked.

Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

NASA Astrophysics Data System (ADS)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

Method of conditional moments (MCM) for the Chemical Master Equation: a unified framework for the method of moments and hybrid stochastic-deterministic models.

PubMed

Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J

2014-09-01

The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.

Pattern activation/recognition theory of mind.

PubMed

du Castel, Bertrand

2015-01-01

In his 2012 book How to Create a Mind, Ray Kurzweil defines a "Pattern Recognition Theory of Mind" that states that the brain uses millions of pattern recognizers, plus modules to check, organize, and augment them. In this article, I further the theory to go beyond pattern recognition and include also pattern activation, thus encompassing both sensory and motor functions. In addition, I treat checking, organizing, and augmentation as patterns of patterns instead of separate modules, therefore handling them the same as patterns in general. Henceforth I put forward a unified theory I call "Pattern Activation/Recognition Theory of Mind." While the original theory was based on hierarchical hidden Markov models, this evolution is based on their precursor: stochastic grammars. I demonstrate that a class of self-describing stochastic grammars allows for unifying pattern activation, recognition, organization, consistency checking, metaphor, and learning, into a single theory that expresses patterns throughout. I have implemented the model as a probabilistic programming language specialized in activation/recognition grammatical and neural operations. I use this prototype to compute and present diagrams for each stochastic grammar and corresponding neural circuit. I then discuss the theory as it relates to artificial network developments, common coding, neural reuse, and unity of mind, concluding by proposing potential paths to validation.

Drift-driven evolution of electric signals in a Neotropical knifefish.

PubMed

Picq, Sophie; Alda, Fernando; Bermingham, Eldredge; Krahe, Rüdiger

2016-09-01

Communication signals are highly diverse traits. This diversity is usually assumed to be shaped by selective forces, whereas the null hypothesis of divergence through drift is often not considered. In Panama, the weakly electric fish Brachyhypopomus occidentalis is widely distributed in multiple independent drainage systems, which provide a natural evolutionary laboratory for the study of genetic and signal divergence in separate populations. We quantified geographic variation in the electric signals of 109 fish from five populations, and compared it to the neutral genetic variation estimated from cytochrome oxidase I (COI) sequences of the same individuals, to test whether drift may be driving divergence of their signals. Signal distances were highly correlated with genetic distances, even after controlling for geographic distances, suggesting that drift alone is sufficient to explain geographic variation in electric signals. Significant differences at smaller geographic scales (within drainages) showed, however, that electric signals may evolve at a faster rate than expected under drift, raising the possibility that additional adaptive forces may be contributing to their evolution. Overall, our data point to stochastic forces as main drivers of signal evolution in this species and extend the role of drift in the evolution of communication systems to fish and electrocommunication. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.

Ecological constraint and the evolution of sexual dichromatism in darters.

PubMed

Bossu, Christen M; Near, Thomas J

2015-05-01

It is not known how environmental pressures and sexual selection interact to influence the evolution of extravagant male traits. Sexual and natural selection are often viewed as antagonistic forces shaping the evolution of visual signals, where conspicuousness is favored by sexual selection and crypsis is favored by natural selection. Although typically investigated independently, the interaction between natural and sexual selection remains poorly understood. Here, we investigate whether sexual dichromatism evolves stochastically, independent from, or in concert with habitat use in darters, a species-rich lineage of North American freshwater fish. We find the evolution of sexual dichromatism is coupled to habitat use in darter species. Comparative analyses reveal that mid-water darter lineages exhibit a narrow distribution of dichromatism trait space surrounding a low optimum, suggesting a constraint imposed on the evolution of dichromatism, potentially through predator-mediated selection. Alternatively, the transition to benthic habitats coincides with greater variability in the levels of dichromatism that surround a higher optimum, likely due to relaxation of the predator-mediated selection and heterogeneous microhabitat dependent selection regimes. These results suggest a complex interaction of sexual selection with potentially two mechanisms of natural selection, predation and sensory drive, that influence the evolution of diverse male nuptial coloration in darters. © 2015 The Author(s).

Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

Asymptotic stability of spectral-based PDF modeling for homogeneous turbulent flows

NASA Astrophysics Data System (ADS)

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2015-11-01

Engineering models of turbulence, based on one-point statistics, neglect spectral information inherent in a turbulence field. It is well known, however, that the evolution of turbulence is dictated by a complex interplay between the spectral modes of velocity. For example, for homogeneous turbulence, the pressure-rate-of-strain depends on the integrated energy spectrum weighted by components of the wave vectors. The Interacting Particle Representation Model (IPRM) (Kassinos & Reynolds, 1996) and the Velocity/Wave-Vector PDF model (Van Slooten & Pope, 1997) emulate spectral information in an attempt to improve the modeling of turbulence. We investigate the evolution and asymptotic stability of the IPRM using three different approaches. The first approach considers the Lagrangian evolution of individual realizations (idealized as particles) of the stochastic process defined by the IPRM. The second solves Lagrangian evolution equations for clusters of realizations conditional on a given wave vector. The third evolves the solution of the Eulerian conditional PDF corresponding to the aforementioned clusters. This last method avoids issues related to discrete particle noise and slow convergence associated with Lagrangian particle-based simulations.

Viruses Roll the Dice: The Stochastic Behavior of Viral Genome Molecules Accelerates Viral Adaptation at the Cell and Tissue Levels

PubMed Central

Miyashita, Shuhei; Ishibashi, Kazuhiro; Kishino, Hirohisa; Ishikawa, Masayuki

2015-01-01

Recent studies on evolutionarily distant viral groups have shown that the number of viral genomes that establish cell infection after cell-to-cell transmission is unexpectedly small (1–20 genomes). This aspect of viral infection appears to be important for the adaptation and survival of viruses. To clarify how the number of viral genomes that establish cell infection is determined, we developed a simulation model of cell infection for tomato mosaic virus (ToMV), a positive-strand RNA virus. The model showed that stochastic processes that govern the replication or degradation of individual genomes result in the infection by a small number of genomes, while a large number of infectious genomes are introduced in the cell. It also predicted two interesting characteristics regarding cell infection patterns: stochastic variation among cells in the number of viral genomes that establish infection and stochastic inequality in the accumulation of their progenies in each cell. Both characteristics were validated experimentally by inoculating tobacco cells with a library of nucleotide sequence–tagged ToMV and analyzing the viral genomes that accumulated in each cell using a high-throughput sequencer. An additional simulation model revealed that these two characteristics enhance selection during tissue infection. The cell infection model also predicted a mechanism that enhances selection at the cellular level: a small difference in the replication abilities of coinfected variants results in a large difference in individual accumulation via the multiple-round formation of the replication complex (i.e., the replication machinery). Importantly, this predicted effect was observed in vivo. The cell infection model was robust to changes in the parameter values, suggesting that other viruses could adopt similar adaptation mechanisms. Taken together, these data reveal a comprehensive picture of viral infection processes including replication, cell-to-cell transmission, and evolution, which are based on the stochastic behavior of the viral genome molecules in each cell. PMID:25781391

Intermittency inhibited by transport: An exactly solvable model

NASA Astrophysics Data System (ADS)

Zanette, Damián H.

1994-04-01

Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.

Empirical tests of Zipf's law mechanism in open source Linux distribution.

PubMed

Maillart, T; Sornette, D; Spaeth, S; von Krogh, G

2008-11-21

Zipf's power law is a ubiquitous empirical regularity found in many systems, thought to result from proportional growth. Here, we establish empirically the usually assumed ingredients of stochastic growth models that have been previously conjectured to be at the origin of Zipf's law. We use exceptionally detailed data on the evolution of open source software projects in Linux distributions, which offer a remarkable example of a growing complex self-organizing adaptive system, exhibiting Zipf's law over four full decades.

Formation and distribution of fragments in the spontaneous fission of 240 Pu

DOE PAGES

Sadhukhan, Jhilam; Zhang, Chunli; Nazarewicz, Witold; ...

2017-12-18

We use the stochastic Langevin framework to simulate the nuclear evolution after the system tunnels through the multidimensional potential barrier. For a representative sample of different initial configurations along the outer turning-point line, we define effective fission paths by computing a large number of Langevin trajectories. We extract the relative contribution of each such path to the fragment distribution. We then use nucleon localization functions along effective fission pathways to analyze the characteristics of prefragments at prescission configurations.

Multilevel ensemble Kalman filtering

DOE PAGES

Hoel, Hakon; Law, Kody J. H.; Tempone, Raul

2016-06-14

This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

Molecular Epidemiology and Evolution of West Nile Virus in North America

PubMed Central

Mann, Brian R.; McMullen, Allison R.; Swetnam, Daniele M.; Barrett, Alan D. T.

2013-01-01

West Nile virus (WNV) was introduced to New York in 1999 and rapidly spread throughout North America and into parts of Central and South America. Displacement of the original New York (NY99) genotype by the North America/West Nile 2002 (NA/WN02) genotype occurred in 2002 with subsequent identification of a novel genotype in 2003 in isolates collected from the southwestern Unites States region (SW/WN03 genotype). Both genotypes co-circulate to date. Subsequent WNV surveillance studies have confirmed additional genotypes in the United States that have become extinct due to lack of a selective advantage or stochastic effect; however, the dynamic emergence, displacement, and extinction of multiple WNV genotypes in the US from 1999–2012 indicates the continued evolution of WNV in North America. PMID:24135819

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

Modeling lung cancer evolution and preclinical response by orthotopic mouse allografts.

PubMed

Ambrogio, Chiara; Carmona, Francisco J; Vidal, August; Falcone, Mattia; Nieto, Patricia; Romero, Octavio A; Puertas, Sara; Vizoso, Miguel; Nadal, Ernest; Poggio, Teresa; Sánchez-Céspedes, Montserrat; Esteller, Manel; Mulero, Francisca; Voena, Claudia; Chiarle, Roberto; Barbacid, Mariano; Santamaría, David; Villanueva, Alberto

2014-11-01

Cancer evolution is a process that is still poorly understood because of the lack of versatile in vivo longitudinal studies. By generating murine non-small cell lung cancer (NSCLC) orthoallobanks and paired primary cell lines, we provide a detailed description of an in vivo, time-dependent cancer malignization process. We identify the acquisition of metastatic dissemination potential, the selection of co-driver mutations, and the appearance of naturally occurring intratumor heterogeneity, thus recapitulating the stochastic nature of human cancer development. This approach combines the robustness of genetically engineered cancer models with the flexibility of allograft methodology. We have applied this tool for the preclinical evaluation of therapeutic approaches. This system can be implemented to improve the design of future treatments for patients with NSCLC. ©2014 American Association for Cancer Research.

Quantum corrections of the truncated Wigner approximation applied to an exciton transport model.

PubMed

Ivanov, Anton; Breuer, Heinz-Peter

2017-04-01

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

Tit for tat in heterogeneous populations

NASA Astrophysics Data System (ADS)

Nowak, Martin A.; Sigmund, Karl

1992-01-01

THE 'iterated prisoner's dilemma' is now the orthodox paradigm for the evolution of cooperation among selfish individuals. This viewpoint is strongly supported by Axelrod's computer tournaments, where 'tit for tat' (TFT) finished first1. This has stimulated interest in the role of reciprocity in biological societies1-8. Most theoretical investigations, however, assumed homogeneous populations (the setting for evolutionary stable strategies9,10) and programs immune to errors. Here we try to come closer to the biological situation by following a program6 that takes stochasticities into account and investigates representative samples. We find that a small fraction of TFT players is essential for the emergence of reciprocation in a heterogeneous population, but only paves the way for a more generous strategy. TFT is the pivot, rather than the aim, of an evolution towards cooperation.

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

NASA Technical Reports Server (NTRS)

Fridlind, Ann; Seifert, Axel; Ackerman, Andrew; Jensen, Eric

2004-01-01

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

Suppressing relaxation in superconducting qubits by quasiparticle pumping.

PubMed

Gustavsson, Simon; Yan, Fei; Catelani, Gianluigi; Bylander, Jonas; Kamal, Archana; Birenbaum, Jeffrey; Hover, David; Rosenberg, Danna; Samach, Gabriel; Sears, Adam P; Weber, Steven J; Yoder, Jonilyn L; Clarke, John; Kerman, Andrew J; Yoshihara, Fumiki; Nakamura, Yasunobu; Orlando, Terry P; Oliver, William D

2016-12-23

Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. We investigate a complementary, stochastic approach to reducing errors: Instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. A 70% reduction in the quasiparticle density results in a threefold enhancement in qubit relaxation times and a comparable reduction in coherence variability. Copyright © 2016, American Association for the Advancement of Science.

Exploiting temporal collateral sensitivity in tumor clonal evolution

PubMed Central

Zhao, Boyang; Sedlak, Joseph C.; Srinivas, Raja; Creixell, Pau; Pritchard, Justin R.; Tidor, Bruce; Lauffenburger, Douglas A.; Hemann, Michael T.

2016-01-01

SUMMARY The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities; a notion that we term ‘temporal collateral sensitivity’. Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph+ acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1 targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models, and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities. PMID:26924578

Reactive strategies in indirect reciprocity.

PubMed

Ohtsuki, Hisashi

2004-04-07

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean 'discriminatoriness' in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.

Social cohesion among kin, gene flow without dispersal and the evolution of population genetic structure in the killer whale (Orcinus orca).

PubMed

Pilot, M; Dahlheim, M E; Hoelzel, A R

2010-01-01

In social species, breeding system and gregarious behavior are key factors influencing the evolution of large-scale population genetic structure. The killer whale is a highly social apex predator showing genetic differentiation in sympatry between populations of foraging specialists (ecotypes), and low levels of genetic diversity overall. Our comparative assessments of kinship, parentage and dispersal reveal high levels of kinship within local populations and ongoing male-mediated gene flow among them, including among ecotypes that are maximally divergent within the mtDNA phylogeny. Dispersal from natal populations was rare, implying that gene flow occurs without dispersal, as a result of reproduction during temporary interactions. Discordance between nuclear and mitochondrial phylogenies was consistent with earlier studies suggesting a stochastic basis for the magnitude of mtDNA differentiation between matrilines. Taken together our results show how the killer whale breeding system, coupled with social, dispersal and foraging behaviour, contributes to the evolution of population genetic structure.

The Evolution of Phenotypic Switching in Subdivided Populations

PubMed Central

Carja, Oana; Liberman, Uri; Feldman, Marcus W.

2014-01-01

Stochastic switching is an example of phenotypic bet hedging, where offspring can express a phenotype different from that of their parents. Phenotypic switching is well documented in viruses, yeast, and bacteria and has been extensively studied when the selection pressures vary through time. However, there has been little work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here we use a population genetic model to explore the interaction of temporal and spatial variation in determining the evolutionary dynamics of phenotypic switching. We find that the stable switching rate is mainly determined by the rate of environmental change and the migration rate. This stable rate is also a decreasing function of the recombination rate, although this is a weaker effect than those of either the period of environmental change or the migration rate. This study highlights the interplay of spatial and temporal environmental variability, offering new insights into how migration can influence the evolution of phenotypic switching rates, mutation rates, or other sources of phenotypic variation. PMID:24496012

Dynamics of Tumor Heterogeneity Derived from Clonal Karyotypic Evolution.

PubMed

Laughney, Ashley M; Elizalde, Sergi; Genovese, Giulio; Bakhoum, Samuel F

2015-08-04

Numerical chromosomal instability is a ubiquitous feature of human neoplasms. Due to experimental limitations, fundamental characteristics of karyotypic changes in cancer are poorly understood. Using an experimentally inspired stochastic model, based on the potency and chromosomal distribution of oncogenes and tumor suppressor genes, we show that cancer cells have evolved to exist within a narrow range of chromosome missegregation rates that optimizes phenotypic heterogeneity and clonal survival. Departure from this range reduces clonal fitness and limits subclonal diversity. Mapping of the aneuploid fitness landscape reveals a highly favorable, commonly observed, near-triploid state onto which evolving diploid- and tetraploid-derived populations spontaneously converge, albeit at a much lower fitness cost for the latter. Finally, by analyzing 1,368 chromosomal translocation events in five human cancers, we find that karyotypic evolution also shapes chromosomal translocation patterns by selecting for more oncogenic derivative chromosomes. Thus, chromosomal instability can generate the heterogeneity required for Darwinian tumor evolution. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Exploiting Temporal Collateral Sensitivity in Tumor Clonal Evolution.

PubMed

Zhao, Boyang; Sedlak, Joseph C; Srinivas, Raja; Creixell, Pau; Pritchard, Justin R; Tidor, Bruce; Lauffenburger, Douglas A; Hemann, Michael T

2016-03-24

The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities-a notion that we term "temporal collateral sensitivity." Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph(+) acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1-targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small-molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities. Copyright © 2016 Elsevier Inc. All rights reserved.

Environment overwhelms both nature and nurture in a model spin glass

NASA Astrophysics Data System (ADS)

Middleton, A. Alan; Yang, Jie

We are interested in exploring what information determines the particular history of the glassy long term dynamics in a disordered material. We study the effect of initial configurations and the realization of stochastic dynamics on the long time evolution of configurations in a two-dimensional Ising spin glass model. The evolution of nearest neighbor correlations is computed using patchwork dynamics, a coarse-grained numerical heuristic for temporal evolution. The dependence of the nearest neighbor spin correlations at long time on both initial spin configurations and noise histories are studied through cross-correlations of long-time configurations and the spin correlations are found to be independent of both. We investigate how effectively rigid bond clusters coarsen. Scaling laws are used to study the convergence of configurations and the distribution of sizes of nearly rigid clusters. The implications of the computational results on simulations and phenomenological models of spin glasses are discussed. We acknowledge NSF support under DMR-1410937 (CMMT program).

Folded gastrulation and T48 drive the evolution of coordinated mesoderm internalization in flies

PubMed Central

Urbansky, Silvia; González Avalos, Paula; Wosch, Maike; Lemke, Steffen

2016-01-01

Gastrulation constitutes a fundamental yet diverse morphogenetic process of metazoan development. Modes of gastrulation range from stochastic translocation of individual cells to coordinated infolding of an epithelial sheet. How such morphogenetic differences are genetically encoded and whether they have provided specific developmental advantages is unclear. Here we identify two genes, folded gastrulation and t48, which in the evolution of fly gastrulation acted as a likely switch from an ingression of individual cells to the invagination of the blastoderm epithelium. Both genes are expressed and required for mesoderm invagination in the fruit fly Drosophila melanogaster but do not appear during mesoderm ingression of the midge Chironomus riparius. We demonstrate that early expression of either or both of these genes in C.riparius is sufficient to invoke mesoderm invagination similar to D.melanogaster. The possible genetic simplicity and a measurable increase in developmental robustness might explain repeated evolution of similar transitions in animal gastrulation. DOI: http://dx.doi.org/10.7554/eLife.18318.001 PMID:27685537

Inference of tumor evolution during chemotherapy by computational modeling and in situ analysis of genetic and phenotypic cellular diversity.

PubMed

Almendro, Vanessa; Cheng, Yu-Kang; Randles, Amanda; Itzkovitz, Shalev; Marusyk, Andriy; Ametller, Elisabet; Gonzalez-Farre, Xavier; Muñoz, Montse; Russnes, Hege G; Helland, Aslaug; Rye, Inga H; Borresen-Dale, Anne-Lise; Maruyama, Reo; van Oudenaarden, Alexander; Dowsett, Mitchell; Jones, Robin L; Reis-Filho, Jorge; Gascon, Pere; Gönen, Mithat; Michor, Franziska; Polyak, Kornelia

2014-02-13

Cancer therapy exerts a strong selection pressure that shapes tumor evolution, yet our knowledge of how tumors change during treatment is limited. Here, we report the analysis of cellular heterogeneity for genetic and phenotypic features and their spatial distribution in breast tumors pre- and post-neoadjuvant chemotherapy. We found that intratumor genetic diversity was tumor-subtype specific, and it did not change during treatment in tumors with partial or no response. However, lower pretreatment genetic diversity was significantly associated with pathologic complete response. In contrast, phenotypic diversity was different between pre- and posttreatment samples. We also observed significant changes in the spatial distribution of cells with distinct genetic and phenotypic features. We used these experimental data to develop a stochastic computational model to infer tumor growth patterns and evolutionary dynamics. Our results highlight the importance of integrated analysis of genotypes and phenotypes of single cells in intact tissues to predict tumor evolution. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Inference of tumor evolution during chemotherapy by computational modeling and in situ analysis of cellular diversity for genetic and phenotypic features

PubMed Central

Almendro, Vanessa; Cheng, Yu-Kang; Randles, Amanda; Itzkovitz, Shalev; Marusyk, Andriy; Ametller, Elisabet; Gonzalez-Farre, Xavier; Muñoz, Montse; Russnes, Hege G.; Helland, Åslaug; Rye, Inga H.; Borresen-Dale, Anne-Lise; Maruyama, Reo; van Oudenaarden, Alexander; Dowsett, Mitchell; Jones, Robin L.; Reis-Filho, Jorge; Gascon, Pere; Gönen, Mithat; Michor, Franziska; Polyak, Kornelia

2014-01-01

SUMMARY Cancer therapy exerts a strong selection pressure that shapes tumor evolution, yet our knowledge of how tumors change during treatment is limited. Here we report the analysis of cellular heterogeneity for genetic and phenotypic features and their spatial distribution in breast tumors pre- and post-neoadjuvant chemotherapy. We found that intratumor genetic diversity was tumor subtype-specific and it did not change during treatment in tumors with partial or no response. However, lower pre-treatment genetic diversity was significantly associated with complete pathologic response. In contrast, phenotypic diversity was different between pre- and post-treatment samples. We also observed significant changes in the spatial distribution of cells with distinct genetic and phenotypic features. We used these experimental data to develop a stochastic computational model to infer tumor growth patterns and evolutionary dynamics. Our results highlight the importance of integrated analysis of genotypes and phenotypes of single cells in intact tissues to predict tumor evolution. PMID:24462293

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

Inference of tumor evolution during chemotherapy by computational modeling and in situ analysis of genetic and phenotypic cellular diversity

DOE PAGES

Almendro, Vanessa; Cheng, Yu -Kang; Randles, Amanda; ...

2014-02-01

Cancer therapy exerts a strong selection pressure that shapes tumor evolution, yet our knowledge of how tumors change during treatment is limited. Here, we report the analysis of cellular heterogeneity for genetic and phenotypic features and their spatial distribution in breast tumors pre- and post-neoadjuvant chemotherapy. We found that intratumor genetic diversity was tumor-subtype specific, and it did not change during treatment in tumors with partial or no response. However, lower pretreatment genetic diversity was significantly associated with pathologic complete response. In contrast, phenotypic diversity was different between pre- and post-treatment samples. We also observed significant changes in the spatialmore » distribution of cells with distinct genetic and phenotypic features. We used these experimental data to develop a stochastic computational model to infer tumor growth patterns and evolutionary dynamics. Our results highlight the importance of integrated analysis of genotypes and phenotypes of single cells in intact tissues to predict tumor evolution.« less

On the long-term fitness of cells in periodically switching environments.

PubMed

Pang, Ning-Ning; Tzeng, Wen-Jer

2008-01-01

Because all the cell populations are capable of making switches between different genetic expression states in response to the environmental change, Thattai and van Oudenaarden (Genetics 167, 523-530, 2004) have raised a very interesting question: In a constantly fluctuating environment, which type of cell population (heterogeneous or homogeneous) is fitter in the long term? This problem is very important to development and evolution biology. We thus take an extensive analysis about how the cell population evolves in a periodically switching environment either with symmetrical time-span or asymmetrical time-span. A complete picture of the phase diagrams for both cases is obtained. Furthermore, we find that the systems with time-dependent cellular transitions all collapse to the same set of dynamical equations with the modified parameters. Furthermore, we also explain in detail how the fitness problem bears much resemblance to the phenomenon, stochastic resonance, in physical sciences. Our results could be helpful for the biologists to design artificial evolution experiments and unveil the mystery of development and evolution.

cuTauLeaping: A GPU-Powered Tau-Leaping Stochastic Simulator for Massive Parallel Analyses of Biological Systems

PubMed Central

Besozzi, Daniela; Pescini, Dario; Mauri, Giancarlo

2014-01-01

Tau-leaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tau-leaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU) provides power-efficient high-performance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tau-leaping simulations, by fully exploiting the Nvidia's Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tau-leaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPU-based tau-leaping implementation when the number of parallel simulations increases, with a break-even directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep analysis to study the oscillatory regimes in the Ras/cAMP/PKA pathway in S. cerevisiae. PMID:24663957

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Impacts of a Stochastic Ice Mass-Size Relationship on Squall Line Ensemble Simulations

NASA Astrophysics Data System (ADS)

Stanford, M.; Varble, A.; Morrison, H.; Grabowski, W.; McFarquhar, G. M.; Wu, W.

2017-12-01

Cloud and precipitation structure, evolution, and cloud radiative forcing of simulated mesoscale convective systems (MCSs) are significantly impacted by ice microphysics parameterizations. Most microphysics schemes assume power law relationships with constant parameters for ice particle mass, area, and terminal fallspeed relationships as a function of size, despite observations showing that these relationships vary in both time and space. To account for such natural variability, a stochastic representation of ice microphysical parameters was developed using the Predicted Particle Properties (P3) microphysics scheme in the Weather Research and Forecasting model, guided by in situ aircraft measurements from a number of field campaigns. Here, the stochastic framework is applied to the "a" and "b" parameters of the unrimed ice mass-size (m-D) relationship (m=aDb) with co-varying "a" and "b" values constrained by observational distributions tested over a range of spatiotemporal autocorrelation scales. Diagnostically altering a-b pairs in three-dimensional (3D) simulations of the 20 May 2011 Midlatitude Continental Convective Clouds Experiment (MC3E) squall line suggests that these parameters impact many important characteristics of the simulated squall line, including reflectivity structure (particularly in the anvil region), surface rain rates, surface and top of atmosphere radiative fluxes, buoyancy and latent cooling distributions, and system propagation speed. The stochastic a-b P3 scheme is tested using two frameworks: (1) a large ensemble of two-dimensional idealized squall line simulations and (2) a smaller ensemble of 3D simulations of the 20 May 2011 squall line, for which simulations are evaluated using observed radar reflectivity and radial velocity at multiple wavelengths, surface meteorology, and surface and satellite measured longwave and shortwave radiative fluxes. Ensemble spreads are characterized and compared against initial condition ensemble spreads for a range of variables.

Discrete and continuous models for tissue growth and shrinkage.

PubMed

Yates, Christian A

2014-06-07

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems. In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker-Plank equation (FPE) (in this case an advection-diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable. Copyright © 2014 Elsevier Ltd. All rights reserved.

Quantum simulation of a quantum stochastic walk

NASA Astrophysics Data System (ADS)

Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.

2017-03-01

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.

Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainties, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. This includes spectral decomposition calculations for one representative example in full detail.

Critical behavior in a stochastic model of vector mediated epidemics

NASA Astrophysics Data System (ADS)

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-06-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Critical behavior in a stochastic model of vector mediated epidemics.

PubMed

Alfinito, E; Beccaria, M; Macorini, G

2016-06-06

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks.

PubMed

Thanh, Vo Hong; Zunino, Roberto; Priami, Corrado

2017-01-01

Exact stochastic simulation is an indispensable tool for a quantitative study of biochemical reaction networks. The simulation realizes the time evolution of the model by randomly choosing a reaction to fire and update the system state according to a probability that is proportional to the reaction propensity. Two computationally expensive tasks in simulating large biochemical networks are the selection of next reaction firings and the update of reaction propensities due to state changes. We present in this work a new exact algorithm to optimize both of these simulation bottlenecks. Our algorithm employs the composition-rejection on the propensity bounds of reactions to select the next reaction firing. The selection of next reaction firings is independent of the number reactions while the update of propensities is skipped and performed only when necessary. It therefore provides a favorable scaling for the computational complexity in simulating large reaction networks. We benchmark our new algorithm with the state of the art algorithms available in literature to demonstrate its applicability and efficiency.

Fluctuating hyperfine interactions: an updated computational implementation

NASA Astrophysics Data System (ADS)

Zacate, M. O.; Evenson, W. E.

2015-04-01

The stochastic hyperfine interactions modeling library (SHIML) is a set of routines written in the C programming language designed to assist in the analysis of stochastic models of hyperfine interactions. The routines read a text-file description of the model, set up the Blume matrix, upon which the evolution operator of the quantum mechanical system depends, and calculate the eigenvalues and eigenvectors of the Blume matrix, from which theoretical spectra of experimental techniques can be calculated. The original version of SHIML constructs Blume matrices applicable for methods that measure hyperfine interactions with only a single nuclear spin state. In this paper, we report an extension of the library to provide support for methods such as Mössbauer spectroscopy and nuclear resonant scattering of synchrotron radiation, which are sensitive to interactions with two nuclear spin states. Examples will be presented that illustrate the use of this extension of SHIML to generate Mössbauer spectra for polycrystalline samples under a number of fluctuating hyperfine field models.

Delay chemical master equation: direct and closed-form solutions

PubMed Central

Leier, Andre; Marquez-Lago, Tatiana T.

2015-01-01

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616

Delay chemical master equation: direct and closed-form solutions.

PubMed

Leier, Andre; Marquez-Lago, Tatiana T

2015-07-08

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

Nemo: an evolutionary and population genetics programming framework.

PubMed

Guillaume, Frédéric; Rougemont, Jacques

2006-10-15

Nemo is an individual-based, genetically explicit and stochastic population computer program for the simulation of population genetics and life-history trait evolution in a metapopulation context. It comes as both a C++ programming framework and an executable program file. Its object-oriented programming design gives it the flexibility and extensibility needed to implement a large variety of forward-time evolutionary models. It provides developers with abstract models allowing them to implement their own life-history traits and life-cycle events. Nemo offers a large panel of population models, from the Island model to lattice models with demographic or environmental stochasticity and a variety of already implemented traits (deleterious mutations, neutral markers and more), life-cycle events (mating, dispersal, aging, selection, etc.) and output operators for saving data and statistics. It runs on all major computer platforms including parallel computing environments. The source code, binaries and documentation are available under the GNU General Public License at http://nemo2.sourceforge.net.

Fish Processed Production Planning Using Integer Stochastic Programming Model

NASA Astrophysics Data System (ADS)

Firmansyah, Mawengkang, Herman

2011-06-01

Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.

Neutral Community Dynamics and the Evolution of Species Interactions.

PubMed

Coelho, Marco Túlio P; Rangel, Thiago F

2018-04-01

A contemporary goal in ecology is to determine the ecological and evolutionary processes that generate recurring structural patterns in mutualistic networks. One of the great challenges is testing the capacity of neutral processes to replicate observed patterns in ecological networks, since the original formulation of the neutral theory lacks trophic interactions. Here, we develop a stochastic-simulation neutral model adding trophic interactions to the neutral theory of biodiversity. Without invoking ecological differences among individuals of different species, and assuming that ecological interactions emerge randomly, we demonstrate that a spatially explicit multitrophic neutral model is able to capture the recurrent structural patterns of mutualistic networks (i.e., degree distribution, connectance, nestedness, and phylogenetic signal of species interactions). Nonrandom species distribution, caused by probabilistic events of migration and speciation, create nonrandom network patterns. These findings have broad implications for the interpretation of niche-based processes as drivers of ecological networks, as well as for the integration of network structures with demographic stochasticity.

libSRES: a C library for stochastic ranking evolution strategy for parameter estimation.

PubMed

Ji, Xinglai; Xu, Ying

2006-01-01

Estimation of kinetic parameters in a biochemical pathway or network represents a common problem in systems studies of biological processes. We have implemented a C library, named libSRES, to facilitate a fast implementation of computer software for study of non-linear biochemical pathways. This library implements a (mu, lambda)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. Considering the amount of computing time it might require to solve a parameter-estimation problem, an MPI version of libSRES is provided for parallel implementation, as well as a simple user interface. libSRES is freely available and could be used directly in any C program as a library function. We have extensively tested the performance of libSRES on various pathway parameter-estimation problems and found its performance to be satisfactory. The source code (in C) is free for academic users at http://csbl.bmb.uga.edu/~jix/science/libSRES/

Option pricing for stochastic volatility model with infinite activity Lévy jumps

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2016-08-01

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

Stability of Zero-Sum Games in Evolutionary Game Theory

NASA Astrophysics Data System (ADS)

Knebel, Johannes; Krueger, Torben; Weber, Markus F.; Frey, Erwin

2014-03-01

Evolutionary game theory has evolved into a successful theoretical concept to study mechanisms that govern the evolution of ecological communities. On a mathematical level, this theory was formalized in the framework of the celebrated replicator equations (REs) and its stochastic generalizations. In our work, we analyze the long-time behavior of the REs for zero-sum games with arbitrarily many strategies, which are generalized versions of the children's game Rock-Paper-Scissors.[1] We demonstrate how to determine the strategies that survive and those that become extinct in the long run. Our results show that extinction of strategies is exponentially fast in generic setups, and that conditions for the survival can be formulated in terms of the Pfaffian of the REs' antisymmetric payoff matrix. Consequences for the stochastic dynamics, which arise in finite populations, are reflected by a generalized scaling law for the extinction time in the vicinity of critical reaction rates. Our findings underline the relevance of zero-sum games as a reference for the analysis of other models in evolutionary game theory.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Fitness decline under osmotic stress in Caenorhabditis elegans populations subjected to spontaneous mutation accumulation at varying population sizes.

PubMed

Katju, Vaishali; Packard, Lucille B; Keightley, Peter D

2018-04-01

The consequences of mutations for population fitness depends on their individual selection coefficients and the effective population size. An earlier study of Caenorhabditis elegans spontaneous mutation accumulation lines evolved for 409 generations at three population sizes found that N e   = 1 populations declined significantly in fitness whereas the fitness of larger populations (N e   = 5, 50) was indistinguishable from the ancestral control under benign conditions. To test if larger MA populations harbor a load of cryptic deleterious mutations that are obscured under benign laboratory conditions, we measured fitness under osmotic stress via exposure to hypersaline conditions. The fitness of N e   = 1 lines exhibited a further decline under osmotic stress compared to benign conditions. However, the fitness of larger populations remained indistinguishable from that of the ancestral control. The average effects of deleterious mutations in N e   = 1 lines were estimated to be 22% for productivity and 14% for survivorship, exceeding values previously detected under benign conditions. Our results suggest that fitness decline is due to large effect mutations that are rapidly removed via selection even in small populations, with implications for conservation practices. Genetic stochasticity may not be as potent and immediate a threat to the persistence of small populations as other demographic and environmental stochastic factors. © 2018 The Author(s). Evolution © 2018 The Society for the Study of Evolution.

Evidence for r- and K-selection in a wild bird population: a reciprocal link between ecology and evolution.

PubMed

Sæther, Bernt-Erik; Visser, Marcel E; Grøtan, Vidar; Engen, Steinar

2016-04-27

Understanding the variation in selection pressure on key life-history traits is crucial in our rapidly changing world. Density is rarely considered as a selective agent. To study its importance, we partition phenotypic selection in fluctuating environments into components representing the population growth rate at low densities and the strength of density dependence, using a new stochastic modelling framework. We analysed the number of eggs laid per season in a small song-bird, the great tit, and found balancing selection favouring large clutch sizes at small population densities and smaller clutches in years with large populations. A significant interaction between clutch size and population size in the regression for the Malthusian fitness reveals that those females producing large clutch sizes at small population sizes also are those that show the strongest reduction in fitness when population size is increased. This provides empirical support for ongoing r- and K-selection in this population, favouring phenotypes with large growth rates r at small population sizes and phenotypes with high competitive skills when populations are close to the carrying capacity K This selection causes long-term fluctuations around a stable mean clutch size caused by variation in population size, implying that r- and K-selection is an important mechanism influencing phenotypic evolution in fluctuating environments. This provides a general link between ecological dynamics and evolutionary processes, operating through a joint influence of density dependence and environmental stochasticity on fluctuations in population size. © 2016 The Author(s).

Stochastic modeling indicates that aging and somatic evolution in the hematopoetic system are driven by non-cell-autonomous processes.

PubMed

Rozhok, Andrii I; Salstrom, Jennifer L; DeGregori, James

2014-12-01

Age-dependent tissue decline and increased cancer incidence are widely accepted to be rate-limited by the accumulation of somatic mutations over time. Current models of carcinogenesis are dominated by the assumption that oncogenic mutations have defined advantageous fitness effects on recipient stem and progenitor cells, promoting and rate-limiting somatic evolution. However, this assumption is markedly discrepant with evolutionary theory, whereby fitness is a dynamic property of a phenotype imposed upon and widely modulated by environment. We computationally modeled dynamic microenvironment-dependent fitness alterations in hematopoietic stem cells (HSC) within the Sprengel-Liebig system known to govern evolution at the population level. Our model for the first time integrates real data on age-dependent dynamics of HSC division rates, pool size, and accumulation of genetic changes and demonstrates that somatic evolution is not rate-limited by the occurrence of mutations, but instead results from aged microenvironment-driven alterations in the selective/fitness value of previously accumulated genetic changes. Our results are also consistent with evolutionary models of aging and thus oppose both somatic mutation-centric paradigms of carcinogenesis and tissue functional decline. In total, we demonstrate that aging directly promotes HSC fitness decline and somatic evolution via non-cell-autonomous mechanisms.

Natural selection in chemical evolution.

PubMed

Fernando, Chrisantha; Rowe, Jonathan

2007-07-07

We propose that chemical evolution can take place by natural selection if a geophysical process is capable of heterotrophic formation of liposomes that grow at some base rate, divide by external agitation, and are subject to stochastic chemical avalanches, in the absence of nucleotides or any monomers capable of modular heredity. We model this process using a simple hill-climbing algorithm, and an artificial chemistry that is unique in exhibiting conservation of mass and energy in an open thermodynamic system. Selection at the liposome level results in the stabilization of rarely occurring molecular autocatalysts that either catalyse or are consumed in reactions that confer liposome level fitness; typically they contribute in parallel to an increasingly conserved intermediary metabolism. Loss of competing autocatalysts can sometimes be adaptive. Steady-state energy flux by the individual increases due to the energetic demands of growth, but also of memory, i.e. maintaining variations in the chemical network. Self-organizing principles such as those proposed by Kauffman, Fontana, and Morowitz have been hypothesized as an ordering principle in chemical evolution, rather than chemical evolution by natural selection. We reject those notions as either logically flawed or at best insufficient in the absence of natural selection. Finally, a finite population model without elitism shows the practical evolutionary constraints for achieving chemical evolution by natural selection in the lab.

Host-parasite coevolution can promote the evolution of seed banking as a bet-hedging strategy.

PubMed

Verin, Mélissa; Tellier, Aurélien

2018-04-20

Seed (egg) banking is a common bet-hedging strategy maximizing the fitness of organisms facing environmental unpredictability by the delayed emergence of offspring. Yet, this condition often requires fast and drastic stochastic shifts between good and bad years. We hypothesize that the host seed banking strategy can evolve in response to coevolution with parasites because the coevolutionary cycles promote a gradually changing environment over longer times than seed persistence. We study the evolution of host germination fraction as a quantitative trait using both pairwise competition and multiple mutant competition methods, while the germination locus can be genetically linked or unlinked with the host locus under coevolution. In a gene-for-gene model of coevolution, hosts evolve a seed bank strategy under unstable coevolutionary cycles promoted by moderate to high costs of resistance or strong disease severity. Moreover, when assuming genetic linkage between coevolving and germination loci, the resistant genotype always evolves seed banking in contrast to susceptible hosts. Under a matching-allele interaction, both hosts' genotypes exhibit the same seed banking strategy irrespective of the genetic linkage between loci. We suggest host-parasite coevolution as an additional hypothesis for the evolution of seed banking as a temporal bet-hedging strategy. © 2018 The Author(s). Evolution © 2018 The Society for the Study of Evolution.

Somatic clonal evolution: A selection-centric perspective.

PubMed

Scott, Jacob; Marusyk, Andriy

2017-04-01

It is generally accepted that the initiation and progression of cancers is the result of somatic clonal evolution. Despite many peculiarities, evolution within populations of somatic cells should obey the same Darwinian principles as evolution within natural populations, i.e. variability of heritable phenotypes provides the substrate for context-specific selection forces leading to increased population frequencies of phenotypes, which are better adapted to their environment. Yet, within cancer biology, the more prevalent way to view evolution is as being entirely driven by the accumulation of "driver" mutations. Context-specific selection forces are either ignored, or viewed as constraints from which tumor cells liberate themselves during the course of malignant progression. In this review, we will argue that explicitly focusing on selection forces acting on the populations of neoplastic cells as the driving force of somatic clonal evolution might provide for a more accurate conceptual framework compared to the mutation-centric driver gene paradigm. Whereas little can be done to counteract the "bad luck" of stochastic occurrences of cancer-related mutations, changes in selective pressures and the phenotypic adaptations they induce can, in principle, be exploited to limit the incidence of cancers and to increase the efficiency of existing and future therapies. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby. Copyright © 2017 Elsevier B.V. All rights reserved.

Evolution of Circulating Wild Poliovirus and of Vaccine-Derived Poliovirus in an Immunodeficient Patient: a Unifying Model

PubMed Central

Gavrilin, Gene V.; Cherkasova, Elena A.; Lipskaya, Galina Y.; Kew, Olen M.; Agol, Vadim I.

2000-01-01

We determined nucleotide sequences of the VP1 and 2AB genes and portions of the 2C and 3D genes of two evolving poliovirus lineages: circulating wild viruses of T geotype and Sabin vaccine-derived isolates from an immunodeficient patient. Different regions of the viral RNA were found to evolve nonsynchronously, and the rate of evolution of the 2AB region in the vaccine-derived population was not constant throughout its history. Synonymous replacements occurred not completely randomly, suggesting the need for conservation of certain rare codons (possibly to control translation elongation) and the existence of unidentified constraints in the viral RNA structure. Nevertheless the major contribution to the evolution of the two lineages came from linear accumulation of synonymous substitutions. Therefore, in agreement with current theories of viral evolution, we suggest that the majority of the mutations in both lineages were fixed as a result of successive sampling, from the heterogeneous populations, of random portions containing predominantly neutral and possibly adverse mutations. As a result of such a mode of evolution, the virus fitness may be maintained at a more or less constant level or may decrease unless more-fit variants are stochastically generated. The proposed unifying model of natural poliovirus evolution has important implications for the epidemiology of poliomyelitis. PMID:10906191

Real-Time Optimal Flood Control Decision Making and Risk Propagation Under Multiple Uncertainties

NASA Astrophysics Data System (ADS)

Zhu, Feilin; Zhong, Ping-An; Sun, Yimeng; Yeh, William W.-G.

2017-12-01

Multiple uncertainties exist in the optimal flood control decision-making process, presenting risks involving flood control decisions. This paper defines the main steps in optimal flood control decision making that constitute the Forecast-Optimization-Decision Making (FODM) chain. We propose a framework for supporting optimal flood control decision making under multiple uncertainties and evaluate risk propagation along the FODM chain from a holistic perspective. To deal with uncertainties, we employ stochastic models at each link of the FODM chain. We generate synthetic ensemble flood forecasts via the martingale model of forecast evolution. We then establish a multiobjective stochastic programming with recourse model for optimal flood control operation. The Pareto front under uncertainty is derived via the constraint method coupled with a two-step process. We propose a novel SMAA-TOPSIS model for stochastic multicriteria decision making. Then we propose the risk assessment model, the risk of decision-making errors and rank uncertainty degree to quantify the risk propagation process along the FODM chain. We conduct numerical experiments to investigate the effects of flood forecast uncertainty on optimal flood control decision making and risk propagation. We apply the proposed methodology to a flood control system in the Daduhe River basin in China. The results indicate that the proposed method can provide valuable risk information in each link of the FODM chain and enable risk-informed decisions with higher reliability.

Kinematic dynamo, supersymmetry breaking, and chaos

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Enßlin, Torsten A.

2016-04-01

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

Mean field analysis of a spatial stochastic model of a gene regulatory network.

PubMed

Sturrock, M; Murray, P J; Matzavinos, A; Chaplain, M A J

2015-10-01

A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.

A stochastic approach for quantifying immigrant integration: the Spanish test case

NASA Astrophysics Data System (ADS)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-10-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors

NASA Astrophysics Data System (ADS)

Mehanna Ismail, Mohammed Ali

The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the implementation of time splitting, variable stochastic fluid particle mass control, and a second order time accurate (predictor-corrector) scheme used for solving the stochastic differential equations governing the particles evolution. The model compared well against experimental data found in the literature for two different configurations: bluff body and swirl stabilized combustors. The generalized stochastic reactor is a newly developed model. This model relies on the generalization of the concept of the classical stochastic reactor theory in the sense that it accounts for both finite micro- and macro-mixing processes. (Abstract shortened by UMI.)

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

2017-09-01

We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

Gain in Student Understanding of the Role of Random Variation in Evolution Following Teaching Intervention Based on Luria-Delbruck Experiment†

PubMed Central

Robson, Rachel L.; Burns, Susan

2011-01-01

Undergraduate students in introductory biology classes are typically saddled with pre-existing popular beliefs that impede their ability to learn about biological evolution. One of the most common misconceptions about evolution is that the environment causes advantageous mutations, rather than the correct view that mutations occur randomly and the environment only selects for mutants with advantageous traits. In this study, a significant gain in student understanding of the role of randomness in evolution was observed after students participated in an inquiry-based pedagogical intervention based on the Luria-Delbruck experiment. Questionnaires with isomorphic questions regarding environmental selection among random mutants were administered to study participants (N = 82) in five separate sections of a sophomore-level microbiology class before and after the teaching intervention. Demographic data on each participant was also collected, in a way that preserved anonymity. Repeated measures analysis showed that post-test scores were significantly higher than pre-test scores with regard to the questions about evolution (F(1, 77) = 25.913, p < 0.001). Participants’ pre-existing beliefs about evolution had no significant effect on gain in understanding of this concept. This study indicates that conducting and discussing an experiment about phage resistance in E. coli may improve student understanding of the role of stochastic events in evolution more broadly, as post-test answers showed that students were able to apply the lesson of the Luria-Delbruck experiment to other organisms subjected to other kinds of selection. PMID:23653732

Evolution of Inbreeding Avoidance and Inbreeding Preference through Mate Choice among Interacting Relatives.

PubMed

Duthie, A Bradley; Reid, Jane M

2016-12-01

While extensive population genetic theory predicts conditions favoring evolution of self-fertilization versus outcrossing, there is no analogous theory that predicts conditions favoring evolution of inbreeding avoidance or inbreeding preference enacted through mate choice given obligate biparental reproduction. Multiple interacting processes complicate the dynamics of alleles underlying such inbreeding strategies, including sexual conflict, distributions of kinship, genetic drift, purging of mutation load, direct costs, and restricted kin discrimination. We incorporated these processes into an individual-based model to predict conditions where selection should increase or decrease frequencies of alleles causing inbreeding avoidance or inbreeding preference when females or males controlled mating. Selection for inbreeding avoidance occurred given strong inbreeding depression when either sex chose mates, while selection for inbreeding preference occurred given very weak inbreeding depression when females chose but never occurred when males chose. Selection for both strategies was constrained by direct costs and restricted kin discrimination. Purging was negligible, but allele frequencies were strongly affected by drift in small populations, while selection for inbreeding avoidance was weak in larger populations because inbreeding risk decreased. Therefore, while selection sometimes favored alleles underlying inbreeding avoidance or preference, evolution of such strategies may be much more restricted and stochastic than is commonly presumed.

Simulations of Fluvial Landscapes

NASA Astrophysics Data System (ADS)

Cattan, D.; Birnir, B.

2013-12-01

The Smith-Bretherton-Birnir (SBB) model for fluvial landsurfaces consists of a pair of partial differential equations, one governing water flow and one governing the sediment flow. Numerical solutions of these equations have been shown to provide realistic models in the evolution of fluvial landscapes. Further analysis of these equations shows that they possess scaling laws (Hack's Law) that are known to exist in nature. However, the simulations are highly dependent on the numerical methods used; with implicit methods exhibiting the correct scaling laws, but the explicit methods fail to do so. These equations, and the resulting models, help to bridge the gap between the deterministic and the stochastic theories of landscape evolution. Slight modifications of the SBB equations make the results of the model more realistic. By modifying the sediment flow equation, the model obtains more pronounced meandering rivers. Typical landsurface with rivers.

Optional games on cycles and complete graphs.

PubMed

Jeong, Hyeong-Chai; Oh, Seung-Yoon; Allen, Benjamin; Nowak, Martin A

2014-09-07

We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure. Copyright © 2014 Elsevier Ltd. All rights reserved.

Extremal Optimization: Methods Derived from Co-Evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boettcher, S.; Percus, A.G.

1999-07-13

We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, rather than ''breeding'' better components. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, Extremal Optimization improves on a single candidate solution by treating each of its components as species co-evolving according to Darwinian principles. Unlike Simulated Annealing, its non-equilibrium approach effects an algorithm requiring few parameters to tune. With only one adjustable parameter, its performance provesmore » competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem.« less

Quantifying the evolution of individual scientific impact.

PubMed

Sinatra, Roberta; Wang, Dashun; Deville, Pierre; Song, Chaoming; Barabási, Albert-László

2016-11-04

Despite the frequent use of numerous quantitative indicators to gauge the professional impact of a scientist, little is known about how scientific impact emerges and evolves in time. Here, we quantify the changes in impact and productivity throughout a career in science, finding that impact, as measured by influential publications, is distributed randomly within a scientist's sequence of publications. This random-impact rule allows us to formulate a stochastic model that uncouples the effects of productivity, individual ability, and luck and unveils the existence of universal patterns governing the emergence of scientific success. The model assigns a unique individual parameter Q to each scientist, which is stable during a career, and it accurately predicts the evolution of a scientist's impact, from the h-index to cumulative citations, and independent recognitions, such as prizes. Copyright © 2016, American Association for the Advancement of Science.

Probing elastically or plastically induced structural heterogeneities in bulk metallic glasses by nanoindentation pop-in tests

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Tingkun; Gao, Yanfei; Bei, Hongbin

Shear banding dynamics in bulk metallic glasses (BMGs) is manifested by the spatiotemporal evolution of strain fields which in turn depend on structural heterogeneities. The spacing of these heterogeneities, as a characteristic length scale, was determined from the analysis of nanoindentation pop-in tests using a stochastic model. Furthermore, the pre-stress by elastic bending and residual stress by plastic bending of BMG plates were found to dramatically decrease such spacings, thus increasing heterogeneity density and mechanically rejuvenating the glass structure.

Probing elastically or plastically induced structural heterogeneities in bulk metallic glasses by nanoindentation pop-in tests

DOE PAGES

Liu, Tingkun; Gao, Yanfei; Bei, Hongbin

2017-07-21

Shear banding dynamics in bulk metallic glasses (BMGs) is manifested by the spatiotemporal evolution of strain fields which in turn depend on structural heterogeneities. The spacing of these heterogeneities, as a characteristic length scale, was determined from the analysis of nanoindentation pop-in tests using a stochastic model. Furthermore, the pre-stress by elastic bending and residual stress by plastic bending of BMG plates were found to dramatically decrease such spacings, thus increasing heterogeneity density and mechanically rejuvenating the glass structure.

Dwarf galaxies: a lab to investigate the neutron capture elements production

NASA Astrophysics Data System (ADS)

Cescutti, Gabriele

2018-06-01

In this contribution, I focus on the neutron capture elements observed in the spectra of old halo and ultra faint galaxies stars. Adopting a stochastic chemical evolution model and the Galactic halo as a benchmark, I present new constraints on the rate and time scales of r-process events, based on the discovery of the r-process rich stars in the ultra faint galaxy Reticulum 2. I also show that an s-process activated by rotation in massive stars can play an important role in the production of heavy elements.

Suppression of Beneficial Mutations in Dynamic Microbial Populations

NASA Astrophysics Data System (ADS)

Bittihn, Philip; Hasty, Jeff; Tsimring, Lev S.

2017-01-01

Quantitative predictions for the spread of mutations in bacterial populations are essential to interpret evolution experiments and to improve the stability of synthetic gene circuits. We derive analytical expressions for the suppression factor for beneficial mutations in populations that undergo periodic dilutions, covering arbitrary population sizes, dilution factors, and growth advantages in a single stochastic model. We find that the suppression factor grows with the dilution factor and depends nontrivially on the growth advantage, resulting in the preferential elimination of mutations with certain growth advantages. We confirm our results by extensive numerical simulations.

The topological particle and Morse theory

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-09-01

Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved space, is used to give an explicit and simple expression for the matrix elements of the evolution operator for the BRST Hamiltonian. These matrix elements lead to a representation of the manifold cohomology in terms of critical points of h along lines developed by Witten (Witten E 1982 J. Diff. Geom. 17 661-92).

Evolution of the concentration PDF in random environments modeled by global random walk

NASA Astrophysics Data System (ADS)

Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter

2013-04-01

The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and speeds up the computation by orders of magnitude. The approach is illustrated for the transport of passive scalars in heterogeneous aquifers, with hydraulic conductivity modeled as a random field.

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

NASA Astrophysics Data System (ADS)

Sewerin, Fabian; Rigopoulos, Stelios

2017-10-01

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

A theoretical stochastic control framework for adapting radiotherapy to hypoxia

NASA Astrophysics Data System (ADS)

Saberian, Fatemeh; Ghate, Archis; Kim, Minsun

2016-10-01

Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton’s method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course. Through these simulations, we also gain insights into when and why dynamic planning is likely to yield the largest benefits.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

Stochastic dynamics of time correlation in complex systems with discrete time

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail

2000-11-01

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

NASA Astrophysics Data System (ADS)

Seif, Dariush; Ghoniem, Nasr M.

2014-12-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô's calculus, rate equations for the first five moments of the size distribution in helium-vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium-vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the implementation of a path-integral approach may proceed if the distribution is known experimentally to significantly stray from a Gaussian description.

Capturing the Large Scale Behavior of Many Particle Systems Through Coarse-Graining

NASA Astrophysics Data System (ADS)

Punshon-Smith, Samuel

This dissertation is concerned with two areas of investigation: the first is understanding the mathematical structures behind the emergence of macroscopic laws and the effects of small scales fluctuations, the second involves the rigorous mathematical study of such laws and related questions of well-posedness. To address these areas of investigation the dissertation involves two parts: Part I concerns the theory of coarse-graining of many particle systems. We first investigate the mathematical structure behind the Mori-Zwanzig (projection operator) formalism by introducing two perturbative approaches to coarse-graining of systems that have an explicit scale separation. One concerns systems with little dissipation, while the other concerns systems with strong dissipation. In both settings we obtain an asymptotic series of `corrections' to the limiting description which are small with respect to the scaling parameter, these corrections represent the effects of small scales. We determine that only certain approximations give rise to dissipative effects in the resulting evolution. Next we apply this framework to the problem of coarse-graining the locally conserved quantities of a classical Hamiltonian system. By lumping conserved quantities into a collection of mesoscopic cells, we obtain, through a series of approximations, a stochastic particle system that resembles a discretization of the non-linear equations of fluctuating hydrodynamics. We study this system in the case that the transport coefficients are constant and prove well-posedness of the stochastic dynamics. Part II concerns the mathematical description of models where the underlying characteristics are stochastic. Such equations can model, for instance, the dynamics of a passive scalar in a random (turbulent) velocity field or the statistical behavior of a collection of particles subject to random environmental forces. First, we study general well-posedness properties of stochastic transport equation with rough diffusion coefficients. Our main result is strong existence and uniqueness under certain regularity conditions on the coefficients, and uses the theory of renormalized solutions of transport equations adapted to the stochastic setting. Next, in a work undertaken with collaborator Scott-Smith we study the Boltzmann equation with a stochastic forcing. The noise describing the forcing is white in time and colored in space and describes the effects of random environmental forces on a rarefied gas undergoing instantaneous, binary collisions. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. Tightness of the appropriate quantities is proved by an extension of the Skorohod theorem to non-metric spaces.

General predictive model of friction behavior regimes for metal contacts based on the formation stability and evolution of nanocrystalline surface films.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argibay, Nicolas; Cheng, Shengfeng; Sawyer, W. G.

2015-09-01

The prediction of macro-scale friction and wear behavior based on first principles and material properties has remained an elusive but highly desirable target for tribologists and material scientists alike. Stochastic processes (e.g. wear), statistically described parameters (e.g. surface topography) and their evolution tend to defeat attempts to establish practical general correlations between fundamental nanoscale processes and macro-scale behaviors. We present a model based on microstructural stability and evolution for the prediction of metal friction regimes, founded on recently established microstructural deformation mechanisms of nanocrystalline metals, that relies exclusively on material properties and contact stress models. We show through complementary experimentalmore » and simulation results that this model overcomes longstanding practical challenges and successfully makes accurate and consistent predictions of friction transitions for a wide range of contact conditions. This framework not only challenges the assumptions of conventional causal relationships between hardness and friction, and between friction and wear, but also suggests a pathway for the design of higher performance metal alloys.« less

Event-by-event picture for the medium-induced jet evolution

NASA Astrophysics Data System (ADS)

Escobedo, Miguel A.; Iancu, Edmond

2017-08-01

We discuss the evolution of an energetic jet which propagates through a dense quark-gluon plasma and radiates gluons due to its interactions with the medium. Within perturbative QCD, this evolution can be described as a stochastic branching process, that we have managed to solve exactly. We present exact, analytic, results for the gluon spectrum (the average gluon distribution) and for the higher n-point functions, which describe correlations and fluctuations. Using these results, we construct the event-by-event picture of the gluon distribution produced via medium-induced gluon branching. In contrast to what happens in a usual QCD cascade in vacuum, the medium-induced branchings are quasi-democratic, with offspring gluons carrying sizable fractions of the energy of their parent parton. We find large fluctuations in the energy loss and in the multiplicity of soft gluons. The multiplicity distribution is predicted to exhibit KNO (Koba-Nielsen-Olesen) scaling. These predictions can be tested in Pb+Pb collisions at the LHC, via event-by-event measurements of the di-jet asymmetry. Based on [1, 2].

Event-by-event picture for the medium-induced jet evolution

NASA Astrophysics Data System (ADS)

Escobedo, Miguel A.; Iancu, Edmond

2017-03-01

We discuss the evolution of an energetic jet which propagates through a dense quark-gluon plasma and radiates gluons due to its interactions with the medium. Within perturbative QCD, this evolution can be described as a stochastic branching process, that we have managed to solve exactly. We present exact, analytic, results for the gluon spectrum (the average gluon distribution) and for the higher n-point functions, which describe correlations and fluctuations. Using these results, we construct the event-by-event picture of the gluon distribution produced via medium-induced gluon branching. In contrast to what happens in a usual QCD cascade in vacuum, the medium-induced branchings are quasi-democratic, with offspring gluons carrying sizable fractions of the energy of their parent parton. We find large fluctuations in the energy loss and in the multiplicity of soft gluons. The multiplicity distribution is predicted to exhibit KNO (Koba-Nielsen-Olesen) scaling. These predictions can be tested in Pb+Pb collisions at the LHC, via event-by-event measurements of the di-jet asymmetry. Based on [1, 2].

Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks

NASA Astrophysics Data System (ADS)

Luo, Chao; Zhang, Xiaolin; Zheng, YuanJie

2017-06-01

In this article, the evolution of prisoner's dilemma game with volunteering on interdependent networks is investigated. Different from the traditional two-strategy game, voluntary participation as an additional strategy is involved in repeated game, that can introduce more complex evolutionary dynamics. And, interdependent networks provide a more generalized network architecture to study the intricate variability of dynamics. We have showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks. We further discussed the influence of interdependent strength on the densities of different strategies and found that an intermediate interdependence would play a bigger role on the evolution of dynamics. Subsequently, the critical values of the defection temptation for phase transitions under different conditions have been studied. Moreover, the global oscillations induced by the circle of dominance of three strategies on interdependent networks have been quantitatively investigated. Counter-intuitively, the oscillations of strategy densities are not periodic or stochastic, but have rich dynamical behaviors. By means of various analysis tools, we have demonstrated the global oscillations of strategy densities possessed chaotic characteristics.

A coarse-grained biophysical model of sequence evolution and the population size dependence of the speciation rate

PubMed Central

Khatri, Bhavin S.; Goldstein, Richard A.

2015-01-01

Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineages leads to incompatibilities. To develop a tractable analytical theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution that accounts for the fact that natural selection acts on phenotypes, but variation arises from mutations in sequences; the Smoluchowski equation includes selection due to both gradients in fitness and gradients in sequence entropy, which is the logarithm of the number of sequences that correspond to a particular binding energy. This simple consideration predicts that smaller populations develop incompatibilities more quickly in the weak mutation regime; this trend arises as sequence entropy poises smaller populations closer to incompatible regions of phenotype space. These results suggest a generic coarse-grained approach to evolutionary stochastic dynamics, allowing realistic modelling at the phenotypic level. PMID:25936759

The evolution and consequences of sex-specific reproductive variance.

PubMed

Mullon, Charles; Reuter, Max; Lehmann, Laurent

2014-01-01

Natural selection favors alleles that increase the number of offspring produced by their carriers. But in a world that is inherently uncertain within generations, selection also favors alleles that reduce the variance in the number of offspring produced. If previous studies have established this principle, they have largely ignored fundamental aspects of sexual reproduction and therefore how selection on sex-specific reproductive variance operates. To study the evolution and consequences of sex-specific reproductive variance, we present a population-genetic model of phenotypic evolution in a dioecious population that incorporates previously neglected components of reproductive variance. First, we derive the probability of fixation for mutations that affect male and/or female reproductive phenotypes under sex-specific selection. We find that even in the simplest scenarios, the direction of selection is altered when reproductive variance is taken into account. In particular, previously unaccounted for covariances between the reproductive outputs of different individuals are expected to play a significant role in determining the direction of selection. Then, the probability of fixation is used to develop a stochastic model of joint male and female phenotypic evolution. We find that sex-specific reproductive variance can be responsible for changes in the course of long-term evolution. Finally, the model is applied to an example of parental-care evolution. Overall, our model allows for the evolutionary analysis of social traits in finite and dioecious populations, where interactions can occur within and between sexes under a realistic scenario of reproduction.

The Evolution and Consequences of Sex-Specific Reproductive Variance

PubMed Central

Mullon, Charles; Reuter, Max; Lehmann, Laurent

2014-01-01

Natural selection favors alleles that increase the number of offspring produced by their carriers. But in a world that is inherently uncertain within generations, selection also favors alleles that reduce the variance in the number of offspring produced. If previous studies have established this principle, they have largely ignored fundamental aspects of sexual reproduction and therefore how selection on sex-specific reproductive variance operates. To study the evolution and consequences of sex-specific reproductive variance, we present a population-genetic model of phenotypic evolution in a dioecious population that incorporates previously neglected components of reproductive variance. First, we derive the probability of fixation for mutations that affect male and/or female reproductive phenotypes under sex-specific selection. We find that even in the simplest scenarios, the direction of selection is altered when reproductive variance is taken into account. In particular, previously unaccounted for covariances between the reproductive outputs of different individuals are expected to play a significant role in determining the direction of selection. Then, the probability of fixation is used to develop a stochastic model of joint male and female phenotypic evolution. We find that sex-specific reproductive variance can be responsible for changes in the course of long-term evolution. Finally, the model is applied to an example of parental-care evolution. Overall, our model allows for the evolutionary analysis of social traits in finite and dioecious populations, where interactions can occur within and between sexes under a realistic scenario of reproduction. PMID:24172130

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

PubMed Central

Iijima, Leo; Suzuki, Shingo; Hashimoto, Tomomi; Oyake, Ayana; Kobayashi, Hisaka; Someya, Yuki; Narisawa, Dai; Yomo, Tetsuya

2015-01-01

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution. PMID:26177190

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process.

PubMed

Kishimoto, Toshihiko; Ying, Bei-Wen; Tsuru, Saburo; Iijima, Leo; Suzuki, Shingo; Hashimoto, Tomomi; Oyake, Ayana; Kobayashi, Hisaka; Someya, Yuki; Narisawa, Dai; Yomo, Tetsuya

2015-07-01

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.

Lazy Updating of hubs can enable more realistic models by speeding up stochastic simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehlert, Kurt; Loewe, Laurence, E-mail: loewe@wisc.edu; Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, Wisconsin 53715

2014-11-28

To respect the nature of discrete parts in a system, stochastic simulation algorithms (SSAs) must update for each action (i) all part counts and (ii) each action's probability of occurring next and its timing. This makes it expensive to simulate biological networks with well-connected “hubs” such as ATP that affect many actions. Temperature and volume also affect many actions and may be changed significantly in small steps by the network itself during fever and cell growth, respectively. Such trends matter for evolutionary questions, as cell volume determines doubling times and fever may affect survival, both key traits for biological evolution.more » Yet simulations often ignore such trends and assume constant environments to avoid many costly probability updates. Such computational convenience precludes analyses of important aspects of evolution. Here we present “Lazy Updating,” an add-on for SSAs designed to reduce the cost of simulating hubs. When a hub changes, Lazy Updating postpones all probability updates for reactions depending on this hub, until a threshold is crossed. Speedup is substantial if most computing time is spent on such updates. We implemented Lazy Updating for the Sorting Direct Method and it is easily integrated into other SSAs such as Gillespie's Direct Method or the Next Reaction Method. Testing on several toy models and a cellular metabolism model showed >10× faster simulations for its use-cases—with a small loss of accuracy. Thus we see Lazy Updating as a valuable tool for some special but important simulation problems that are difficult to address efficiently otherwise.« less

Measuring Transcription Factor–Binding Site Turnover: A Maximum Likelihood Approach Using Phylogenies

PubMed Central

Otto, Wolfgang; Stadler, Peter F.; López-Giraldéz, Francesc; Townsend, Jeffrey P.; Lynch, Vincent J.

2009-01-01

A major mode of gene expression evolution is based on changes in cis-regulatory elements (CREs) whose function critically depends on the presence of transcription factor–binding sites (TFBS). Because CREs experience extensive TFBS turnover even with conserved function, alignment-based studies of CRE sequence evolution are limited to very closely related species. Here, we propose an alternative approach based on a stochastic model of TFBS turnover. We implemented a maximum likelihood model that permits variable turnover rates in different parts of the species tree. This model can be used to detect changes in turnover rate as a proxy for differences in the selective pressures acting on TFBS in different clades. We applied this method to five TFBS in the fungi methionine biosynthesis pathway and three TFBS in the HoxA clusters of vertebrates. We find that the estimated turnover rate is generally high, with half-life ranging between ∼5 and 150 My and a mode around tens of millions of years. This rate is consistent with the finding that even functionally conserved enhancers can show very low sequence similarity. We also detect statistically significant differences in the equilibrium densities of estrogen- and progesterone-response elements in the HoxA clusters between mammal and nonmammal vertebrates. Even more extreme clade-specific differences were found in the fungal data. We conclude that stochastic models of TFBS turnover enable the detection of shifts in the selective pressures acting on CREs in different organisms. The analysis tool, called CRETO (Cis-Regulatory Element Turn-Over) can be downloaded from http://www.bioinf.uni-leipzig.de/Software/creto/. PMID:20333180

Statistics, distillation, and ordering emergence in a two-dimensional stochastic model of particles in counterflowing streams

NASA Astrophysics Data System (ADS)

Stock, Eduardo Velasco; da Silva, Roberto; Fernandes, H. A.

2017-07-01

In this paper, we propose a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework that describes the transport in random systems by taking into account two different scenarios: particles can work as mobile obstacles, whereas particles of one species move in the opposite direction to the particles of the other species, or particles of a given species work as fixed obstacles remaining in their places during the time evolution. We conduct a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming are also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observe in our study the formation of patterns of lanes which reach the steady state regardless of the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principles modeling.

Light induced kickoff of magnetic domain walls in Ising chains

NASA Astrophysics Data System (ADS)

Bogani, Lapo

2012-02-01

Controlling the speed at which systems evolve is a challenge shared by all disciplines, and otherwise unrelated areas use common theoretical frameworks towards this goal. A particularly widespread model is Glauber dynamics, which describes the time evolution of the Ising model and can be applied to any binary system. Here we show, using molecular nanowires under irradiation, that Glauber dynamics can be controlled by a novel domain-wall kickoff mechanism. Contrary to known processes, the kickoff has unambiguous fingerprints, slowing down the spin-flip attempt rate by several orders of magnitude, and following a scaling law. The required irradiation power is very low, a substantial improvement over present methods of magnetooptical switching: in our experimental demonstration we switched molecular nanowires with light, using powers thousands of times lower than in previous optical switching methods. This manipulation of stochastic dynamic processes is extremely clean, leading to fingerprint signatures and scaling laws. These observations can be used, in material science, to better study domain-wall displacements and solitons in discrete lattices. These results provide a new way to control and study stochastic dynamic processes. Being general for Glauber dynamics, they can be extended to different kinds of magnetic nanowires and to a myriad of fields, ranging from social evolution to neural networks and chemical reactivity. For nanoelectronics and molecular spintronics the kickoff affords external control of molecular spin-valves and a magnetic fingerprint in single molecule measurements. It can also be applied to the dynamics of mechanical switches and the related study of phasons and order-disorder transitions.

Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

NASA Astrophysics Data System (ADS)

Tenkès, Lucille-Marie; Hollerbach, Rainer; Kim, Eun-jin

2017-12-01

A probabilistic description is essential for understanding growth processes in non-stationary states. In this paper, we compute time-dependent probability density functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models. We consider different types of short-correlated multiplicative and additive noise sources and compare the time-dependent PDFs in the two models, elucidating the effects of the additive and multiplicative noises on the form of PDFs. We demonstrate an interesting transition from a unimodal to a bimodal PDF as the multiplicative noise increases for a fixed value of the additive noise. A much weaker (leaky) attractor in the Gompertz model leads to a significant (singular) growth of the population of a very small size. We point out the limitation of using stationary PDFs, mean value and variance in understanding statistical properties of the growth in non-stationary states, highlighting the importance of time-dependent PDFs. We further compare these two models from the perspective of information change that occurs during the growth process. Specifically, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory quantifies the total number of different states that the system undergoes in time, and is called the information length. We show that the time-evolution of the two models become more similar when measured in units of the information length and point out the merit of using the information length in unifying and understanding the dynamic evolution of different growth processes.

Reconstructing quantum entropy production to probe irreversibility and correlations

NASA Astrophysics Data System (ADS)

Gherardini, Stefano; Müller, Matthias M.; Trombettoni, Andrea; Ruffo, Stefano; Caruso, Filippo

2018-07-01

One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.

Test-electron analysis of the magnetic reconnection topology

NASA Astrophysics Data System (ADS)

Borgogno, D.; Perona, A.; Grasso, D.

2017-12-01

Three-dimensional (3D) investigations of the magnetic reconnection field topology in space and laboratory plasmas have identified the abidance of magnetic coherent structures in the stochastic region, which develop during the nonlinear stage of the reconnection process. Further analytical and numerical analyses highlighted the efficacy of some of these structures in limiting the magnetic transport. The question then arises as to what is the possible role played by these patterns in the dynamics of the plasma particles populating the chaotic region. In order to explore this aspect, we provide a detailed description of the nonlinear 3D magnetic field topology in a collisionless magnetic reconnection event with a strong guide field. In parallel, we study the evolution of a population of test electrons in the guiding-center approximation all along the reconnection process. In particular, we focus on the nonlinear spatial redistribution of the initially thermal electrons and show how the electron dynamics in the stochastic region depends on the sign and on the value of their velocities. While the particles with the highest positive speed populate the coherent current structures that survive in the chaotic sea, the presence of the manifolds calculated in the stochastic region defines the confinement area for the electrons with the largest negative velocity. These results stress the link between the magnetic topology and the electron motion and contribute to the overall picture of a non-stationary fluid magnetic reconnection description in a geometry proper to physical systems where the effects of the curvature can be neglected.

Particle Acceleration in Mildly Relativistic Shearing Flows: The Interplay of Systematic and Stochastic Effects, and the Origin of the Extended High-energy Emission in AGN Jets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Ruo-Yu; Rieger, F. M.; Aharonian, F. A., E-mail: ruoyu@mpi-hd.mpg.de, E-mail: frank.rieger@mpi-hd.mpg.de, E-mail: aharon@mpi-hd.mpg.de

The origin of the extended X-ray emission in the large-scale jets of active galactic nuclei (AGNs) poses challenges to conventional models of acceleration and emission. Although electron synchrotron radiation is considered the most feasible radiation mechanism, the formation of the continuous large-scale X-ray structure remains an open issue. As astrophysical jets are expected to exhibit some turbulence and shearing motion, we here investigate the potential of shearing flows to facilitate an extended acceleration of particles and evaluate its impact on the resultant particle distribution. Our treatment incorporates systematic shear and stochastic second-order Fermi effects. We show that for typical parametersmore » applicable to large-scale AGN jets, stochastic second-order Fermi acceleration, which always accompanies shear particle acceleration, can play an important role in facilitating the whole process of particle energization. We study the time-dependent evolution of the resultant particle distribution in the presence of second-order Fermi acceleration, shear acceleration, and synchrotron losses using a simple Fokker–Planck approach and provide illustrations for the possible emergence of a complex (multicomponent) particle energy distribution with different spectral branches. We present examples for typical parameters applicable to large-scale AGN jets, indicating the relevance of the underlying processes for understanding the extended X-ray emission and the origin of ultrahigh-energy cosmic rays.« less

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

Minimum-noise production of translation factor eIF4G maps to a mechanistically determined optimal rate control window for protein synthesis

PubMed Central

Meng, Xiang; Firczuk, Helena; Pietroni, Paola; Westbrook, Richard; Dacheux, Estelle; Mendes, Pedro; McCarthy, John E.G.

2017-01-01

Gene expression noise influences organism evolution and fitness. The mechanisms determining the relationship between stochasticity and the functional role of translation machinery components are critical to viability. eIF4G is an essential translation factor that exerts strong control over protein synthesis. We observe an asymmetric, approximately bell-shaped, relationship between the average intracellular abundance of eIF4G and rates of cell population growth and global mRNA translation, with peak rates occurring at normal physiological abundance. This relationship fits a computational model in which eIF4G is at the core of a multi-component–complex assembly pathway. This model also correctly predicts a plateau-like response of translation to super-physiological increases in abundance of the other cap-complex factors, eIF4E and eIF4A. Engineered changes in eIF4G abundance amplify noise, demonstrating that minimum stochasticity coincides with physiological abundance of this factor. Noise is not increased when eIF4E is overproduced. Plasmid-mediated synthesis of eIF4G imposes increased global gene expression stochasticity and reduced viability because the intrinsic noise for this factor influences total cellular gene noise. The naturally evolved eIF4G gene expression noise minimum maps within the optimal activity zone dictated by eIF4G's mechanistic role. Rate control and noise are therefore interdependent and have co-evolved to share an optimal physiological abundance point. PMID:27928055

Emergent irreversibility and entanglement spectrum statistics

NASA Astrophysics Data System (ADS)

Mucciolo, Eduardo; Chamon, Claudio; Hamma, Alioscia

2014-03-01

We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than Hamitonian, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wavefunction level and offers a new route to study quantum chaos and quantum integrability. We acknowledge financial support from the U.S. National Science Foundation through grants CCF 1116590 and CCF 1117241, from the National Basic Research Program of China through grants 2011CBA00300 and 2011CBA00301, and from the National Natural Science Fo.

Aerodynamic optimization of supersonic compressor cascade using differential evolution on GPU

NASA Astrophysics Data System (ADS)

Aissa, Mohamed Hasanine; Verstraete, Tom; Vuik, Cornelis

2016-06-01

Differential Evolution (DE) is a powerful stochastic optimization method. Compared to gradient-based algorithms, DE is able to avoid local minima but requires at the same time more function evaluations. In turbomachinery applications, function evaluations are performed with time-consuming CFD simulation, which results in a long, non affordable, design cycle. Modern High Performance Computing systems, especially Graphic Processing Units (GPUs), are able to alleviate this inconvenience by accelerating the design evaluation itself. In this work we present a validated CFD Solver running on GPUs, able to accelerate the design evaluation and thus the entire design process. An achieved speedup of 20x to 30x enabled the DE algorithm to run on a high-end computer instead of a costly large cluster. The GPU-enhanced DE was used to optimize the aerodynamics of a supersonic compressor cascade, achieving an aerodynamic loss minimization of 20%.

Fixation of slightly beneficial mutations: effects of life history.

PubMed

Vindenes, Yngvild; Lee, Aline Magdalena; Engen, Steinar; Saether, Bernt-Erik

2010-04-01

Recent studies of rates of evolution have revealed large systematic differences among organisms with different life histories, both within and among taxa. Here, we consider how life history may affect the rate of evolution via its influence on the fixation probability of slightly beneficial mutations. Our approach is based on diffusion modeling for a finite, stage-structured population with stochastic population dynamics. The results, which are verified by computer simulations, demonstrate that even with complex population structure just two demographic parameters are sufficient to give an accurate approximation of the fixation probability of a slightly beneficial mutation. These are the reproductive value of the stage in which the mutation first occurs and the demographic variance of the population. The demographic variance also determines what influence population size has on the fixation probability. This model represents a substantial generalization of earlier models, covering a large range of life histories.

The Origin and Evolution of the Galaxy Star Formation Rate-Stellar Mass Correlation

NASA Astrophysics Data System (ADS)

Gawiser, Eric; Iyer, Kartheik

2018-01-01

The existence of a tight correlation between galaxies’ star formation rates and stellar masses is far more surprising than usually noted. However, a simple analytical calculation illustrates that the evolution of the normalization of this correlation is driven primarily by the inverse age of the universe, and that the underlying correlation is one between galaxies’ instantaneous star formation rates and their average star formation rates since the Big Bang.Our new Dense Basis method of SED fitting (Iyer & Gawiser 2017, ApJ 838, 127) allows star formation histories (SFHs) to be reconstructed, along with uncertainties, for >10,000 galaxies in the CANDELS and 3D-HST catalogs at 0.5

Modeling Day-to-day Flow Dynamics on Degradable Transport Network

PubMed Central

Gao, Bo; Zhang, Ronghui; Lou, Xiaoming

2016-01-01

Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties. PMID:27959903

Dynamic control of magnetic nanowires by light-induced domain-wall kickoffs

NASA Astrophysics Data System (ADS)

Heintze, Eric; El Hallak, Fadi; Clauß, Conrad; Rettori, Angelo; Pini, Maria Gloria; Totti, Federico; Dressel, Martin; Bogani, Lapo

2013-03-01

Controlling the speed at which systems evolve is a challenge shared by all disciplines, and otherwise unrelated areas use common theoretical frameworks towards this goal. A particularly widespread model is Glauber dynamics, which describes the time evolution of the Ising model and can be applied to any binary system. Here we show, using molecular nanowires under irradiation, that Glauber dynamics can be controlled by a novel domain-wall kickoff mechanism. In contrast to known processes, the kickoff has unambiguous fingerprints, slowing down the spin-flip attempt rate by several orders of magnitude, and following a scaling law. The required irradiance is very low, a substantial improvement over present methods of magneto-optical switching. These results provide a new way to control and study stochastic dynamic processes. Being general for Glauber dynamics, they can be extended to different kinds of magnetic nanowires and to numerous fields, ranging from social evolution to neural networks and chemical reactivity.

Aerodynamic optimization of supersonic compressor cascade using differential evolution on GPU

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aissa, Mohamed Hasanine; Verstraete, Tom; Vuik, Cornelis

Differential Evolution (DE) is a powerful stochastic optimization method. Compared to gradient-based algorithms, DE is able to avoid local minima but requires at the same time more function evaluations. In turbomachinery applications, function evaluations are performed with time-consuming CFD simulation, which results in a long, non affordable, design cycle. Modern High Performance Computing systems, especially Graphic Processing Units (GPUs), are able to alleviate this inconvenience by accelerating the design evaluation itself. In this work we present a validated CFD Solver running on GPUs, able to accelerate the design evaluation and thus the entire design process. An achieved speedup of 20xmore » to 30x enabled the DE algorithm to run on a high-end computer instead of a costly large cluster. The GPU-enhanced DE was used to optimize the aerodynamics of a supersonic compressor cascade, achieving an aerodynamic loss minimization of 20%.« less

Critical behavior in a stochastic model of vector mediated epidemics

PubMed Central

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-01-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation. PMID:27264105

The role of the airline transportation network in the prediction and predictability of global epidemics.

PubMed

Colizza, Vittoria; Barrat, Alain; Barthélemy, Marc; Vespignani, Alessandro

2006-02-14

The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large-scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this article, we present a stochastic computational framework for the forecast of global epidemics that considers the complete worldwide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: (i) we study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; and (ii) we evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. To address these issues we define a set of quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation A2 term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

Optimum Damping in a Non-Linear Base Isolation System

NASA Astrophysics Data System (ADS)

Jangid, R. S.

1996-02-01

Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.

Stochastic modeling and experimental analysis of phenotypic switching and survival of cancer cells under stress

NASA Astrophysics Data System (ADS)

Zamani Dahaj, Seyed Alireza; Kumar, Niraj; Sundaram, Bala; Celli, Jonathan; Kulkarni, Rahul

The phenotypic heterogeneity of cancer cells is critical to their survival under stress. A significant contribution to heterogeneity of cancer calls derives from the epithelial-mesenchymal transition (EMT), a conserved cellular program that is crucial for embryonic development. Several studies have investigated the role of EMT in growth of early stage tumors into invasive malignancies. Also, EMT has been closely associated with the acquisition of chemoresistance properties in cancer cells. Motivated by these studies, we analyze multi-phenotype stochastic models of the evolution of cancers cell populations under stress. We derive analytical results for time-dependent probability distributions that provide insights into the competing rates underlying phenotypic switching (e.g. during EMT) and the corresponding survival of cancer cells. Experimentally, we evaluate these model-based predictions by imaging human pancreatic cancer cell lines grown with and without cytotoxic agents and measure growth kinetics, survival, morphological changes and (terminal evaluation of) biomarkers with associated epithelial and mesenchymal phenotypes. The results derived suggest approaches for distinguishing between adaptation and selection scenarios for survival in the presence of external stresses.

Revisiting node-based SIR models in complex networks with degree correlations

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alofi, Abdulaziz; AL-Mazrooei, Abdullah; Elaiw, Ahmed

2015-11-01

In this paper, we consider two growing networks which will lead to the degree-degree correlations between two nearest neighbors in the network. When the network grows to some certain size, we introduce an SIR-like disease such as pandemic influenza H1N1/09 to the population. Due to its rapid spread, the population size changes slowly, and thus the disease spreads on correlated networks with approximately fixed size. To predict the disease evolution on correlated networks, we first review two node-based SIR models incorporating degree correlations and an edge-based SIR model without considering degree correlation, and then compare the predictions of these models with stochastic SIR simulations, respectively. We find that the edge-based model, even without considering degree correlations, agrees much better than the node-based models incorporating degree correlations with stochastic SIR simulations in many respects. Moreover, simulation results show that for networks with positive correlation, the edge-based model provides a better upper bound of the cumulative incidence than the node-based SIR models, whereas for networks with negative correlation, it provides a lower bound of the cumulative incidence.

FAST: a framework for simulation and analysis of large-scale protein-silicon biosensor circuits.

PubMed

Gu, Ming; Chakrabartty, Shantanu

2013-08-01

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Enhancing the branching ratios in the dissociation channels for O{sup 16}O{sup 16}O{sup 18} molecule by designing optimum laser pulses: A study using stochastic optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Talukder, Srijeeta; Chaudhury, Pinaki, E-mail: pinakc@rediffmail.com; Sen, Shrabani

We propose a strategy of using a stochastic optimization technique, namely, simulated annealing to design optimum laser pulses (both IR and UV) to achieve greater fluxes along the two dissociating channels (O{sup 18} + O{sup 16}O{sup 16} and O{sup 16} + O{sup 16}O{sup 18}) in O{sup 16}O{sup 16}O{sup 18} molecule. We show that the integrated fluxes obtained along the targeted dissociating channel is larger with the optimized pulse than with the unoptimized one. The flux ratios are also more impressive with the optimized pulse than with the unoptimized one. We also look at the evolution contours of the wavefunctions alongmore » the two channels with time after the actions of both the IR and UV pulses and compare the profiles for unoptimized (initial) and optimized fields for better understanding the results that we achieve. We also report the pulse parameters obtained as well as the final shapes they take.« less

Systems Reliability Framework for Surface Water Sustainability and Risk Management

NASA Astrophysics Data System (ADS)

Myers, J. R.; Yeghiazarian, L.

2016-12-01

With microbial contamination posing a serious threat to the availability of clean water across the world, it is necessary to develop a framework that evaluates the safety and sustainability of water systems in respect to non-point source fecal microbial contamination. The concept of water safety is closely related to the concept of failure in reliability theory. In water quality problems, the event of failure can be defined as the concentration of microbial contamination exceeding a certain standard for usability of water. It is pertinent in watershed management to know the likelihood of such an event of failure occurring at a particular point in space and time. Microbial fate and transport are driven by environmental processes taking place in complex, multi-component, interdependent environmental systems that are dynamic and spatially heterogeneous, which means these processes and therefore their influences upon microbial transport must be considered stochastic and variable through space and time. A physics-based stochastic model of microbial dynamics is presented that propagates uncertainty using a unique sampling method based on artificial neural networks to produce a correlation between watershed characteristics and spatial-temporal probabilistic patterns of microbial contamination. These results are used to address the question of water safety through several sustainability metrics: reliability, vulnerability, resilience and a composite sustainability index. System reliability is described uniquely though the temporal evolution of risk along watershed points or pathways. Probabilistic resilience describes how long the system is above a certain probability of failure, and the vulnerability metric describes how the temporal evolution of risk changes throughout a hierarchy of failure levels. Additionally our approach allows for the identification of contributions in microbial contamination and uncertainty from specific pathways and sources. We expect that this framework will significantly improve the efficiency and precision of sustainable watershed management strategies through providing a better understanding of how watershed characteristics and environmental parameters affect surface water quality and sustainability. With microbial contamination posing a serious threat to the availability of clean water across the world, it is necessary to develop a framework that evaluates the safety and sustainability of water systems in respect to non-point source fecal microbial contamination. The concept of water safety is closely related to the concept of failure in reliability theory. In water quality problems, the event of failure can be defined as the concentration of microbial contamination exceeding a certain standard for usability of water. It is pertinent in watershed management to know the likelihood of such an event of failure occurring at a particular point in space and time. Microbial fate and transport are driven by environmental processes taking place in complex, multi-component, interdependent environmental systems that are dynamic and spatially heterogeneous, which means these processes and therefore their influences upon microbial transport must be considered stochastic and variable through space and time. A physics-based stochastic model of microbial dynamics is presented that propagates uncertainty using a unique sampling method based on artificial neural networks to produce a correlation between watershed characteristics and spatial-temporal probabilistic patterns of microbial contamination. These results are used to address the question of water safety through several sustainability metrics: reliability, vulnerability, resilience and a composite sustainability index. System reliability is described uniquely though the temporal evolution of risk along watershed points or pathways. Probabilistic resilience describes how long the system is above a certain probability of failure, and the vulnerability metric describes how the temporal evolution of risk changes throughout a hierarchy of failure levels. Additionally our approach allows for the identification of contributions in microbial contamination and uncertainty from specific pathways and sources. We expect that this framework will significantly improve the efficiency and precision of sustainable watershed management strategies through providing a better understanding of how watershed characteristics and environmental parameters affect surface water quality and sustainability.

TTLEM: Open access tool for building numerically accurate landscape evolution models in MATLAB

NASA Astrophysics Data System (ADS)

Campforts, Benjamin; Schwanghart, Wolfgang; Govers, Gerard

2017-04-01

Despite a growing interest in LEMs, accuracy assessment of the numerical methods they are based on has received little attention. Here, we present TTLEM which is an open access landscape evolution package designed to develop and test your own scenarios and hypothesises. TTLEM uses a higher order flux-limiting finite-volume method to simulate river incision and tectonic displacement. We show that this scheme significantly influences the evolution of simulated landscapes and the spatial and temporal variability of erosion rates. Moreover, it allows the simulation of lateral tectonic displacement on a fixed grid. Through the use of a simple GUI the software produces visible output of evolving landscapes through model run time. In this contribution, we illustrate numerical landscape evolution through a set of movies spanning different spatial and temporal scales. We focus on the erosional domain and use both spatially constant and variable input values for uplift, lateral tectonic shortening, erodibility and precipitation. Moreover, we illustrate the relevance of a stochastic approach for realistic hillslope response modelling. TTLEM is a fully open source software package, written in MATLAB and based on the TopoToolbox platform (topotoolbox.wordpress.com). Installation instructions can be found on this website and the therefore designed GitHub repository.

Ecological specialization and morphological diversification in Greater Antillean boas.

PubMed

Reynolds, R Graham; Collar, David C; Pasachnik, Stesha A; Niemiller, Matthew L; Puente-Rolón, Alberto R; Revell, Liam J

2016-08-01

Colonization of islands can dramatically influence the evolutionary trajectories of organisms, with both deterministic and stochastic processes driving adaptation and diversification. Some island colonists evolve extremely large or small body sizes, presumably in response to unique ecological circumstances present on islands. One example of this phenomenon, the Greater Antillean boas, includes both small (<90 cm) and large (4 m) species occurring on the Greater Antilles and Bahamas, with some islands supporting pairs or trios of body-size divergent species. These boas have been shown to comprise a monophyletic radiation arising from a Miocene dispersal event to the Greater Antilles, though it is not known whether co-occurrence of small and large species is a result of dispersal or in situ evolution. Here, we provide the first comprehensive species phylogeny for this clade combined with morphometric and ecological data to show that small body size evolved repeatedly on separate islands in association with specialization in substrate use. Our results further suggest that microhabitat specialization is linked to increased rates of head shape diversification among specialists. Our findings show that ecological specialization following island colonization promotes morphological diversity through deterministic body size evolution and cranial morphological diversification that is contingent on island- and species-specific factors. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.

Biological evolution of replicator systems: towards a quantitative approach.

PubMed

Martin, Osmel; Horvath, J E

2013-04-01

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312-316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth's geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Biological Evolution of Replicator Systems: Towards a Quantitative Approach

NASA Astrophysics Data System (ADS)

Martin, Osmel; Horvath, J. E.

2013-04-01

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312-316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth's geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Effects of adaptive dynamical linking in networked games

NASA Astrophysics Data System (ADS)

Yang, Zhihu; Li, Zhi; Wu, Te; Wang, Long

2013-10-01

The role of dynamical topologies in the evolution of cooperation has received considerable attention, as some studies have demonstrated that dynamical networks are much better than static networks in terms of boosting cooperation. Here we study a dynamical model of evolution of cooperation on stochastic dynamical networks in which there are no permanent partners to each agent. Whenever a new link is created, its duration is randomly assigned without any bias or preference. We allow the agent to adaptively adjust the duration of each link during the evolution in accordance with the feedback from game interactions. By Monte Carlo simulations, we find that cooperation can be remarkably promoted by this adaptive dynamical linking mechanism both for the game of pairwise interactions, such as the Prisoner's Dilemma game (PDG), and for the game of group interactions, illustrated by the public goods game (PGG). And the faster the adjusting rate, the more successful the evolution of cooperation. We also show that in this context weak selection favors cooperation much more than strong selection does. What is particularly meaningful is that the prosperity of cooperation in this study indicates that the rationality and selfishness of a single agent in adjusting social ties can lead to the progress of altruism of the whole population.

Multi-Topic Tracking Model for dynamic social network

NASA Astrophysics Data System (ADS)

Li, Yuhua; Liu, Changzheng; Zhao, Ming; Li, Ruixuan; Xiao, Hailing; Wang, Kai; Zhang, Jun

2016-07-01

The topic tracking problem has attracted much attention in the last decades. However, existing approaches rarely consider network structures and textual topics together. In this paper, we propose a novel statistical model based on dynamic bayesian network, namely Multi-Topic Tracking Model for Dynamic Social Network (MTTD). It takes influence phenomenon, selection phenomenon, document generative process and the evolution of textual topics into account. Specifically, in our MTTD model, Gibbs Random Field is defined to model the influence of historical status of users in the network and the interdependency between them in order to consider the influence phenomenon. To address the selection phenomenon, a stochastic block model is used to model the link generation process based on the users' interests to topics. Probabilistic Latent Semantic Analysis (PLSA) is used to describe the document generative process according to the users' interests. Finally, the dependence on the historical topic status is also considered to ensure the continuity of the topic itself in topic evolution model. Expectation Maximization (EM) algorithm is utilized to estimate parameters in the proposed MTTD model. Empirical experiments on real datasets show that the MTTD model performs better than Popular Event Tracking (PET) and Dynamic Topic Model (DTM) in generalization performance, topic interpretability performance, topic content evolution and topic popularity evolution performance.

On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

NASA Astrophysics Data System (ADS)

Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

2012-04-01

The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

Multi-Scale Modeling of the Gamma Radiolysis of Nitrate Solutions.

PubMed

Horne, Gregory P; Donoclift, Thomas A; Sims, Howard E; Orr, Robin M; Pimblott, Simon M

2016-11-17

A multiscale modeling approach has been developed for the extended time scale long-term radiolysis of aqueous systems. The approach uses a combination of stochastic track structure and track chemistry as well as deterministic homogeneous chemistry techniques and involves four key stages: radiation track structure simulation, the subsequent physicochemical processes, nonhomogeneous diffusion-reaction kinetic evolution, and homogeneous bulk chemistry modeling. The first three components model the physical and chemical evolution of an isolated radiation chemical track and provide radiolysis yields, within the extremely low dose isolated track paradigm, as the input parameters for a bulk deterministic chemistry model. This approach to radiation chemical modeling has been tested by comparison with the experimentally observed yield of nitrite from the gamma radiolysis of sodium nitrate solutions. This is a complex radiation chemical system which is strongly dependent on secondary reaction processes. The concentration of nitrite is not just dependent upon the evolution of radiation track chemistry and the scavenging of the hydrated electron and its precursors but also on the subsequent reactions of the products of these scavenging reactions with other water radiolysis products. Without the inclusion of intratrack chemistry, the deterministic component of the multiscale model is unable to correctly predict experimental data, highlighting the importance of intratrack radiation chemistry in the chemical evolution of the irradiated system.

Correction to verdonck and tuerlinckx (2014).

PubMed

2015-01-01

Reports an error in "The Ising Decision Maker: A binary stochastic network for choice response time" by Stijn Verdonck and Francis Tuerlinckx (Psychological Review, 2014[Jul], Vol 121[3], 422-462). An inaccurate assumption in Appendix B (provided in the erratum) led to an oversimplified result in Equation 18 (the diffusion equations associated with the microscopically defined dynamics). The authors sincerely thank Rani Moran for making them aware of the problem. Only the expression of the diffusion coefficient D is incorrect, and should be changed, as indicated in the erratum. Both the cause of the problem and the solution are also explained in the erratum. (The following abstract of the original article appeared in record 2014-31650-006.) The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Climate and weather across scales: singularities and stochastic Levy-Clifford algebra

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127.