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.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

Extended forms of the second law for general time-dependent stochastic processes.

PubMed

Ge, Hao

2009-08-01

The second law of thermodynamics represents a universal principle applicable to all natural processes, physical systems, and engineering devices. Hatano and Sasa have recently put forward an extended form of the second law for transitions between nonequilibrium stationary states [Phys. Rev. Lett. 86, 3463 (2001)]. In this paper we further extend this form to an instantaneous interpretation, which is satisfied by quite general time-dependent stochastic processes including master-equation models and Langevin dynamics without the requirements of the stationarity for the initial and final states. The theory is applied to several thermodynamic processes, and its consistence with the classical thermodynamics is shown.

Effective stochastic generator with site-dependent interactions

NASA Astrophysics Data System (ADS)

Khamehchi, Masoumeh; Jafarpour, Farhad H.

2017-11-01

It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper, we investigate this possibility by considering systems of classical particles moving on a one-dimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process, or there can be many arbitrary particles at a single site in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of an unconditioned process can be local but site-dependent. As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above-mentioned constraints.

A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

NASA Astrophysics Data System (ADS)

Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

2018-02-01

The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.

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.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

Experimentally modeling stochastic processes with less memory by the use of a quantum processor

PubMed Central

Palsson, Matthew S.; Gu, Mile; Ho, Joseph; Wiseman, Howard M.; Pryde, Geoff J.

2017-01-01

Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. However, the most interesting systems are often so complex that simulating their future behavior demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows that quantum theory can reduce this memory requirement beyond ultimate classical limits, as measured by a process’ statistical complexity, C. We experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of Cq = 0.05 ± 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulations of more complex systems. PMID:28168218

Physical Models of Cognition

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.

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.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type

NASA Astrophysics Data System (ADS)

Scarpa, Luca

2017-08-01

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form dXt - div γ (∇Xt) dt + β (Xt) dt ∋ B (t ,Xt) dWt, where γ and β are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on Rd and R respectively, and W is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray-Lions conditions on γ and with no restrictive smoothness or growth assumptions on β. The operator B is assumed to be Hilbert-Schmidt and to satisfy some classical Lipschitz conditions in the second variable.

Stochastic goal-oriented error estimation with memory

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Marotzke, Jochem; Korn, Peter

2017-11-01

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

Open Quantum Systems and Classical Trajectories

NASA Astrophysics Data System (ADS)

Rebolledo, Rolando

2004-09-01

A Quantum Markov Semigroup consists of a family { T} = ({ T}t)_{t ∈ B R+} of normal ω*- continuous completely positive maps on a von Neumann algebra 𝔐 which preserve the unit and satisfy the semigroup property. This class of semigroups has been extensively used to represent open quantum systems. This article is aimed at studying the existence of a { T} -invariant abelian subalgebra 𝔄 of 𝔐. When this happens, the restriction of { T}t to 𝔄 defines a classical Markov semigroup T = (Tt)t ∈ ∝ + say, associated to a classical Markov process X = (Xt)t ∈ ∝ +. The structure (𝔄, T, X) unravels the quantum Markov semigroup { T} , providing a bridge between open quantum systems and classical stochastic processes.

Bridging Quantum, Classical and Stochastic Shortcuts to Adiabaticity

NASA Astrophysics Data System (ADS)

Patra, Ayoti

Adiabatic invariants - quantities that are preserved under the slow driving of a system's external parameters - are important in classical mechanics, quantum mechanics and thermodynamics. Adiabatic processes allow a system to be guided to evolve to a desired final state. However, the slow driving of a quantum system makes it vulnerable to environmental decoherence, and for both quantum and classical systems, it is often desirable and time-efficient to speed up a process. Shortcuts to adiabaticity are strategies for preserving adiabatic invariants under rapid driving, typically by means of an auxiliary field that suppresses excitations, otherwise generated during rapid driving. Several theoretical approaches have been developed to construct such shortcuts. In this dissertation we focus on two different approaches, namely counterdiabatic driving and fast-forward driving, which were originally developed for quantum systems. The counterdiabatic approach introduced independently by Dermirplak and Rice [J. Phys. Chem. A, 107:9937, 2003], and Berry [J. Phys. A: Math. Theor., 42:365303, 2009] formally provides an exact expression for the auxiliary Hamiltonian, which however is abstract and difficult to translate into an experimentally implementable form. By contrast, the fast-forward approach developed by Masuda and Nakamura [Proc. R. Soc. A, 466(2116):1135, 2010] provides an auxiliary potential that may be experimentally implementable but generally applies only to ground states. The central theme of this dissertation is that classical shortcuts to adiabaticity can provide useful physical insights and lead to experimentally implementable shortcuts for analogous quantum systems. We start by studying a model system of a tilted piston to provide a proof of principle that quantum shortcuts can successfully be constructed from their classical counterparts. In the remainder of the dissertation, we develop a general approach based on flow-fields which produces simple expressions for auxiliary terms required for both counterdiabatic and fast-forward driving. We demonstrate the applicability of this approach for classical, quantum as well as stochastic systems. We establish strong connections between counterdiabatic and fast-forward approaches, and also between shortcut protocols required for classical, quantum and stochastic systems. In particular, we show how the fast-forward approach can be extended to highly excited states of quantum systems.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Representation of Reserves Through a Brownian Motion Model

NASA Astrophysics Data System (ADS)

Andrade, M.; Ferreira, M. A. M.; Filipe, J. A.

2012-11-01

The Brownian Motion is commonly used as an approximation for some Random Walks and also for the Classic Risk Process. As the Random Walks and the Classic Risk Process are used frequently as stochastic models to represent reserves, it is natural to consider the Brownian Motion with the same purpose. In this study a model, based on the Brownian Motion, is presented to represent reserves. The Brownian Motion is used in this study to estimate the ruin probability of a fund. This kind of models is considered often in the study of pensions funds.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

NASA Astrophysics Data System (ADS)

Grain, Julien; Vennin, Vincent

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ``slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

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.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

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

Grain, Julien; Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue.more » The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.« less

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

NASA Astrophysics Data System (ADS)

Lorenzen, F.; de Ponte, M. A.; Moussa, M. H. Y.

2009-09-01

In this paper, employing the Itô stochastic Schrödinger equation, we extend Bell’s beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm’s causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm’s causal dynamics regarding stationary states in quantum mechanics.

Universal ideal behavior and macroscopic work relation of linear irreversible stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Ma, Yi-An; Qian, Hong

2015-06-01

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic ‘equation of state’ of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.

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.

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

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 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.

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.

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments

PubMed Central

Collignon, Bertrand; Séguret, Axel; Halloy, José

2016-01-01

Collective motion is one of the most ubiquitous behaviours displayed by social organisms and has led to the development of numerous models. Recent advances in the understanding of sensory system and information processing by animals impels one to revise classical assumptions made in decisional algorithms. In this context, we present a model describing the three-dimensional visual sensory system of fish that adjust their trajectory according to their perception field. Furthermore, we introduce a stochastic process based on a probability distribution function to move in targeted directions rather than on a summation of influential vectors as is classically assumed by most models. In parallel, we present experimental results of zebrafish (alone or in group of 10) swimming in both homogeneous and heterogeneous environments. We use these experimental data to set the parameter values of our model and show that this perception-based approach can simulate the collective motion of species showing cohesive behaviour in heterogeneous environments. Finally, we discuss the advances of this multilayer model and its possible outcomes in biological, physical and robotic sciences. PMID:26909173

Stochastic Kuramoto oscillators with discrete phase states.

PubMed

Jörg, David J

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

Stochastic Kuramoto oscillators with discrete phase states

NASA Astrophysics Data System (ADS)

Jörg, David J.

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

Approximation methods of European option pricing in multiscale stochastic volatility model

NASA Astrophysics Data System (ADS)

Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.

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.

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.

Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel.

PubMed

Mahoney, John R; Aghamohammadi, Cina; Crutchfield, James P

2016-02-15

A stochastic process' statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process' cryptic order--a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost-one trades off prediction for generation complexity.

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.

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.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

NASA Astrophysics Data System (ADS)

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-10-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

PubMed Central

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-01-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype. PMID:27786253

Effects of fuel cetane number on the structure of diesel spray combustion: An accelerated Eulerian stochastic fields method

NASA Astrophysics Data System (ADS)

Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song

2015-09-01

An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.

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.

An application of information theory to stochastic classical gravitational fields

NASA Astrophysics Data System (ADS)

Angulo, J.; Angulo, J. C.; Angulo, J. M.

2018-06-01

The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

Probabilistic measures of persistence and extinction in measles (meta)populations.

PubMed

Gunning, Christian E; Wearing, Helen J

2013-08-01

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre-vaccine era US cities, alongside a classic England & Wales data set. We first infer the per-population quasi-continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium-sized populations in metapopulation persistence. © 2013 John Wiley & Sons Ltd/CNRS.

Rayleigh instability at small length scales.

PubMed

Gopan, Nandu; Sathian, Sarith P

2014-09-01

The Rayleigh instability (also called the Plateau-Rayleigh instability) of a nanosized liquid propane thread is investigated using molecular dynamics (MD). The validity of classical predictions at small length scales is verified by comparing the temporal evolution of liquid thread simulated by MD against classical predictions. Previous works have shown that thermal fluctuations become dominant at small length scales. The role and influence of the stochastic nature of thermal fluctuations in determining the instability at small length scale is also investigated. Thermal fluctuations are seen to dominate and accelerate the breakup process only during the last stages of breakup. The simulations also reveal that the breakup profile of nanoscale threads undergo modification due to reorganization of molecules by the evaporation-condensation process.

The Sharma-Parthasarathy stochastic two-body problem

NASA Astrophysics Data System (ADS)

Cresson, J.; Pierret, F.; Puig, B.

2015-03-01

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in ["Dynamics of a stochastically perturbed two-body problem," Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.

Analytical determination of the heat transfer coefficient for gas, liquid and liquid metal flows in the tube based on stochastic equations and equivalence of measures for continuum

NASA Astrophysics Data System (ADS)

Dmitrenko, Artur V.

2017-11-01

The stochastic equations of continuum are used for determining the heat transfer coefficients. As a result, the formulas for Nusselt (Nu) number dependent on the turbulence intensity and scale instead of only on the Reynolds (Peclet) number are proposed for the classic flows of a nonisothermal fluid in a round smooth tube. It is shown that the new expressions for the classical heat transfer coefficient Nu, which depend only on the Reynolds number, should be obtained from these new general formulas if to use the well-known experimental data for the initial turbulence. It is found that the limitations of classical empirical and semiempirical formulas for heat transfer coefficients and their deviation from the experimental data depend on different parameters of initial fluctuations in the flow for different experiments in a wide range of Reynolds or Peclet numbers. Based on these new dependences, it is possible to explain that the differences between the experimental results for the fixed Reynolds or Peclet numbers are caused by the difference in values of flow fluctuations for each experiment instead of only due to the systematic error in the experiment processing. Accordingly, the obtained general dependences of Nu for a smooth round tube can serve as the basis for clarifying the experimental results and empirical formulas used for continuum flows in various power devices. Obtained results show that both for isothermal and for nonisothermal flows, the reason for the process of transition from a deterministic state into a turbulent one is determined by the physical law of equivalence of measures between them. Also the theory of stochastic equations and the law of equivalence of measures could determine mechanics which is basis in different phenomena of self-organization and chaos theory.

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets.

PubMed

Chen, Jiao; Weihs, Daphne; Vermolen, Fred J

2018-04-01

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler-Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.

Asymmetric and Stochastic Behavior in Magnetic Vortices Studied by Soft X-ray Microscopy

NASA Astrophysics Data System (ADS)

Im, Mi-Young

Asymmetry and stochasticity in spin processes are not only long-standing fundamental issues but also highly relevant to technological applications of nanomagnetic structures to memory and storage nanodevices. Those nontrivial phenomena have been studied by direct imaging of spin structures in magnetic vortices utilizing magnetic transmission soft x-ray microscopy (BL6.1.2 at ALS). Magnetic vortices have attracted enormous scientific interests due to their fascinating spin structures consisting of circularity rotating clockwise (c = + 1) or counter-clockwise (c = -1) and polarity pointing either up (p = + 1) or down (p = -1). We observed a symmetry breaking in the formation process of vortex structures in circular permalloy (Ni80Fe20) disks. The generation rates of two different vortex groups with the signature of cp = + 1 and cp =-1 are completely asymmetric. The asymmetric nature was interpreted to be triggered by ``intrinsic'' Dzyaloshinskii-Moriya interaction (DMI) arising from the spin-orbit coupling due to the lack of inversion symmetry near the disk surface and ``extrinsic'' factors such as roughness and defects. We also investigated the stochastic behavior of vortex creation in the arrays of asymmetric disks. The stochasticity was found to be very sensitive to the geometry of disk arrays, particularly interdisk distance. The experimentally observed phenomenon couldn't be explained by thermal fluctuation effect, which has been considered as a main reason for the stochastic behavior in spin processes. We demonstrated for the first time that the ultrafast dynamics at the early stage of vortex creation, which has a character of classical chaos significantly affects the stochastic nature observed at the steady state in asymmetric disks. This work provided the new perspective of dynamics as a critical factor contributing to the stochasticity in spin processes and also the possibility for the control of the intrinsic stochastic nature by optimizing the design of asymmetric disk arrays. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, by Leading Foreign Research Institute Recruitment Program through the NRF.

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.

Hidden Statistics of Schroedinger Equation

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Stochastic models to study the impact of mixing on a fed-batch culture of Saccharomyces cerevisiae.

PubMed

Delvigne, F; Lejeune, A; Destain, J; Thonart, P

2006-01-01

The mechanisms of interaction between microorganisms and their environment in a stirred bioreactor can be modeled by a stochastic approach. The procedure comprises two submodels: a classical stochastic model for the microbial cell circulation and a Markov chain model for the concentration gradient calculus. The advantage lies in the fact that the core of each submodel, i.e., the transition matrix (which contains the probabilities to shift from a perfectly mixed compartment to another in the bioreactor representation), is identical for the two cases. That means that both the particle circulation and fluid mixing process can be analyzed by use of the same modeling basis. This assumption has been validated by performing inert tracer (NaCl) and stained yeast cells dispersion experiments that have shown good agreement with simulation results. The stochastic model has been used to define a characteristic concentration profile experienced by the microorganisms during a fermentation test performed in a scale-down reactor. The concentration profiles obtained in this way can explain the scale-down effect in the case of a Saccharomyces cerevisiae fed-batch process. The simulation results are analyzed in order to give some explanations about the effect of the substrate fluctuation dynamics on S. cerevisiae.

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

NASA Astrophysics Data System (ADS)

Holubec, Viktor; Novotný, Tomáš

2018-05-01

We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced performance is observed already for the effectively classical systems, with no significant qualitative change in the quantum cases, which suggests that the noise-induced-coherence-enhancement mechanism is caused by static interference phenomena.

The Sharma-Parthasarathy stochastic two-body problem

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

Cresson, J.; SYRTE/Observatoire de Paris, 75014 Paris; Pierret, F.

2015-03-15

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Occam’s Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel

NASA Astrophysics Data System (ADS)

Mahoney, John R.; Aghamohammadi, Cina; Crutchfield, James P.

2016-02-01

A stochastic process’ statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process’ cryptic order-a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost-one trades off prediction for generation complexity.

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

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

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

Rényi entropy measure of noise-aided information transmission in a binary channel.

PubMed

Chapeau-Blondeau, François; Rousseau, David; Delahaies, Agnès

2010-05-01

This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise-aided binary image transmission.

A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis

PubMed Central

Refahi, Yassin; Brunoud, Géraldine; Farcot, Etienne; Jean-Marie, Alain; Pulkkinen, Minna; Vernoux, Teva; Godin, Christophe

2016-01-01

Exploration of developmental mechanisms classically relies on analysis of pattern regularities. Whether disorders induced by biological noise may carry information on building principles of developmental systems is an important debated question. Here, we addressed theoretically this question using phyllotaxis, the geometric arrangement of plant aerial organs, as a model system. Phyllotaxis arises from reiterative organogenesis driven by lateral inhibitions at the shoot apex. Motivated by recurrent observations of disorders in phyllotaxis patterns, we revisited in depth the classical deterministic view of phyllotaxis. We developed a stochastic model of primordia initiation at the shoot apex, integrating locality and stochasticity in the patterning system. This stochastic model recapitulates phyllotactic patterns, both regular and irregular, and makes quantitative predictions on the nature of disorders arising from noise. We further show that disorders in phyllotaxis instruct us on the parameters governing phyllotaxis dynamics, thus that disorders can reveal biological watermarks of developmental systems. DOI: http://dx.doi.org/10.7554/eLife.14093.001 PMID:27380805

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

NASA Astrophysics Data System (ADS)

Deng, M. L.; Zhu, W. Q.

2007-10-01

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Itô stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Knowledge-based processing for aircraft flight control

NASA Technical Reports Server (NTRS)

Painter, John H.; Glass, Emily; Economides, Gregory; Russell, Paul

1994-01-01

This Contractor Report documents research in Intelligent Control using knowledge-based processing in a manner dual to methods found in the classic stochastic decision, estimation, and control discipline. Such knowledge-based control has also been called Declarative, and Hybid. Software architectures were sought, employing the parallelism inherent in modern object-oriented modeling and programming. The viewpoint adopted was that Intelligent Control employs a class of domain-specific software architectures having features common over a broad variety of implementations, such as management of aircraft flight, power distribution, etc. As much attention was paid to software engineering issues as to artificial intelligence and control issues. This research considered that particular processing methods from the stochastic and knowledge-based worlds are duals, that is, similar in a broad context. They provide architectural design concepts which serve as bridges between the disparate disciplines of decision, estimation, control, and artificial intelligence. This research was applied to the control of a subsonic transport aircraft in the airport terminal area.

Bird's-eye view on noise-based logic.

PubMed

Kish, Laszlo B; Granqvist, Claes G; Horvath, Tamas; Klappenecker, Andreas; Wen, He; Bezrukov, Sergey M

2014-01-01

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss various questions such as ( i ) What does practical determinism mean? ( ii ) Is noise-based logic a Turing machine? ( iii ) Is there hope to beat (the dreams of) quantum computation by a classical physical noise-based processor, and what are the minimum hardware requirements for that? Finally, ( iv ) we address the problem of random number generators and show that the common belief that quantum number generators are superior to classical (thermal) noise-based generators is nothing but a myth.

Bird's-eye view on noise-based logic

NASA Astrophysics Data System (ADS)

Kish, Laszlo B.; Granqvist, Claes G.; Horvath, Tamas; Klappenecker, Andreas; Wen, He; Bezrukov, Sergey M.

2014-09-01

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss various questions such as (i) What does practical determinism mean? (ii) Is noise-based logic a Turing machine? (iii) Is there hope to beat (the dreams of) quantum computation by a classical physical noise-based processor, and what are the minimum hardware requirements for that? Finally, (iv) we address the problem of random number generators and show that the common belief that quantum number generators are superior to classical (thermal) noise-based generators is nothing but a myth.

Increasing complexity with quantum physics.

PubMed

Anders, Janet; Wiesner, Karoline

2011-09-01

We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity. We identify correlations as a central concept connecting quantum information and complex systems science. We present two examples for the power of correlations: using quantum resources to simulate the correlations of a stochastic process and to implement a classically impossible computational task.

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

PubMed Central

2017-01-01

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics. PMID:28932256

Stochastic Modeling of Direct Radiation Transmission in Particle-Laden Turbulent Flows

NASA Astrophysics Data System (ADS)

Banko, Andrew; Villafane, Laura; Kim, Ji Hoon; Esmaily Moghadam, Mahdi; Eaton, John K.

2017-11-01

Direct radiation transmission in turbulent flows laden with heavy particles plays a fundamental role in systems such as clouds, spray combustors, and particle-solar-receivers. Owing to their inertia, the particles preferentially concentrate and the resulting voids and clusters lead to deviations in mean transmission from the classical Beer-Lambert law for exponential extinction. Additionally, the transmission fluctuations can exceed those of Poissonian media by an order of magnitude, which implies a gross misprediction in transmission statistics if the correlations in particle positions are neglected. On the other hand, tracking millions of particles in a turbulence simulation can be prohibitively expensive. This work presents stochastic processes as computationally cheap reduced order models for the instantaneous particle number density field and radiation transmission therein. Results from the stochastic processes are compared to Monte Carlo Ray Tracing (MCRT) simulations using the particle positions obtained from the point-particle DNS of isotropic turbulence at a Taylor Reynolds number of 150. Accurate transmission statistics are predicted with respect to MCRT by matching the mean, variance, and correlation length of DNS number density fields. Funded by the U.S. Department of Energy under Grant No. DE-NA0002373-1 and the National Science Foundation under Grant No. DGE-114747.

Price sensitive demand with random sales price - a newsboy problem

NASA Astrophysics Data System (ADS)

Sankar Sana, Shib

2012-03-01

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Classification of Four-Qubit States by Means of a Stochastic Local Operation and the Classical Communication Invariant

NASA Astrophysics Data System (ADS)

Zha, Xin-Wei; Ma, Gang-Long

2011-02-01

It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants. Verstraete et al.[Phys. Rev. A 65 (2002) 052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes. Li et al.[Phys. Rev. A 76 (2007) 052311] showed that there are at feast 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant. We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.

A methodology for the stochastic generation of hourly synthetic direct normal irradiation time series

NASA Astrophysics Data System (ADS)

Larrañeta, M.; Moreno-Tejera, S.; Lillo-Bravo, I.; Silva-Pérez, M. A.

2018-02-01

Many of the available solar radiation databases only provide global horizontal irradiance (GHI) while there is a growing need of extensive databases of direct normal radiation (DNI) mainly for the development of concentrated solar power and concentrated photovoltaic technologies. In the present work, we propose a methodology for the generation of synthetic DNI hourly data from the hourly average GHI values by dividing the irradiance into a deterministic and stochastic component intending to emulate the dynamics of the solar radiation. The deterministic component is modeled through a simple classical model. The stochastic component is fitted to measured data in order to maintain the consistency of the synthetic data with the state of the sky, generating statistically significant DNI data with a cumulative frequency distribution very similar to the measured data. The adaptation and application of the model to the location of Seville shows significant improvements in terms of frequency distribution over the classical models. The proposed methodology applied to other locations with different climatological characteristics better results than the classical models in terms of frequency distribution reaching a reduction of the 50% in the Finkelstein-Schafer (FS) and Kolmogorov-Smirnov test integral (KSI) statistics.

Coherifying quantum channels

NASA Astrophysics Data System (ADS)

Korzekwa, Kamil; Czachórski, Stanisław; Puchała, Zbigniew; Życzkowski, Karol

2018-04-01

Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel Φ, i.e., we look for channels {{{Φ }}}{ \\mathcal C } that induce the same classical transitions T, but are ‘more coherent’. To quantify the coherence of a channel Φ we measure the coherence of the corresponding Jamiołkowski state J Φ. We show that the classical transition matrix T can be coherified to reversible unitary dynamics if and only if T is unistochastic. Otherwise the Jamiołkowski state {J}{{Φ }}{ \\mathcal C } of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To assess the extent to which an optimal process {{{Φ }}}{ \\mathcal C } is indeterministic we find explicit bounds on the entropy and purity of {J}{{Φ }}{ \\mathcal C }, and relate the latter to the unitarity of {{{Φ }}}{ \\mathcal C }. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel Φ and reduces its rank (the minimal number of required Kraus operators) from {d}2 to d.

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

D’Arrigo, A., E-mail: antonio.darrigo@dmfci.unict.it; Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania; Centro Siciliano di Fisica Nucleare e Struttura della Materia

We investigate the phenomenon of bipartite entanglement revivals under purely local operations in systems subject to local and independent classical noise sources. We explain this apparent paradox in the physical ensemble description of the system state by introducing the concept of “hidden” entanglement, which indicates the amount of entanglement that cannot be exploited due to the lack of classical information on the system. For this reason this part of entanglement can be recovered without the action of non-local operations or back-transfer process. For two noninteracting qubits under a low-frequency stochastic noise, we show that entanglement can be recovered by localmore » pulses only. We also discuss how hidden entanglement may provide new insights about entanglement revivals in non-Markovian dynamics.« less

Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.

On a Stochastic Failure Model under Random Shocks

NASA Astrophysics Data System (ADS)

Cha, Ji Hwan

2013-02-01

In most conventional settings, the events caused by an external shock are initiated at the moments of its occurrence. In this paper, we study a new classes of shock model, where each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in classical extreme shock models, but with delay of some random time. We derive the corresponding survival and failure rate functions. Furthermore, we study the limiting behaviour of the failure rate function where it is applicable.

FAST TRACK COMMUNICATION: Quantum anomalies and linear response theory

NASA Astrophysics Data System (ADS)

Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen, Doron

2010-08-01

The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ɛ2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time tɛ, and a self-generated (intrinsic) dephasing process leads to nonlinear dependence of D on ɛ2.

Exact and approximate stochastic simulation of intracellular calcium dynamics.

PubMed

Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

2011-01-01

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks.

PubMed

Navarro Jimenez, M; Le Maître, O P; Knio, O M

2016-12-28

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

DOE PAGES

Navarro Jimenez, M.; Le Maître, O. P.; Knio, O. M.

2016-12-23

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes thatmore » the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.« less

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

NASA Astrophysics Data System (ADS)

Navarro Jimenez, M.; Le Maître, O. P.; Knio, O. M.

2016-12-01

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

Kinetics of autocatalysis in small systems

NASA Astrophysics Data System (ADS)

Arslan, Erdem; Laurenzi, Ian J.

2008-01-01

Autocatalysis is a ubiquitous chemical process that drives a plethora of biological phenomena, including the self-propagation of prions etiological to the Creutzfeldt-Jakob disease and bovine spongiform encephalopathy. To explain the dynamics of these systems, we have solved the chemical master equation for the irreversible autocatalytic reaction A +B→2A. This solution comprises the first closed form expression describing the probabilistic time evolution of the populations of autocatalytic and noncatalytic molecules from an arbitrary initial state. Grand probability distributions are likewise presented for autocatalysis in the equilibrium limit (A+B⇌2A), allowing for the first mechanistic comparison of this process with chemical isomerization (B⇌A) in small systems. Although the average population of autocatalytic (i.e., prion) molecules largely conforms to the predictions of the classical "rate law" approach in time and the law of mass action at equilibrium, thermodynamic differences between the entropies of isomerization and autocatalysis are revealed, suggesting a "mechanism dependence" of state variables for chemical reaction processes. These results demonstrate the importance of chemical mechanism and molecularity in the development of stochastic processes for chemical systems and the relationship between the stochastic approach to chemical kinetics and nonequilibrium thermodynamics.

Quantum learning of classical stochastic processes: The completely positive realization problem

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

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

NASA Astrophysics Data System (ADS)

Alpert, Peter A.; Knopf, Daniel A.

2016-02-01

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of Jhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. The model simulations allow for a quantitative experimental uncertainty analysis for parameters Ntot, T, RH, and the ISA variability. The implications of our results for experimental analysis and interpretation of the immersion freezing process are discussed.

Application of TDCR-Geant4 modeling to standardization of 63Ni.

PubMed

Thiam, C; Bobin, C; Chauvenet, B; Bouchard, J

2012-09-01

As an alternative to the classical TDCR model applied to liquid scintillation (LS) counting, a stochastic approach based on the Geant4 toolkit is presented for the simulation of light emission inside the dedicated three-photomultiplier detection system. To this end, the Geant4 modeling includes a comprehensive description of optical properties associated with each material constituting the optical chamber. The objective is to simulate the propagation of optical photons from their creation in the LS cocktail to the production of photoelectrons in the photomultipliers. First validated for the case of radionuclide standardization based on Cerenkov emission, the scintillation process has been added to a TDCR-Geant4 modeling using the Birks expression in order to account for the light-emission nonlinearity owing to ionization quenching. The scintillation yield of the commercial Ultima Gold LS cocktail has been determined from double-coincidence detection efficiencies obtained for (60)Co and (54)Mn with the 4π(LS)β-γ coincidence method. In this paper, the stochastic TDCR modeling is applied for the case of the standardization of (63)Ni (pure β(-)-emitter; E(max)=66.98 keV) and the activity concentration is compared with the result given by the classical model. Copyright © 2012 Elsevier Ltd. All rights reserved.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Classical Molecular Dynamics with Mobile Protons.

PubMed

Lazaridis, Themis; Hummer, Gerhard

2017-11-27

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Dissipation in microwave quantum circuits with hybrid nanowire Josephson elements

NASA Astrophysics Data System (ADS)

Mugnai, D.; Ranfagni, A.; Agresti, A.

2017-04-01

Recent experiments on hybrid Josephson junctions have made the argument a topical subject. However, a quantity which remains still unknown is the tunneling (or response) time, which is strictly connected to the role that dissipation plays in the dynamics of the complete system. A simple way for evaluating dissipation in microwave circuits, previously developed for describing the dynamics of conventional Josephson junctions, is now presented as suitable for application even to non-conventional junctions. The method is based on a stochastic model, as derived from the telegrapher's equation, and is particularly devoted to the case of junctions loaded by real transmission lines. When the load is constituted by lumped-constant circuits, a connection with the stochastic model is also maintained. The theoretical model demonstrated its ability to analyze both classically-allowed and forbidden processes, and has found a wide field of applicability, namely in all cases in which dissipative effects cannot be ignored.

Stochastic transport in the presence of spatial disorder: Fluctuation-induced corrections to homogenization

NASA Astrophysics Data System (ADS)

Russell, Matthew J.; Jensen, Oliver E.; Galla, Tobias

2016-10-01

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyze the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.

A robust component mode synthesis method for stochastic damped vibroacoustics

NASA Astrophysics Data System (ADS)

Tran, Quang Hung; Ouisse, Morvan; Bouhaddi, Noureddine

2010-01-01

In order to reduce vibrations or sound levels in industrial vibroacoustic problems, the low-cost and efficient way consists in introducing visco- and poro-elastic materials either on the structure or on cavity walls. Depending on the frequency range of interest, several numerical approaches can be used to estimate the behavior of the coupled problem. In the context of low frequency applications related to acoustic cavities with surrounding vibrating structures, the finite elements method (FEM) is one of the most efficient techniques. Nevertheless, industrial problems lead to large FE models which are time-consuming in updating or optimization processes. A classical way to reduce calculation time is the component mode synthesis (CMS) method, whose classical formulation is not always efficient to predict dynamical behavior of structures including visco-elastic and/or poro-elastic patches. Then, to ensure an efficient prediction, the fluid and structural bases used for the model reduction need to be updated as a result of changes in a parametric optimization procedure. For complex models, this leads to prohibitive numerical costs in the optimization phase or for management and propagation of uncertainties in the stochastic vibroacoustic problem. In this paper, the formulation of an alternative CMS method is proposed and compared to classical ( u, p) CMS method: the Ritz basis is completed with static residuals associated to visco-elastic and poro-elastic behaviors. This basis is also enriched by the static response of residual forces due to structural modifications, resulting in a so-called robust basis, also adapted to Monte Carlo simulations for uncertainties propagation using reduced models.

Comparative analysis of the effectiveness of three immunization strategies in controlling disease outbreaks in realistic social networks.

PubMed

Xu, Zhijing; Zu, Zhenghu; Zheng, Tao; Zhang, Wendou; Xu, Qing; Liu, Jinjie

2014-01-01

The high incidence of emerging infectious diseases has highlighted the importance of effective immunization strategies, especially the stochastic algorithms based on local available network information. Present stochastic strategies are mainly evaluated based on classical network models, such as scale-free networks and small-world networks, and thus are insufficient. Three frequently referred stochastic immunization strategies-acquaintance immunization, community-bridge immunization, and ring vaccination-were analyzed in this work. The optimal immunization ratios for acquaintance immunization and community-bridge immunization strategies were investigated, and the effectiveness of these three strategies in controlling the spreading of epidemics were analyzed based on realistic social contact networks. The results show all the strategies have decreased the coverage of the epidemics compared to baseline scenario (no control measures). However the effectiveness of acquaintance immunization and community-bridge immunization are very limited, with acquaintance immunization slightly outperforming community-bridge immunization. Ring vaccination significantly outperforms acquaintance immunization and community-bridge immunization, and the sensitivity analysis shows it could be applied to controlling the epidemics with a wide infectivity spectrum. The effectiveness of several classical stochastic immunization strategies was evaluated based on realistic contact networks for the first time in this study. These results could have important significance for epidemic control research and practice.

Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Lytvynov, Eugene

2011-03-01

Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.

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.

Gene selection heuristic algorithm for nutrigenomics studies.

PubMed

Valour, D; Hue, I; Grimard, B; Valour, B

2013-07-15

Large datasets from -omics studies need to be deeply investigated. The aim of this paper is to provide a new method (LEM method) for the search of transcriptome and metabolome connections. The heuristic algorithm here described extends the classical canonical correlation analysis (CCA) to a high number of variables (without regularization) and combines well-conditioning and fast-computing in "R." Reduced CCA models are summarized in PageRank matrices, the product of which gives a stochastic matrix that resumes the self-avoiding walk covered by the algorithm. Then, a homogeneous Markov process applied to this stochastic matrix converges the probabilities of interconnection between genes, providing a selection of disjointed subsets of genes. This is an alternative to regularized generalized CCA for the determination of blocks within the structure matrix. Each gene subset is thus linked to the whole metabolic or clinical dataset that represents the biological phenotype of interest. Moreover, this selection process reaches the aim of biologists who often need small sets of genes for further validation or extended phenotyping. The algorithm is shown to work efficiently on three published datasets, resulting in meaningfully broadened gene networks.

New Insights to Compare and Choose TKTD Models for Survival Based on an Interlaboratory Study for Lymnaea stagnalis Exposed to Cd.

PubMed

Baudrot, Virgile; Preux, Sara; Ducrot, Virginie; Pave, Alain; Charles, Sandrine

2018-02-06

Toxicokinetic-toxicodynamic (TKTD) models, as the General Unified Threshold model of Survival (GUTS), provide a consistent process-based framework compared to classical dose-response models to analyze both time and concentration-dependent data sets. However, the extent to which GUTS models (Stochastic Death (SD) and Individual Tolerance (IT)) lead to a better fitting than classical dose-response model at a given target time (TT) has poorly been investigated. Our paper highlights that GUTS estimates are generally more conservative and have a reduced uncertainty through smaller credible intervals for the studied data sets than classical TT approaches. Also, GUTS models enable estimating any x% lethal concentration at any time (LC x,t ), and provide biological information on the internal processes occurring during the experiments. While both GUTS-SD and GUTS-IT models outcompete classical TT approaches, choosing one preferentially to the other is still challenging. Indeed, the estimates of survival rate over time and LC x,t are very close between both models, but our study also points out that the joint posterior distributions of SD model parameters are sometimes bimodal, while two parameters of the IT model seems strongly correlated. Therefore, the selection between these two models has to be supported by the experimental design and the biological objectives, and this paper provides some insights to drive this choice.

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.

Greek classicism in living structure? Some deductive pathways in animal morphology.

PubMed

Zweers, G A

1985-01-01

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's "stochastic margin". Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a "Greek Classical" situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods. Three deductive methods for explanation of living structure in animal morphology are proposed: the parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the "optimal design" serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. Full explanation of living structure asks for three entries: functional design within architectural and transformational constraints. The transformational constraint brings necessarily in a stochastic component: an at random variation being a sort of "free management space". This variation must be a variation from the deterministic principle of the optimal design, since any transformation requires space for plasticity in structure and action, and flexibility in role fulfilling. Nevertheless, finally the question comes up whether for animal structure a similar situation exists as in Greek Classical temples. This means that the at random variation, that is found when the optimal design is used to explain structure, comprises apart from a stochastic part also real deviations being yet another deterministic part. This deterministic part could be a set of rules that governs actualization in the "free management space".

Prequantum classical statistical field theory: background field as a source of everything?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2011-07-01

Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's "double solution" approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special "prequantum fields": the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the "photonic field" (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of "vacuum fluctuations") might play the role of a source of such pulses, i.e., the source of everything.

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

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

Alpert, Peter A.; Knopf, Daniel A.

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimentalmore » data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, N tot, and the heterogeneous ice nucleation rate coefficient, J het( T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of J het is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. Finally, the model simulations allow for a quantitative experimental uncertainty analysis for parameters N tot, T, RH, and the ISA variability. We discuss the implications of our results for experimental analysis and interpretation of the immersion freezing process.« less

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

DOE PAGES

Alpert, Peter A.; Knopf, Daniel A.

2016-02-24

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimentalmore » data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, N tot, and the heterogeneous ice nucleation rate coefficient, J het( T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of J het is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. Finally, the model simulations allow for a quantitative experimental uncertainty analysis for parameters N tot, T, RH, and the ISA variability. We discuss the implications of our results for experimental analysis and interpretation of the immersion freezing process.« less

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

MetaPIGA v2.0: maximum likelihood large phylogeny estimation using the metapopulation genetic algorithm and other stochastic heuristics.

PubMed

Helaers, Raphaël; Milinkovitch, Michel C

2010-07-15

The development, in the last decade, of stochastic heuristics implemented in robust application softwares has made large phylogeny inference a key step in most comparative studies involving molecular sequences. Still, the choice of a phylogeny inference software is often dictated by a combination of parameters not related to the raw performance of the implemented algorithm(s) but rather by practical issues such as ergonomics and/or the availability of specific functionalities. Here, we present MetaPIGA v2.0, a robust implementation of several stochastic heuristics for large phylogeny inference (under maximum likelihood), including a Simulated Annealing algorithm, a classical Genetic Algorithm, and the Metapopulation Genetic Algorithm (metaGA) together with complex substitution models, discrete Gamma rate heterogeneity, and the possibility to partition data. MetaPIGA v2.0 also implements the Likelihood Ratio Test, the Akaike Information Criterion, and the Bayesian Information Criterion for automated selection of substitution models that best fit the data. Heuristics and substitution models are highly customizable through manual batch files and command line processing. However, MetaPIGA v2.0 also offers an extensive graphical user interface for parameters setting, generating and running batch files, following run progress, and manipulating result trees. MetaPIGA v2.0 uses standard formats for data sets and trees, is platform independent, runs in 32 and 64-bits systems, and takes advantage of multiprocessor and multicore computers. The metaGA resolves the major problem inherent to classical Genetic Algorithms by maintaining high inter-population variation even under strong intra-population selection. Implementation of the metaGA together with additional stochastic heuristics into a single software will allow rigorous optimization of each heuristic as well as a meaningful comparison of performances among these algorithms. MetaPIGA v2.0 gives access both to high customization for the phylogeneticist, as well as to an ergonomic interface and functionalities assisting the non-specialist for sound inference of large phylogenetic trees using nucleotide sequences. MetaPIGA v2.0 and its extensive user-manual are freely available to academics at http://www.metapiga.org.

MetaPIGA v2.0: maximum likelihood large phylogeny estimation using the metapopulation genetic algorithm and other stochastic heuristics

PubMed Central

2010-01-01

Background The development, in the last decade, of stochastic heuristics implemented in robust application softwares has made large phylogeny inference a key step in most comparative studies involving molecular sequences. Still, the choice of a phylogeny inference software is often dictated by a combination of parameters not related to the raw performance of the implemented algorithm(s) but rather by practical issues such as ergonomics and/or the availability of specific functionalities. Results Here, we present MetaPIGA v2.0, a robust implementation of several stochastic heuristics for large phylogeny inference (under maximum likelihood), including a Simulated Annealing algorithm, a classical Genetic Algorithm, and the Metapopulation Genetic Algorithm (metaGA) together with complex substitution models, discrete Gamma rate heterogeneity, and the possibility to partition data. MetaPIGA v2.0 also implements the Likelihood Ratio Test, the Akaike Information Criterion, and the Bayesian Information Criterion for automated selection of substitution models that best fit the data. Heuristics and substitution models are highly customizable through manual batch files and command line processing. However, MetaPIGA v2.0 also offers an extensive graphical user interface for parameters setting, generating and running batch files, following run progress, and manipulating result trees. MetaPIGA v2.0 uses standard formats for data sets and trees, is platform independent, runs in 32 and 64-bits systems, and takes advantage of multiprocessor and multicore computers. Conclusions The metaGA resolves the major problem inherent to classical Genetic Algorithms by maintaining high inter-population variation even under strong intra-population selection. Implementation of the metaGA together with additional stochastic heuristics into a single software will allow rigorous optimization of each heuristic as well as a meaningful comparison of performances among these algorithms. MetaPIGA v2.0 gives access both to high customization for the phylogeneticist, as well as to an ergonomic interface and functionalities assisting the non-specialist for sound inference of large phylogenetic trees using nucleotide sequences. MetaPIGA v2.0 and its extensive user-manual are freely available to academics at http://www.metapiga.org. PMID:20633263

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

Stochastic flux freezing and magnetic dynamo.

PubMed

Eyink, Gregory L

2011-05-01

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered. © 2011 American Physical Society

Design Of Combined Stochastic Feedforward/Feedback Control

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1989-01-01

Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.

Stochastic Routing and Scheduling Policies for Energy Harvesting Communication Networks

NASA Astrophysics Data System (ADS)

Calvo-Fullana, Miguel; Anton-Haro, Carles; Matamoros, Javier; Ribeiro, Alejandro

2018-07-01

In this paper, we study the joint routing-scheduling problem in energy harvesting communication networks. Our policies, which are based on stochastic subgradient methods on the dual domain, act as an energy harvesting variant of the stochastic family of backpresure algorithms. Specifically, we propose two policies: (i) the Stochastic Backpressure with Energy Harvesting (SBP-EH), in which a node's routing-scheduling decisions are determined by the difference between the Lagrange multipliers associated to their queue stability constraints and their neighbors'; and (ii) the Stochastic Soft Backpressure with Energy Harvesting (SSBP-EH), an improved algorithm where the routing-scheduling decision is of a probabilistic nature. For both policies, we show that given sustainable data and energy arrival rates, the stability of the data queues over all network nodes is guaranteed. Numerical results corroborate the stability guarantees and illustrate the minimal gap in performance that our policies offer with respect to classical ones which work with an unlimited energy supply.

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

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.

Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems

NASA Astrophysics Data System (ADS)

Deco, Gustavo; Martí, Daniel

2007-03-01

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.

Delay compensation in integrated communication and control systems. I - Conceptual development and analysis

NASA Technical Reports Server (NTRS)

Luck, Rogelio; Ray, Asok

1990-01-01

A procedure for compensating for the effects of distributed network-induced delays in integrated communication and control systems (ICCS) is proposed. The problem of analyzing systems with time-varying and possibly stochastic delays could be circumvented by use of a deterministic observer which is designed to perform under certain restrictive but realistic assumptions. The proposed delay-compensation algorithm is based on a deterministic state estimator and a linear state-variable-feedback control law. The deterministic observer can be replaced by a stochastic observer without any structural modifications of the delay compensation algorithm. However, if a feedforward-feedback control law is chosen instead of the state-variable feedback control law, the observer must be modified as a conventional nondelayed system would be. Under these circumstances, the delay compensation algorithm would be accordingly changed. The separation principle of the classical Luenberger observer holds true for the proposed delay compensator. The algorithm is suitable for ICCS in advanced aircraft, spacecraft, manufacturing automation, and chemical process applications.

Five-wave-packet quantum error correction based on continuous-variable cluster entanglement

PubMed Central

Hao, Shuhong; Su, Xiaolong; Tian, Caixing; Xie, Changde; Peng, Kunchi

2015-01-01

Quantum error correction protects the quantum state against noise and decoherence in quantum communication and quantum computation, which enables one to perform fault-torrent quantum information processing. We experimentally demonstrate a quantum error correction scheme with a five-wave-packet code against a single stochastic error, the original theoretical model of which was firstly proposed by S. L. Braunstein and T. A. Walker. Five submodes of a continuous variable cluster entangled state of light are used for five encoding channels. Especially, in our encoding scheme the information of the input state is only distributed on three of the five channels and thus any error appearing in the remained two channels never affects the output state, i.e. the output quantum state is immune from the error in the two channels. The stochastic error on a single channel is corrected for both vacuum and squeezed input states and the achieved fidelities of the output states are beyond the corresponding classical limit. PMID:26498395

Stochastic cooling of bunched beams from fluctuation and kinetic theory

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

Chattopadhyay, S.

1982-09-01

A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlationmore » of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented.« less

Past observable dynamics of a continuously monitored qubit

NASA Astrophysics Data System (ADS)

García-Pintos, Luis Pedro; Dressel, Justin

2017-12-01

Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process, such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit, this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.

An adaptive unsaturated bistable stochastic resonance method and its application in mechanical fault diagnosis

NASA Astrophysics Data System (ADS)

Qiao, Zijian; Lei, Yaguo; Lin, Jing; Jia, Feng

2017-02-01

In mechanical fault diagnosis, most traditional methods for signal processing attempt to suppress or cancel noise imbedded in vibration signals for extracting weak fault characteristics, whereas stochastic resonance (SR), as a potential tool for signal processing, is able to utilize the noise to enhance fault characteristics. The classical bistable SR (CBSR), as one of the most widely used SR methods, however, has the disadvantage of inherent output saturation. The output saturation not only reduces the output signal-to-noise ratio (SNR) but also limits the enhancement capability for fault characteristics. To overcome this shortcoming, a novel method is proposed to extract the fault characteristics, where a piecewise bistable potential model is established. Simulated signals are used to illustrate the effectiveness of the proposed method, and the results show that the method is able to extract weak fault characteristics and has good enhancement performance and anti-noise capability. Finally, the method is applied to fault diagnosis of bearings and planetary gearboxes, respectively. The diagnosis results demonstrate that the proposed method can obtain larger output SNR, higher spectrum peaks at fault characteristic frequencies and therefore larger recognizable degree than the CBSR method.

Statistics of transmission eigenvalues in two-dimensional quantum cavities: Ballistic versus stochastic scattering

NASA Astrophysics Data System (ADS)

Rotter, Stefan; Aigner, Florian; Burgdörfer, Joachim

2007-03-01

We investigate the statistical distribution of transmission eigenvalues in phase-coherent transport through quantum dots. In two-dimensional ab initio simulations for both clean and disordered two-dimensional cavities, we find markedly different quantum-to-classical crossover scenarios for these two cases. In particular, we observe the emergence of “noiseless scattering states” in clean cavities, irrespective of sharp-edged entrance and exit lead mouths. We find the onset of these “classical” states to be largely independent of the cavity’s classical chaoticity, but very sensitive with respect to bulk disorder. Our results suggest that for weakly disordered cavities, the transmission eigenvalue distribution is determined both by scattering at the disorder potential and the cavity walls. To properly account for this intermediate parameter regime, we introduce a hybrid crossover scheme, which combines previous models that are valid in the ballistic and the stochastic limit, respectively.

First assembly times and equilibration in stochastic coagulation-fragmentation

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

D’Orsogna, Maria R.; Department of Mathematics, CSUN, Los Angeles, California 91330-8313; Lei, Qi

2015-07-07

We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations ofmore » total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.« less

Modelling information dissemination under privacy concerns in social media

NASA Astrophysics Data System (ADS)

Zhu, Hui; Huang, Cheng; Lu, Rongxing; Li, Hui

2016-05-01

Social media has recently become an important platform for users to share news, express views, and post messages. However, due to user privacy preservation in social media, many privacy setting tools are employed, which inevitably change the patterns and dynamics of information dissemination. In this study, a general stochastic model using dynamic evolution equations was introduced to illustrate how privacy concerns impact the process of information dissemination. Extensive simulations and analyzes involving the privacy settings of general users, privileged users, and pure observers were conducted on real-world networks, and the results demonstrated that user privacy settings affect information differently. Finally, we also studied the process of information diffusion analytically and numerically with different privacy settings using two classic networks.

Wave-optics modeling of the optical-transport line for passive optical stochastic cooling

NASA Astrophysics Data System (ADS)

Andorf, M. B.; Lebedev, V. A.; Piot, P.; Ruan, J.

2018-03-01

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystemcritical to the OSC scheme is the focusing optics used to image radiation from the upstream "pickup" undulator to the downstream "kicker" undulator. In this paper, we present simulation results using wave-optics calculation carried out with the SYNCHROTRON RADIATION WORKSHOP (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters: Theory and application to microfilaments

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

Li, Tong; Gu, YuanTong, E-mail: yuantong.gu@qut.edu.au

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grainedmore » level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.« less

Non-Gaussian, non-dynamical stochastic resonance

NASA Astrophysics Data System (ADS)

Szczepaniec, Krzysztof; Dybiec, Bartłomiej

2013-11-01

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the "most" periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.

Robust stochastic optimization for reservoir operation

NASA Astrophysics Data System (ADS)

Pan, Limeng; Housh, Mashor; Liu, Pan; Cai, Ximing; Chen, Xin

2015-01-01

Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.

Dynamics of a prey-predator system under Poisson white noise excitation

NASA Astrophysics Data System (ADS)

Pan, Shan-Shan; Zhu, Wei-Qiu

2014-10-01

The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

The Sense of Confidence during Probabilistic Learning: A Normative Account.

PubMed

Meyniel, Florent; Schlunegger, Daniel; Dehaene, Stanislas

2015-06-01

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable "feeling of knowing" or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process.

The Sense of Confidence during Probabilistic Learning: A Normative Account

PubMed Central

Meyniel, Florent; Schlunegger, Daniel; Dehaene, Stanislas

2015-01-01

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable “feeling of knowing” or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process. PMID:26076466

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.

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow

PubMed Central

Lan, Yueheng; Aurell, Erik

2015-01-01

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism. PMID:26194015

Nonisothermal fluctuating hydrodynamics and Brownian motion

NASA Astrophysics Data System (ADS)

Falasco, G.; Kroy, K.

2016-03-01

The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

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

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-03-15

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

PubMed

Mertens, Ulf Kai; Voss, Andreas; Radev, Stefan

2018-01-01

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

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.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

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

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com; Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr; Çelik, Nuri, E-mail: ncelik@bartin.edu.tr

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

CP function: an alpha spending function based on conditional power.

PubMed

Jiang, Zhiwei; Wang, Ling; Li, Chanjuan; Xia, Jielai; Wang, William

2014-11-20

Alpha spending function and stochastic curtailment are two frequently used methods in group sequential design. In the stochastic curtailment approach, the actual type I error probability cannot be well controlled within the specified significance level. But conditional power (CP) in stochastic curtailment is easier to be accepted and understood by clinicians. In this paper, we develop a spending function based on the concept of conditional power, named CP function, which combines desirable features of alpha spending and stochastic curtailment. Like other two-parameter functions, CP function is flexible to fit the needs of the trial. A simulation study is conducted to explore the choice of CP boundary in CP function that maximizes the trial power. It is equivalent to, even better than, classical Pocock, O'Brien-Fleming, and quadratic spending function as long as a proper ρ0 is given, which is pre-specified CP threshold for efficacy. It also well controls the overall type I error type I error rate and overcomes the disadvantage of stochastic curtailment. Copyright © 2014 John Wiley & Sons, Ltd.

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.)

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

Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when onemore » or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.« less

Quantum stochastic calculus associated with quadratic quantum noises

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

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

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.

A Black-Scholes Approach to Satisfying the Demand in a Failure-Prone Manufacturing System

NASA Technical Reports Server (NTRS)

Chavez-Fuentes, Jorge R.; Gonzalex, Oscar R.; Gray, W. Steven

2007-01-01

The goal of this paper is to use a financial model and a hedging strategy in a systems application. In particular, the classical Black-Scholes model, which was developed in 1973 to find the fair price of a financial contract, is adapted to satisfy an uncertain demand in a manufacturing system when one of two production machines is unreliable. This financial model together with a hedging strategy are used to develop a closed formula for the production strategies of each machine. The strategy guarantees that the uncertain demand will be met in probability at the final time of the production process. It is assumed that the production efficiency of the unreliable machine can be modeled as a continuous-time stochastic process. Two simple examples illustrate the result.

Modalities of gene action predicted by the classical evolutionary biological theory of aging.

PubMed

Martin, George M

2007-04-01

What might now be referred to as the "classical" evolutionary biological theory of why we age has had a number of serious challenges in recent years. While the theory might therefore have to be modified under certain circumstances, in the author's opinion, it still provides the soundest theoretical basis for thinking about how we age. Nine modalities of gene action that have the potential to modulate processes of aging are reviewed, including the two most widely reviewed and accepted concepts ("antagonistic pleiotropy" and "mutation accumulation"). While several of these nine mechanisms can be regarded as derivatives of the antagonistic pleiotropic concept, they frame more specific questions for future research. Such research should pursue what appears to be the dominant factor in the determination of intraspecific variations in longevity-stochastic mechanisms, most likely based upon epigenetics. This contrasts with the dominant factor in the determination of interspecific variations in longevity-the constitutional genome, most likely based upon variations in regulatory loci.

A H-infinity Fault Detection and Diagnosis Scheme for Discrete Nonlinear System Using Output Probability Density Estimation

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

Zhang Yumin; Lum, Kai-Yew; Wang Qingguo

In this paper, a H-infinity fault detection and diagnosis (FDD) scheme for a class of discrete nonlinear system fault using output probability density estimation is presented. Unlike classical FDD problems, the measured output of the system is viewed as a stochastic process and its square root probability density function (PDF) is modeled with B-spline functions, which leads to a deterministic space-time dynamic model including nonlinearities, uncertainties. A weighting mean value is given as an integral function of the square root PDF along space direction, which leads a function only about time and can be used to construct residual signal. Thus,more » the classical nonlinear filter approach can be used to detect and diagnose the fault in system. A feasible detection criterion is obtained at first, and a new H-infinity adaptive fault diagnosis algorithm is further investigated to estimate the fault. Simulation example is given to demonstrate the effectiveness of the proposed approaches.« less

A H-infinity Fault Detection and Diagnosis Scheme for Discrete Nonlinear System Using Output Probability Density Estimation

NASA Astrophysics Data System (ADS)

Zhang, Yumin; Wang, Qing-Guo; Lum, Kai-Yew

2009-03-01

In this paper, a H-infinity fault detection and diagnosis (FDD) scheme for a class of discrete nonlinear system fault using output probability density estimation is presented. Unlike classical FDD problems, the measured output of the system is viewed as a stochastic process and its square root probability density function (PDF) is modeled with B-spline functions, which leads to a deterministic space-time dynamic model including nonlinearities, uncertainties. A weighting mean value is given as an integral function of the square root PDF along space direction, which leads a function only about time and can be used to construct residual signal. Thus, the classical nonlinear filter approach can be used to detect and diagnose the fault in system. A feasible detection criterion is obtained at first, and a new H-infinity adaptive fault diagnosis algorithm is further investigated to estimate the fault. Simulation example is given to demonstrate the effectiveness of the proposed approaches.

Wave-Optics Modeling of the Optical-Transport Line for Passive Optical Stochastic Cooling

DOE PAGES

Andorf, M. B.; Lebedev, V. A.; Piot, P.; ...

2018-03-01

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystemcritical to the OSC scheme is the focusing optics used to image radiation from the upstream “pickup” undulator to the downstream “kicker” undulator. In this paper, we present simulation results using wave-optics calculation carried out with the Synchrotron Radiation Workshop (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrablemore » Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.« less

Mechanical Autonomous Stochastic Heat Engine

NASA Astrophysics Data System (ADS)

Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara

2016-07-01

Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

Mechanical Autonomous Stochastic Heat Engine.

PubMed

Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara

2016-07-01

Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

A quantum extended Kalman filter

NASA Astrophysics Data System (ADS)

Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.

2017-06-01

In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Classical and quantum localization and delocalization in the Fermi accelerator, kicked rotor and two-sided kicked rotor models

NASA Astrophysics Data System (ADS)

Zaslavsky, M.

1996-06-01

The phenomena of dynamical localization, both classical and quantum, are studied in the Fermi accelerator model. The model consists of two vertical oscillating walls and a ball bouncing between them. The classical localization boundary is calculated in the case of ``sinusoidal velocity transfer'' [A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, Berlin, 1983)] on the basis of the analysis of resonances. In the case of the ``sawtooth'' wall velocity we show that the quantum localization is determined by the analytical properties of the canonical transformations to the action and angle coordinates of the unperturbed Hamiltonian, while the existence of the classical localization is determined by the number of continuous derivatives of the distance between the walls with respect to time.

Obtaining a W state from a Greenberger-Horne-Zeilinger state via stochastic local operations and classical communication with a rate approaching unity.

PubMed

Yu, Nengkun; Guo, Cheng; Duan, Runyao

2014-04-25

We introduce a notion of the entanglement transformation rate to characterize the asymptotic comparability of two multipartite pure entangled states under stochastic local operations and classical communication (SLOCC). For two well known SLOCC inequivalent three-qubit states |GHZ⟩=(1/2)(|000⟩+|111⟩) and |W⟩=(1/3)(|100⟩+|010⟩+|001⟩), we show that the entanglement transformation rate from |GHZ⟩ to |W⟩ is exactly 1. That means that we can obtain one copy of the W state from one copy of the Greenberg-Horne-Zeilinger (GHZ) state by SLOCC, asymptotically. We then apply similar techniques to obtain a lower bound on the entanglement transformation rates from an N-partite GHZ state to a class of Dicke states, and prove the tightness of this bound for some special cases which naturally generalize the |W⟩ state. A new lower bound on the tensor rank of the matrix permanent is also obtained by evaluating the tensor rank of Dicke states.

Nonequilibrium steady state in open quantum systems: Influence action, stochastic equation and power balance

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

Hsiang, J.-T., E-mail: cosmology@gmail.com; Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan; Hu, B.L.

2015-11-15

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculatingmore » the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics. -- Highlights: •Nonequilibrium steady state (NESS) for interacting quantum many-body systems. •Derivation of stochastic equations for quantum oscillator chain with two heat baths. •Explicit calculation of the energy flow from one bath to the chain to the other bath. •Power balance relation shows the existence of NESS insensitive to initial conditions. •Functional method as a viable platform for issues in quantum thermodynamics.« less

Off-diagonal expansion quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Characterizing quantum channels with non-separable states of classical light

NASA Astrophysics Data System (ADS)

Ndagano, Bienvenu; Perez-Garcia, Benjamin; Roux, Filippus S.; McLaren, Melanie; Rosales-Guzman, Carmelo; Zhang, Yingwen; Mouane, Othmane; Hernandez-Aranda, Raul I.; Konrad, Thomas; Forbes, Andrew

2017-04-01

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

Off-diagonal expansion quantum Monte Carlo.

PubMed

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

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.

The stochastic energy-Casimir method

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review

NASA Astrophysics Data System (ADS)

Falsone, G.

2018-03-01

In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

Seeking parsimony in hydrology and water resources technology

NASA Astrophysics Data System (ADS)

Koutsoyiannis, D.

2009-04-01

The principle of parsimony, also known as the principle of simplicity, the principle of economy and Ockham's razor, advises scientists to prefer the simplest theory among those that fit the data equally well. In this, it is an epistemic principle but reflects an ontological characterization that the universe is ultimately parsimonious. Is this principle useful and can it really be reconciled with, and implemented to, our modelling approaches of complex hydrological systems, whose elements and events are extraordinarily numerous, different and unique? The answer underlying the mainstream hydrological research of the last two decades seems to be negative. Hopes were invested to the power of computers that would enable faithful and detailed representation of the diverse system elements and the hydrological processes, based on merely "first principles" and resulting in "physically-based" models that tend to approach in complexity the real world systems. Today the account of such research endeavour seems not positive, as it did not improve model predictive capacity and processes comprehension. A return to parsimonious modelling seems to be again the promising route. The experience from recent research and from comparisons of parsimonious and complicated models indicates that the former can facilitate insight and comprehension, improve accuracy and predictive capacity, and increase efficiency. In addition - and despite aspiration that "physically based" models will have lower data requirements and, even, they ultimately become "data-free" - parsimonious models require fewer data to achieve the same accuracy with more complicated models. Naturally, the concepts that reconcile the simplicity of parsimonious models with the complexity of hydrological systems are probability theory and statistics. Probability theory provides the theoretical basis for moving from a microscopic to a macroscopic view of phenomena, by mapping sets of diverse elements and events of hydrological systems to single numbers (a probability or an expected value), and statistics provides the empirical basis of summarizing data, making inference from them, and supporting decision making in water resource management. Unfortunately, the current state of the art in probability, statistics and their union, often called stochastics, is not fully satisfactory for the needs of modelling of hydrological and water resource systems. A first problem is that stochastic modelling has traditionally relied on classical statistics, which is based on the independent "coin-tossing" prototype, rather than on the study of real-world systems whose behaviour is very different from the classical prototype. A second problem is that the stochastic models (particularly the multivariate ones) are often not parsimonious themselves. Therefore, substantial advancement of stochastics is necessary in a new paradigm of parsimonious hydrological modelling. These ideas are illustrated using several examples, namely: (a) hydrological modelling of a karst system in Bosnia and Herzegovina using three different approaches ranging from parsimonious to detailed "physically-based"; (b) parsimonious modelling of a peculiar modified catchment in Greece; (c) a stochastic approach that can replace parameter-excessive ARMA-type models with a generalized algorithm that produces any shape of autocorrelation function (consistent with the accuracy provided by the data) using a couple of parameters; (d) a multivariate stochastic approach which replaces a huge number of parameters estimated from data with coefficients estimated by the principle of maximum entropy; and (e) a parsimonious approach for decision making in multi-reservoir systems using a handful of parameters instead of thousands of decision variables.

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

Classical confinement and outward convection of impurity ions in the MST RFP

NASA Astrophysics Data System (ADS)

Kumar, S. T. A.; Den Hartog, D. J.; Mirnov, V. V.; Caspary, K. J.; Magee, R. M.; Brower, D. L.; Chapman, B. E.; Craig, D.; Ding, W. X.; Eilerman, S.; Fiksel, G.; Lin, L.; Nornberg, M.; Parke, E.; Reusch, J. A.; Sarff, J. S.

2012-05-01

Impurity ion dynamics measured with simultaneously high spatial and temporal resolution reveal classical ion transport in the reversed-field pinch. The boron, carbon, oxygen, and aluminum impurity ion density profiles are obtained in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] using a fast, active charge-exchange-recombination-spectroscopy diagnostic. Measurements are made during improved-confinement plasmas obtained using inductive control of tearing instability to mitigate stochastic transport. At the onset of the transition to improved confinement, the impurity ion density profile becomes hollow, with a slow decay in the core region concurrent with an increase in the outer region, implying an outward convection of impurities. Impurity transport from Coulomb collisions in the reversed-field pinch is classical for all collisionality regimes, and analysis shows that the observed hollow profile and outward convection can be explained by the classical temperature screening mechanism. The profile agrees well with classical expectations. Experiments performed with impurity pellet injection provide further evidence for classical impurity ion confinement.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach

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

Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochasticmore » Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.« 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.

OPEN PROBLEM: Orbits' statistics in chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Arnold, V.

2008-07-01

This paper shows how the measurement of the stochasticity degree of a finite sequence of real numbers, published by Kolmogorov in Italian in a journal of insurances' statistics, can be usefully applied to measure the objective stochasticity degree of sequences, originating from dynamical systems theory and from number theory. Namely, whenever the value of Kolmogorov's stochasticity parameter of a given sequence of numbers is too small (or too big), one may conclude that the conjecture describing this sequence as a sample of independent values of a random variables is highly improbable. Kolmogorov used this strategy fighting (in a paper in 'Doklady', 1940) against Lysenko, who had tried to disprove the classical genetics' law of Mendel experimentally. Calculating his stochasticity parameter value for the numbers from Lysenko's experiment reports, Kolmogorov deduced, that, while these numbers were different from the exact fulfilment of Mendel's 3 : 1 law, any smaller deviation would be a manifestation of the report's number falsification. The calculation of the values of the stochasticity parameter would be useful for many other generators of pseudorandom numbers and for many other chaotically looking statistics, including even the prime numbers distribution (discussed in this paper as an example).

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.

On the motion of classical three-body system with consideration of quantum fluctuations

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

Waiting time distribution for continuous stochastic systems

NASA Astrophysics Data System (ADS)

Gernert, Robert; Emary, Clive; Klapp, Sabine H. L.

2014-12-01

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012), 10.1103/PhysRevE.86.061135]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

Stochastic game theory: for playing games, not just for doing theory.

PubMed

Goeree, J K; Holt, C A

1999-09-14

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

A "Hands on" Strategy for Teaching Genetic Algorithms to Undergraduates

ERIC Educational Resources Information Center

Venables, Anne; Tan, Grace

2007-01-01

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

Mathematical Model of Armed Helicopter vs Tank Duel

DTIC Science & Technology

The purpose of this thesis is to mathematically model a duel between the armed helicopter and the tank. In addition to providing a parametric...analysis of B. O. Koopman’s classical Detection-Destruction Duel , two additional models were constructed and analyzed. All three models stem from stochastic

Stochastic Community Assembly: Does It Matter in Microbial Ecology?

PubMed

Zhou, Jizhong; Ning, Daliang

2017-12-01

Understanding the mechanisms controlling community diversity, functions, succession, and biogeography is a central, but poorly understood, topic in ecology, particularly in microbial ecology. Although stochastic processes are believed to play nonnegligible roles in shaping community structure, their importance relative to deterministic processes is hotly debated. The importance of ecological stochasticity in shaping microbial community structure is far less appreciated. Some of the main reasons for such heavy debates are the difficulty in defining stochasticity and the diverse methods used for delineating stochasticity. Here, we provide a critical review and synthesis of data from the most recent studies on stochastic community assembly in microbial ecology. We then describe both stochastic and deterministic components embedded in various ecological processes, including selection, dispersal, diversification, and drift. We also describe different approaches for inferring stochasticity from observational diversity patterns and highlight experimental approaches for delineating ecological stochasticity in microbial communities. In addition, we highlight research challenges, gaps, and future directions for microbial community assembly research. Copyright © 2017 American Society for Microbiology.

Brownian Motion and its Conditional Descendants

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

It happened before [1] that I have concluded my publication with a special dedication to John R. Klauder. Then, the reason was John's PhD thesis [2] and the questions (perhaps outdated in the eyes of the band-wagon jumpers, albeit still retaining their full vitality [3]): (i) What are the uses of the classical (c-number, non-Grassmann) spinor fields, especially nonlinear ones, what are they for at all ? (ii) What are, if any, the classical partners for Fermi models and fields in particular ? The present dedication, even if not as conspicuously motivated as the previous one by John's research, nevertheless pertains to investigations pursued by John through the years and devoted to the analysis of random noise. Sometimes, re-reading old papers and re-analysing old, frequently forgotten ideas might prove more rewarding than racing the fashions. Following this attitude, let us take as the departure point Schrödinger's original suggestion [4] of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of the Brownian motion and its Wiener's codification. The original analysis due to Schrodinger of the probabilistic significance of the heat equation and of its time adjoint in parallel, remained unnoticed by the physics community, and since then forgotten. It reappeared however in the mathematical literature as an inspiration to generalise the concept of Markovian diffusions to the case of Bernstein stochastic processes. But, it stayed without consequences for a deeper understanding of the possible physical phenomena which might underly the corresponding abstract formalism. Schrödinger's objective was to initiate investigations of possible links between quantum theory and the theory of Brownian motion, an attempt which culminated later in the so-called Nelson's stochastic mechanics [8] and its encompassing formalism [7] in which the issue of the Brownian implementation of quantum dynamics is placed in the framework of Markov-Bernstein diffusions…

Stochastic architecture for Hopfield neural nets

NASA Technical Reports Server (NTRS)

Pavel, Sandy

1992-01-01

An expandable stochastic digital architecture for recurrent (Hopfield like) neural networks is proposed. The main features and basic principles of stochastic processing are presented. The stochastic digital architecture is based on a chip with n full interconnected neurons with a pipeline, bit processing structure. For large applications, a flexible way to interconnect many such chips is provided.

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.

Dynamics of tripartite quantum entanglement and discord under a classical dephasing random telegraph noise

NASA Astrophysics Data System (ADS)

Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius

2017-02-01

We address the dynamics of quantum correlations, including entanglement and quantum discord of a three-qubit system interacting with a classical pure dephasing random telegraph noise (RTN) in three different physical environmental situations (independent, mixed and common environments). Two initial entangled states of the system are examined, namely the Greenberger-Horne-Zeilinger (GHZ)- and Werner (W)-type states. The classical noise is introduced as a stochastic process affecting the energy splitting of the qubits. With the help of suitable measures of tripartite entanglement (entanglement witnesses and lower bound of concurrence) and quantum discord (global quantum discord and quantum dissension), we show that the evolution of quantum correlations is not only affected by the type of the system-environment interaction but also by the input configuration of the qubits and the memory properties of the environmental noise. Indeed, depending on the memory properties of the environmental noise and the initial state considered, we find that independent, common and mixed environments can play opposite roles in preserving quantum correlations, and that the sudden death and revival phenomena or the survival of quantum correlations may occur. On the other hand, we also show that the W-type state has strong dynamics under this noise than the GHZ-type ones.

Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes.

PubMed

Li, Jinghao; Zhang, Qingling; Yan, Xing-Gang; Spurgeon, Sarah K

2017-09-19

This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.

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

Andorf, M. B.; Lebedev, V. A.; Piot, P.

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystemcritical to the OSC scheme is the focusing optics used to image radiation from the upstream “pickup” undulator to the downstream “kicker” undulator. In this paper, we present simulation results using wave-optics calculation carried out with the Synchrotron Radiation Workshop (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrablemore » Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.« less

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

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

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

A Stochastic Diffusion Process for the Dirichlet Distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-03-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle.more » Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.« less

Estimating size and scope economies in the Portuguese water sector using the Bayesian stochastic frontier analysis.

PubMed

Carvalho, Pedro; Marques, Rui Cunha

2016-02-15

This study aims to search for economies of size and scope in the Portuguese water sector applying Bayesian and classical statistics to make inference in stochastic frontier analysis (SFA). This study proves the usefulness and advantages of the application of Bayesian statistics for making inference in SFA over traditional SFA which just uses classical statistics. The resulting Bayesian methods allow overcoming some problems that arise in the application of the traditional SFA, such as the bias in small samples and skewness of residuals. In the present case study of the water sector in Portugal, these Bayesian methods provide more plausible and acceptable results. Based on the results obtained we found that there are important economies of output density, economies of size, economies of vertical integration and economies of scope in the Portuguese water sector, pointing out to the huge advantages in undertaking mergers by joining the retail and wholesale components and by joining the drinking water and wastewater services. Copyright © 2015 Elsevier B.V. All rights reserved.

Indeterminism in Classical Dynamics of Particle Motion

NASA Astrophysics Data System (ADS)

Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian; Aluie, Hussein; Kanov, Kalin; Burns, Randal; Meneveau, Charles; Szalay, Alex

2013-03-01

We show that ``God plays dice'' not only in quantum mechanics but also in the classical dynamics of particles advected by turbulent fluids. With a fixed deterministic flow velocity and an exactly known initial position, the particle motion is nevertheless completely unpredictable! In analogy with spontaneous magnetization in ferromagnets which persists as external field is taken to zero, the particle trajectories in turbulent flow remain random as external noise vanishes. The necessary ingredient is a rough advecting field with a power-law energy spectrum extending to smaller scales as noise is taken to zero. The physical mechanism of ``spontaneous stochasticity'' is the explosive dispersion of particle pairs proposed by L. F. Richardson in 1926, so the phenomenon should be observable in laboratory and natural turbulent flows. We present here the first empirical corroboration of these effects in high Reynolds-number numerical simulations of hydrodynamic and magnetohydrodynamic fluid turbulence. Since power-law spectra are seen in many other systems in condensed matter, geophysics and astrophysics, the phenomenon should occur rather widely. Fast reconnection in solar flares and other astrophysical systems can be explained by spontaneous stochasticity of magnetic field-line motion

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Smoothed quantum-classical states in time-irreversible hybrid dynamics

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2017-09-01

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

The Stochastic Early Reaction, Inhibition, and late Action (SERIA) model for antisaccades

PubMed Central

2017-01-01

The antisaccade task is a classic paradigm used to study the voluntary control of eye movements. It requires participants to suppress a reactive eye movement to a visual target and to concurrently initiate a saccade in the opposite direction. Although several models have been proposed to explain error rates and reaction times in this task, no formal model comparison has yet been performed. Here, we describe a Bayesian modeling approach to the antisaccade task that allows us to formally compare different models on the basis of their evidence. First, we provide a formal likelihood function of actions (pro- and antisaccades) and reaction times based on previously published models. Second, we introduce the Stochastic Early Reaction, Inhibition, and late Action model (SERIA), a novel model postulating two different mechanisms that interact in the antisaccade task: an early GO/NO-GO race decision process and a late GO/GO decision process. Third, we apply these models to a data set from an experiment with three mixed blocks of pro- and antisaccade trials. Bayesian model comparison demonstrates that the SERIA model explains the data better than competing models that do not incorporate a late decision process. Moreover, we show that the early decision process postulated by the SERIA model is, to a large extent, insensitive to the cue presented in a single trial. Finally, we use parameter estimates to demonstrate that changes in reaction time and error rate due to the probability of a trial type (pro- or antisaccade) are best explained by faster or slower inhibition and the probability of generating late voluntary prosaccades. PMID:28767650

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Impact of charge carrier injection on single-chain photophysics of conjugated polymers

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

Hofmann, Felix J.; Vogelsang, Jan, E-mail: jan.vogelsang@physik.uni-regensburg.de; Lupton, John M.

Charges in conjugated polymer materials have a strong impact on the photophysics and their interaction with the primary excited state species has to be taken into account in understanding device properties. Here, we employ single-molecule spectroscopy to unravel the influence of charges on several photoluminescence (PL) observables. The charges are injected either stochastically by a photochemical process or deterministically in a hole-injection sandwich device configuration. We find that upon charge injection, besides a blue-shift of the PL emission and a shortening of the PL lifetime due to quenching and blocking of the lowest-energy chromophores, the non-classical photon arrival time distributionmore » of the multichromophoric chain is modified towards a more classical distribution. Surprisingly, the fidelity of photon antibunching deteriorates upon charging, whereas one would actually expect the opposite: the number of chromophores to be reduced. A qualitative model is presented to explain the observed PL changes. The results are of interest to developing a microscopic understanding of the intrinsic charge-exciton quenching interaction in devices.« less

Think globally, act locally: the role of local demographics and vaccination coverage in the dynamic response of measles infection to control.

PubMed

Ferrari, M J; Grenfell, B T; Strebel, P M

2013-08-05

The global reduction of the burden of morbidity and mortality owing to measles has been a major triumph of public health. However, the continued persistence of measles infection probably not only reflects local variation in progress towards vaccination target goals, but may also reflect local variation in dynamic processes of transmission, susceptible replenishment through births and stochastic local extinction. Dynamic models predict that vaccination should increase the mean age of infection and increase inter-annual variability in incidence. Through a comparative approach, we assess national-level patterns in the mean age of infection and measles persistence. We find that while the classic predictions do hold in general, the impact of vaccination on the age distribution of cases and stochastic fadeout are mediated by local birth rate. Thus, broad-scale vaccine coverage goals are unlikely to have the same impact on the interruption of measles transmission in all demographic settings. Indeed, these results suggest that the achievement of further measles reduction or elimination goals is likely to require programmatic and vaccine coverage goals that are tailored to local demographic conditions.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Structure and Randomness of Continuous-Time, Discrete-Event Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2017-10-01

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ɛ -machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

NASA Technical Reports Server (NTRS)

Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe

1994-01-01

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

Adiabatic elimination for systems with inertia driven by compound Poisson colored noise.

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2014-02-01

We consider the dynamics of systems driven by compound Poisson colored noise in the presence of inertia. We study the limit when the frictional relaxation time and the noise autocorrelation time both tend to zero. We show that the Itô and Marcus stochastic calculuses naturally arise depending on these two time scales, and an extra intermediate type occurs when the two time scales are comparable. This leads to three different limiting regimes which are supported by numerical simulations. Furthermore, we establish that when the resulting compound Poisson process tends to the Wiener process in the frequent jump limit the Itô and Marcus calculuses, respectively, tend to the classical Itô and Stratonovich calculuses for Gaussian white noise, and the crossover type calculus tends to a crossover between the Itô and Stratonovich calculuses. Our results would be very helpful for understanding relevant experiments when jump type noise is involved.

A computationally efficient description of heterogeneous freezing: A simplified version of the Soccer ball model

NASA Astrophysics Data System (ADS)

Niedermeier, Dennis; Ervens, Barbara; Clauss, Tina; Voigtländer, Jens; Wex, Heike; Hartmann, Susan; Stratmann, Frank

2014-01-01

In a recent study, the Soccer ball model (SBM) was introduced for modeling and/or parameterizing heterogeneous ice nucleation processes. The model applies classical nucleation theory. It allows for a consistent description of both apparently singular and stochastic ice nucleation behavior, by distributing contact angles over the nucleation sites of a particle population assuming a Gaussian probability density function. The original SBM utilizes the Monte Carlo technique, which hampers its usage in atmospheric models, as fairly time-consuming calculations must be performed to obtain statistically significant results. Thus, we have developed a simplified and computationally more efficient version of the SBM. We successfully used the new SBM to parameterize experimental nucleation data of, e.g., bacterial ice nucleation. Both SBMs give identical results; however, the new model is computationally less expensive as confirmed by cloud parcel simulations. Therefore, it is a suitable tool for describing heterogeneous ice nucleation processes in atmospheric models.

Locality and universality of quantum memory effects.

PubMed

Liu, B-H; Wißmann, S; Hu, X-M; Zhang, C; Huang, Y-F; Li, C-F; Guo, G-C; Karlsson, A; Piilo, J; Breuer, H-P

2014-09-11

The modeling and analysis of the dynamics of complex systems often requires to employ non-Markovian stochastic processes. While there is a clear and well-established mathematical definition for non-Markovianity in the case of classical systems, the extension to the quantum regime recently caused a vivid debate, leading to many different proposals for the characterization and quantification of memory effects in the dynamics of open quantum systems. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment, which reveals the locality and universality of non-Markovianity in the quantum state space and substantially simplifies its numerical and experimental determination. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degree of memory effects in a photonic quantum process with high accuracy.

A System-Oriented Approach for the Optimal Control of Process Chains under Stochastic Influences

NASA Astrophysics Data System (ADS)

Senn, Melanie; Schäfer, Julian; Pollak, Jürgen; Link, Norbert

2011-09-01

Process chains in manufacturing consist of multiple connected processes in terms of dynamic systems. The properties of a product passing through such a process chain are influenced by the transformation of each single process. There exist various methods for the control of individual processes, such as classical state controllers from cybernetics or function mapping approaches realized by statistical learning. These controllers ensure that a desired state is obtained at process end despite of variations in the input and disturbances. The interactions between the single processes are thereby neglected, but play an important role in the optimization of the entire process chain. We divide the overall optimization into two phases: (1) the solution of the optimization problem by Dynamic Programming to find the optimal control variable values for each process for any encountered end state of its predecessor and (2) the application of the optimal control variables at runtime for the detected initial process state. The optimization problem is solved by selecting adequate control variables for each process in the chain backwards based on predefined quality requirements for the final product. For the demonstration of the proposed concept, we have chosen a process chain from sheet metal manufacturing with simplified transformation functions.

Double-Slit Interference Pattern for a Macroscopic Quantum System

NASA Astrophysics Data System (ADS)

Naeij, Hamid Reza; Shafiee, Afshin

2016-12-01

In this study, we solve analytically the Schrödinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classical one. We also show that, depending on the size of the slits, the predictions of quantum approach could be apparently different with those of the aforementioned stochastic description.

Stochastic correlative firing for figure-ground segregation.

PubMed

Chen, Zhe

2005-03-01

Segregation of sensory inputs into separate objects is a central aspect of perception and arises in all sensory modalities. The figure-ground segregation problem requires identifying an object of interest in a complex scene, in many cases given binaural auditory or binocular visual observations. The computations required for visual and auditory figure-ground segregation share many common features and can be cast within a unified framework. Sensory perception can be viewed as a problem of optimizing information transmission. Here we suggest a stochastic correlative firing mechanism and an associative learning rule for figure-ground segregation in several classic sensory perception tasks, including the cocktail party problem in binaural hearing, binocular fusion of stereo images, and Gestalt grouping in motion perception.

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

NASA Astrophysics Data System (ADS)

Bernatowicz, P.; Szymański, S.

2003-09-01

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Interrupted monitoring of a stochastic process

NASA Technical Reports Server (NTRS)

Palmer, E.

1977-01-01

Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies. The optimum strategy is also compared to the strategies used by subjects in a pilot experiment.

An estimator for the relative entropy rate of path measures for stochastic differential equations

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

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

PubMed

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

NASA Astrophysics Data System (ADS)

Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial

2016-09-01

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

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

Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu

2016-09-15

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range ofmore » physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.« less

Differential growth of wrinkled biofilms

NASA Astrophysics Data System (ADS)

Espeso, D. R.; Carpio, A.; Einarsson, B.

2015-02-01

Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and studied. Gene expression regulates cell division and differentiation, which affect the biofilm architecture. Mechanical and chemical processes shape the resulting structure. We gain insight into the interplay between cellular and mechanical processes during biofilm development on air-agar interfaces by means of a hybrid model. Cellular behavior is governed by stochastic rules informed by a cascade of concentration fields for nutrients, waste, and autoinducers. Cellular differentiation and death alter the structure and the mechanical properties of the biofilm, which is deformed according to Föppl-Von Kármán equations informed by cellular processes and the interaction with the substratum. Stiffness gradients due to growth and swelling produce wrinkle branching. We are able to reproduce wrinkled structures often formed by biofilms on air-agar interfaces, as well as spatial distributions of differentiated cells commonly observed with B. subtilis.

Bistable dynamics of a levitated nanoparticle (Presentation Recording)

NASA Astrophysics Data System (ADS)

Ricci, Francesco; Spasenovic, M.; Rica, Raúl A.; Novotny, Lukas; Quidant, Romain

2015-08-01

Bistable systems are ubiquitous in nature. Classical examples in chemistry and biology include relaxation kinetics in chemical reactions [1] and stochastic resonance processes such as neuron firing [2,3]. Likewise, bistable systems play a key role in signal processing and information handling at the nanoscale, giving rise to intriguing applications such as optical switches [4], coherent signal amplification [5,6] and weak forces detection [5]. The interest and applicability of bistable systems are intimately connected with the complexity of their dynamics, typically due to the presence of a large number of parameters and nonlinearities. Appropriate modeling is therefore challenging. Alternatively, the possibility to experimentally recreate bistable systems in a clean and controlled way has recently become very appealing, but elusive and complicated. With this aim, we combined optical tweezers with a novel active feedback-cooling scheme to develop a well-defined opto-mechanical platform reaching unprecedented performances in terms of Q-factor, frequency stability and force sensitivity [7,8]. Our experimental system consists of a single nanoparticle levitated in high vacuum with optical tweezers, which behaves as a non-linear (Duffing) oscillator under appropriate conditions. Here, we prove it to be an ideal tool for a deep study of bistability. We demonstrate bistability of the nanoparticle by noise activated switching between two oscillation states, discussing our results in terms of a double-well potential model. We also show the flexibility of our system in shaping the potential at will, in order to meet the conditions prescribed by any bistable system that could therefore then be simulated with our setup. References [1] T. Amemiya, T. Ohmori, M. Nakaiwa, T. Yamamoto, and T. Yamaguchi, "Modeling of Nonlinear Chemical Reaction Systems and Two-Parameter Stochastic Resonance," J. Biol. Phys. 25 (1999) 73 [2] F. Moss, L. M. Ward, and W. G. Sannita, "Stochastic resonance and sensory information processing: a tutorial and review of application" Clinical neurophysiology 115 (2004) 267 [3] M. Platkov, and M. Gruebele, "Periodic and stochastic thermal modulation of protein folding kinetics" J. Chem. Phys. 141 (2014) 035103 [4] T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya and E. Kuramochi. "Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip". Opt. Lett., 30 (2005) 2575 [5] R. L. Badzey and P. Mohanty. "Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance" Nature, 437 (2005) 995 [6] W. J. Venstra, H. J. R. Westra, and H. S. J. van der Zant. "Stochastic switching of cantilever motion," Nature Communications, 4 (2013) 3624 [7] J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny "Subkelvin parametric feedback cooling of a Laser-Trapped nanoparticle" Phys. Rev. Lett. 109 (2012) 103603 [8] J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, "Nonlinear Mode Coupling and Synchronization of a Vacuum-Trapped Nanoparticle," Phys. Rev. Lett. 112 (2014) 103603

Stochastic Nature in Cellular Processes

NASA Astrophysics Data System (ADS)

Liu, Bo; Liu, Sheng-Jun; Wang, Qi; Yan, Shi-Wei; Geng, Yi-Zhao; Sakata, Fumihiko; Gao, Xing-Fa

2011-11-01

The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

PubMed Central

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-01-01

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity). PMID:25976626

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity.

PubMed

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-05-15

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

NASA Astrophysics Data System (ADS)

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-05-01

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Stochasticity in materials structure, properties, and processing—A review

NASA Astrophysics Data System (ADS)

Hull, Robert; Keblinski, Pawel; Lewis, Dan; Maniatty, Antoinette; Meunier, Vincent; Oberai, Assad A.; Picu, Catalin R.; Samuel, Johnson; Shephard, Mark S.; Tomozawa, Minoru; Vashishth, Deepak; Zhang, Shengbai

2018-03-01

We review the concept of stochasticity—i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes—in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by—or amplify—stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

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?'

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

NASA Astrophysics Data System (ADS)

Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

A dual theory of price and value in a meso-scale economic model with stochastic profit rate

NASA Astrophysics Data System (ADS)

Greenblatt, R. E.

2014-12-01

The problem of commodity price determination in a market-based, capitalist economy has a long and contentious history. Neoclassical microeconomic theories are based typically on marginal utility assumptions, while classical macroeconomic theories tend to be value-based. In the current work, I study a simplified meso-scale model of a commodity capitalist economy. The production/exchange model is represented by a network whose nodes are firms, workers, capitalists, and markets, and whose directed edges represent physical or monetary flows. A pair of multivariate linear equations with stochastic input parameters represent physical (supply/demand) and monetary (income/expense) balance. The input parameters yield a non-degenerate profit rate distribution across firms. Labor time and price are found to be eigenvector solutions to the respective balance equations. A simple relation is derived relating the expected value of commodity price to commodity labor content. Results of Monte Carlo simulations are consistent with the stochastic price/labor content relation.

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Ronco, Michele

2017-10-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Evolutionary inference via the Poisson Indel Process.

PubMed

Bouchard-Côté, Alexandre; Jordan, Michael I

2013-01-22

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

Evolutionary inference via the Poisson Indel Process

PubMed Central

Bouchard-Côté, Alexandre; Jordan, Michael I.

2013-01-01

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114–124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments. PMID:23275296

Universality in the tail of musical note rank distribution

NASA Astrophysics Data System (ADS)

Beltrán del Río, M.; Cocho, G.; Naumis, G. G.

2008-09-01

Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tails. Languages as sequences of symbols have been a popular subject for ranking distributions, and for this purpose, music can be treated as such. Here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution, which arises in the ranking of multiplicative stochastic processes. The parameters a and b are obtained for classical, jazz and rock music, revealing interesting features. Specially, we have obtained a clear trend in the values of the parameters for major and minor tonal modes. Finally, we discuss the distribution of notes for each octave and its connection with the ranking of the notes.

Two-layer symbolic representation for stochastic models with phase-type distributed events

NASA Astrophysics Data System (ADS)

Longo, Francesco; Scarpa, Marco

2015-07-01

Among the techniques that have been proposed for the analysis of non-Markovian models, the state space expansion approach showed great flexibility in terms of modelling capacities.The principal drawback is the explosion of the state space. This paper proposes a two-layer symbolic method for efficiently storing the expanded reachability graph of a non-Markovian model in the case in which continuous phase-type distributions are associated with the firing times of system events, and different memory policies are considered. At the lower layer, the reachability graph is symbolically represented in the form of a set of Kronecker matrices, while, at the higher layer, all the information needed to correctly manage event memory is stored in a multi-terminal multi-valued decision diagram. Such an information is collected by applying a symbolic algorithm, which is based on a couple of theorems. The efficiency of the proposed approach, in terms of memory occupation and execution time, is shown by applying it to a set of non-Markovian stochastic Petri nets and comparing it with a classical explicit expansion algorithm. Moreover, a comparison with a classical symbolic approach is performed whenever possible.

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

NASA Astrophysics Data System (ADS)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Introduction to Stochastic Simulations for Chemical and Physical Processes: Principles and Applications

ERIC Educational Resources Information Center

Weiss, Charles J.

2017-01-01

An introduction to digital stochastic simulations for modeling a variety of physical and chemical processes is presented. Despite the importance of stochastic simulations in chemistry, the prevalence of turn-key software solutions can impose a layer of abstraction between the user and the underlying approach obscuring the methodology being…

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

PubMed

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Combinatoric analysis of heterogeneous stochastic self-assembly.

PubMed

D'Orsogna, Maria R; Zhao, Bingyu; Berenji, Bijan; Chou, Tom

2013-09-28

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

Species sorting, apparent neutrality and lasting priority effects: palaeoecological lessons from an inherently dynamic natural ecosystem

NASA Astrophysics Data System (ADS)

Mergeay, J.; De Meester, L.; Verschuren, D.

2009-04-01

To assess the influence of long-term temporal processes in community assembly, we reconstructed the community changes of two dominant components of freshwater food webs, planktonic Daphnia water fleas and benthic chironomid midge larvae, in a fluctuating tropical lake through eight cycles of major lake-level fluctuation spanning 1800 years. Our results show a highly unpredictable pattern of community assembly in Daphnia, akin to neutrality, but largely dictated by long-lasting priority effects. These priority effects were likely caused by rapid population growth of resident species during lake refilling from a standing stock in a deep crater refuge, thereby pre-empting niche space for new immigrants. Contrastingly, chironomid larvae showed a more classical species sorting response to long-term environmental change, with more limited contribution of stochastic temporal processes. Overall our study emphasizes the importance of temporal processes and niche pre-emption in metacommunity ecology, and suggests a important role for mass effects in time. It also emphasizes the value of paleoecological research to improve understanding of ecological processes in natural ecosystems.

Applications of stochastic mechanics to polyatomic lattices

NASA Astrophysics Data System (ADS)

Beumée, J. G. B.; Vilallonga, E.; Rabitz, H.

1990-03-01

Stochastic quantization in the sense of Nelson provides an alternative interpretation of some aspects of quantum mechanics in the coordinate representation, and it was combined recently with the Ford, Kac, and Mazur (FKM) approximation [J. Math. Phys. 6, 504 (1965)] for large lattices to construct a quantum analog to the Brownian motion process. In this paper a similar approach is applied to model the effect of temperature fluctuations in a one-dimensional ordered chain of atoms with nearest-neighbor linear forces. However, we do not make use of the FKM approximation, and as a consequence the statistical properties of the involved processes are exactly determined by the lattice force field. In particular, we evaluate the covariance matrix for the fluctuations, and we examine its high- and low-temperature behavior. Because of the translation invariance of the interaction potential, the covariance matrix for the fluctuations becomes singular implying that the associated probability density has equal density along the zero eigenvector of the interaction matrix. This behavior is readily interpreted in terms of the motion of the center of mass of the system, which corresponds to a stochastically perturbed translation, while all other modes are bounded with a probability of 1. As is well known, the transformation to internal (bondlength) coordinates leads to a Hamiltonian specified by a nonsingular interaction matrix. We examine the variance of the fluctuations for the internal coordinates, and we show that in the high-temperature limit the result agrees with that of classical statistical mechanics. Both the position and bondlength of the surface atom decrease with time as is expected for a semi-infinite lattice. However, the position of the surface atom is less dependent on substrate-atom positions than is the surface bondlength on substrate bondlengths. Finally, the autocorrelation function of the surface bondlength in the case of a semi-infinite lattice limit is investigated for low- and high-temperature limits.

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS1

PubMed Central

Gary Chan, Kwun Chuen; Wang, Mei-Cheng

2011-01-01

Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER–Medicare linked data set is used to illustrate the proposed methodologies. PMID:21359167

Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case

NASA Astrophysics Data System (ADS)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.

2010-06-01

Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

NASA Astrophysics Data System (ADS)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Theoretical analysis of the distribution of isolated particles in totally asymmetric exclusion processes: Application to mRNA translation rate estimation

NASA Astrophysics Data System (ADS)

Dao Duc, Khanh; Saleem, Zain H.; Song, Yun S.

2018-01-01

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.

Consistent resolution of some relativistic quantum paradoxes

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2002-12-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

First passage times in homogeneous nucleation: Dependence on the total number of particles

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

Yvinec, Romain; Bernard, Samuel; Pujo-Menjouet, Laurent

2016-01-21

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find thatmore » the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.« less

Neural Correlates of Auditory Figure-Ground Segregation Based on Temporal Coherence.

PubMed

Teki, Sundeep; Barascud, Nicolas; Picard, Samuel; Payne, Christopher; Griffiths, Timothy D; Chait, Maria

2016-09-01

To make sense of natural acoustic environments, listeners must parse complex mixtures of sounds that vary in frequency, space, and time. Emerging work suggests that, in addition to the well-studied spectral cues for segregation, sensitivity to temporal coherence-the coincidence of sound elements in and across time-is also critical for the perceptual organization of acoustic scenes. Here, we examine pre-attentive, stimulus-driven neural processes underlying auditory figure-ground segregation using stimuli that capture the challenges of listening in complex scenes where segregation cannot be achieved based on spectral cues alone. Signals ("stochastic figure-ground": SFG) comprised a sequence of brief broadband chords containing random pure tone components that vary from 1 chord to another. Occasional tone repetitions across chords are perceived as "figures" popping out of a stochastic "ground." Magnetoencephalography (MEG) measurement in naïve, distracted, human subjects revealed robust evoked responses, commencing from about 150 ms after figure onset that reflect the emergence of the "figure" from the randomly varying "ground." Neural sources underlying this bottom-up driven figure-ground segregation were localized to planum temporale, and the intraparietal sulcus, demonstrating that this area, outside the "classic" auditory system, is also involved in the early stages of auditory scene analysis." © The Author 2016. Published by Oxford University Press.

First passage times in homogeneous nucleation: Dependence on the total number of particles

NASA Astrophysics Data System (ADS)

Yvinec, Romain; Bernard, Samuel; Hingant, Erwan; Pujo-Menjouet, Laurent

2016-01-01

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

PubMed

Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C

2014-04-01

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

Stochastic switching in biology: from genotype to phenotype

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-03-01

There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a self-contained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels. However, applications to other examples of biological switching are also discussed, including stochastic ion channels, diffusion in randomly switching environments, bacterial chemotaxis, and stochastic neural networks.

Confined trapped alpha behaviour in TFTR deuterium-tritium plasmas

NASA Astrophysics Data System (ADS)

Medley, S. S.; Budny, R. V.; Duong, H. H.; Fisher, R. K.; Petrov, M. P.; Gorelenkov, N. N.; Redi, M. H.; Roquemore, A. L.; White, R. B.

1998-09-01

Confined trapped alpha energy spectra and differential radial density profiles in TFTR D-T plasmas were obtained with the pellet charge exchange (PCX) diagnostic, which measures high energy (Eα = 0.5-3.5 MeV) trapped alphas (v||/v = -0.048) at a single time slice (Δt approx 1 ms) with a spatial resolution of Δr approx 5 cm. Tritons produced in D-D plasmas and RF driven ion tails (H, 3He or T) were also observed and energetic tritium ion tail measurements are discussed. PCX alpha and triton energy spectra extending up to their birth energies were measured in the core of MHD quiescent discharges where the expected classical slowing down and pitch angle scattering effects are not complicated by stochastic ripple diffusion and sawtooth activity. Both the shape of the measured alpha and triton energy distributions and their density ratios are in good agreement with TRANSP predictions, indicating that the PCX measurements are consistent with classical thermalization of the fusion generated alphas and tritons. From calculations, these results set an upper limit on possible anomalous radial diffusion for trapped alphas of Dα <= 0.01 m2·s-1. Outside the core, where the trapped alphas are influenced by stochastic ripple diffusion effects, the PCX measurements are consistent with the functional dependence of the Goldston-White-Boozer stochastic ripple threshold on the alpha energy and the q profile. In the presence of strong sawtooth activity, the PCX diagnostic observes significant redistribution of the alpha signal radial profile wherein alphas are depleted in the core and redistributed to well outside the q = 1 radius, but apparently not beyond the energy dependent stochastic ripple loss boundary. The helical electric field produced during the sawtooth crash plays an essential role in modelling the sawtooth redistribution data. In sawtooth free discharge scenarios with reversed shear operation, the PCX diagnostic also observes radial profiles of the alpha signal that are significantly broader than those for supershots. ORBIT modelling of reversed shear and monotonic shear discharges is in agreement with the q dependent alpha profiles observed. Redistribution of trapped alpha particles in the presence of core localized toroidal Alfvén eigenmode (TAE) activity was observed and modelling of the PCX measurements based on a synergism involving the α-TAE resonance and the effect of stochastic ripple diffusion is in progress.

[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.

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Uncertainty Reduction for Stochastic Processes on Complex Networks

NASA Astrophysics Data System (ADS)

Radicchi, Filippo; Castellano, Claudio

2018-05-01

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by a large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes. However, choosing these points of observation in an optimal way is a highly nontrivial task, depending on the nature of the stochastic process and on the structure of the underlying interaction pattern. In this paper, we introduce a computationally efficient algorithm to determine quasioptimal solutions to the problem. The method leverages network sparsity to reduce computational complexity from exponential to almost quadratic, thus allowing the straightforward application of the method to mid-to-large-size systems. Although the method is exact only for equilibrium stochastic processes defined on trees, it turns out to be effective also for out-of-equilibrium processes on sparse loopy networks.

Habitat connectivity and in-stream vegetation control temporal variability of benthic invertebrate communities.

PubMed

Huttunen, K-L; Mykrä, H; Oksanen, J; Astorga, A; Paavola, R; Muotka, T

2017-05-03

One of the key challenges to understanding patterns of β diversity is to disentangle deterministic patterns from stochastic ones. Stochastic processes may mask the influence of deterministic factors on community dynamics, hindering identification of the mechanisms causing variation in community composition. We studied temporal β diversity (among-year dissimilarity) of macroinvertebrate communities in near-pristine boreal streams across 14 years. To assess whether the observed β diversity deviates from that expected by chance, and to identify processes (deterministic vs. stochastic) through which different explanatory factors affect community variability, we used a null model approach. We observed that at the majority of sites temporal β diversity was low indicating high community stability. When stochastic variation was unaccounted for, connectivity was the only variable explaining temporal β diversity, with weakly connected sites exhibiting higher community variability through time. After accounting for stochastic effects, connectivity lost importance, suggesting that it was related to temporal β diversity via random colonization processes. Instead, β diversity was best explained by in-stream vegetation, community variability decreasing with increasing bryophyte cover. These results highlight the potential of stochastic factors to dampen the influence of deterministic processes, affecting our ability to understand and predict changes in biological communities through time.

Gene regulation and noise reduction by coupling of stochastic processes

NASA Astrophysics Data System (ADS)

Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Gene regulation and noise reduction by coupling of stochastic processes

PubMed Central

Hornos, José Eduardo M.; Reinitz, John

2015-01-01

Here we characterize the low noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the the two gene states depends on protein number. This fact has a very important implication: there exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction. PMID:25768447

Gene regulation and noise reduction by coupling of stochastic processes.

PubMed

Ramos, Alexandre F; Hornos, José Eduardo M; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

The Common Patterns of Nature

PubMed Central

Frank, Steven A.

2010-01-01

We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased or random stochastic fluctuations: random connections of network nodes; amino acid substitutions with no effect on fitness; species that arise or disappear from communities randomly. These neutral generative models often match common patterns of nature. In this paper, I present the theoretical background by which we can understand why these neutral generative models are so successful. I show where the classic patterns come from, such as the Poisson pattern, the normal or Gaussian pattern, and many others. Each classic pattern was often discovered by a simple neutral generative model. The neutral patterns share a special characteristic: they describe the patterns of nature that follow from simple constraints on information. For example, any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves information only about the geometric mean attracts to the power law pattern. I present a simple and consistent informational framework of the common patterns of nature based on the method of maximum entropy. This framework shows that each neutral generative model is a special case that helps to discover a particular set of informational constraints; those informational constraints define a much wider domain of non-neutral generative processes that attract to the same neutral pattern. PMID:19538344

Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

Lei, Xiao-hui; Tan, Qiao-feng; Wang, Xu; Wang, Hao; Wen, Xin; Wang, Chao; Zhang, Jing-wen

2018-02-01

Stochastic dynamic programming (SDP) has been widely used to derive operating policies for reservoirs considering streamflow uncertainties. In SDP, there is a need to calculate the transition probability matrix more accurately and efficiently in order to improve the economic benefit of reservoir operation. In this study, we proposed a stochastic optimization model for hydropower generation reservoirs, in which 1) the transition probability matrix was calculated based on copula functions; and 2) the value function of the last period was calculated by stepwise iteration. Firstly, the marginal distribution of stochastic inflow in each period was built and the joint distributions of adjacent periods were obtained using the three members of the Archimedean copulas, based on which the conditional probability formula was derived. Then, the value in the last period was calculated by a simple recursive equation with the proposed stepwise iteration method and the value function was fitted with a linear regression model. These improvements were incorporated into the classic SDP and applied to the case study in Ertan reservoir, China. The results show that the transition probability matrix can be more easily and accurately obtained by the proposed copula function based method than conventional methods based on the observed or synthetic streamflow series, and the reservoir operation benefit can also be increased.

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed

Capitán, José A; Cuenda, Sara; Alonso, David

2015-09-06

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. © 2015 The Author(s).

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed Central

Capitán, José A.; Cuenda, Sara; Alonso, David

2015-01-01

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. PMID:26269234

Data Analysis Approaches for the Risk-Informed Safety Margins Characterization Toolkit

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

Mandelli, Diego; Alfonsi, Andrea; Maljovec, Daniel P.

2016-09-01

In the past decades, several numerical simulation codes have been employed to simulate accident dynamics (e.g., RELAP5-3D, RELAP-7, MELCOR, MAAP). In order to evaluate the impact of uncertainties into accident dynamics, several stochastic methodologies have been coupled with these codes. These stochastic methods range from classical Monte-Carlo and Latin Hypercube sampling to stochastic polynomial methods. Similar approaches have been introduced into the risk and safety community where stochastic methods (such as RAVEN, ADAPT, MCDET, ADS) have been coupled with safety analysis codes in order to evaluate the safety impact of timing and sequencing of events. These approaches are usually calledmore » Dynamic PRA or simulation-based PRA methods. These uncertainties and safety methods usually generate a large number of simulation runs (database storage may be on the order of gigabytes or higher). The scope of this paper is to present a broad overview of methods and algorithms that can be used to analyze and extract information from large data sets containing time dependent data. In this context, “extracting information” means constructing input-output correlations, finding commonalities, and identifying outliers. Some of the algorithms presented here have been developed or are under development within the RAVEN statistical framework.« less

Performance of quantum annealing on random Ising problems implemented using the D-Wave Two

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Job, Joshua; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.; USC Collaboration; ETH Collaboration

2014-03-01

Detecting a possible speedup of quantum annealing compared to classical algorithms is a pressing task in experimental adiabatic quantum computing. In this talk, we discuss the performance of the D-Wave Two quantum annealing device on Ising spin glass problems. The expected time to solution for the device to solve random instances with up to 503 spins and with specified coupling ranges is evaluated while carefully addressing the issue of statistical errors. We perform a systematic comparison of the expected time to solution between the D-Wave Two and classical stochastic solvers, specifically simulated annealing, and simulated quantum annealing based on quantum Monte Carlo, and discuss the question of speedup.

Solving multiconstraint assignment problems using learning automata.

PubMed

Horn, Geir; Oommen, B John

2010-02-01

This paper considers the NP-hard problem of object assignment with respect to multiple constraints: assigning a set of elements (or objects) into mutually exclusive classes (or groups), where the elements which are "similar" to each other are hopefully located in the same class. The literature reports solutions in which the similarity constraint consists of a single index that is inappropriate for the type of multiconstraint problems considered here and where the constraints could simultaneously be contradictory. This feature, where we permit possibly contradictory constraints, distinguishes this paper from the state of the art. Indeed, we are aware of no learning automata (or other heuristic) solutions which solve this problem in its most general setting. Such a scenario is illustrated with the static mapping problem, which consists of distributing the processes of a parallel application onto a set of computing nodes. This is a classical and yet very important problem within the areas of parallel computing, grid computing, and cloud computing. We have developed four learning-automata (LA)-based algorithms to solve this problem: First, a fixed-structure stochastic automata algorithm is presented, where the processes try to form pairs to go onto the same node. This algorithm solves the problem, although it requires some centralized coordination. As it is desirable to avoid centralized control, we subsequently present three different variable-structure stochastic automata (VSSA) algorithms, which have superior partitioning properties in certain settings, although they forfeit some of the scalability features of the fixed-structure algorithm. All three VSSA algorithms model the processes as automata having first the hosting nodes as possible actions; second, the processes as possible actions; and, third, attempting to estimate the process communication digraph prior to probabilistically mapping the processes. This paper, which, we believe, comprehensively reports the pioneering LA solutions to this problem, unequivocally demonstrates that LA can play an important role in solving complex combinatorial and integer optimization problems.

On the anisotropic advection-diffusion equation with time dependent coefficients

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

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

Evanescent radiation, quantum mechanics and the Casimir effect

NASA Technical Reports Server (NTRS)

Schatten, Kenneth H.

1989-01-01

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

NASA Technical Reports Server (NTRS)

Carter, M. C.; Madison, M. W.

1973-01-01

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Refreeze experiments with water droplets containing different types of ice nuclei interpreted by classical nucleation theory

NASA Astrophysics Data System (ADS)

Kaufmann, Lukas; Marcolli, Claudia; Luo, Beiping; Peter, Thomas

2017-03-01

Homogeneous nucleation of ice in supercooled water droplets is a stochastic process. In its classical description, the growth of the ice phase requires the emergence of a critical embryo from random fluctuations of water molecules between the water bulk and ice-like clusters, which is associated with overcoming an energy barrier. For heterogeneous ice nucleation on ice-nucleating surfaces both stochastic and deterministic descriptions are in use. Deterministic (singular) descriptions are often favored because the temperature dependence of ice nucleation on a substrate usually dominates the stochastic time dependence, and the ease of representation facilitates the incorporation in climate models. Conversely, classical nucleation theory (CNT) describes heterogeneous ice nucleation as a stochastic process with a reduced energy barrier for the formation of a critical embryo in the presence of an ice-nucleating surface. The energy reduction is conveniently parameterized in terms of a contact angle α between the ice phase immersed in liquid water and the heterogeneous surface. This study investigates various ice-nucleating agents in immersion mode by subjecting them to repeated freezing cycles to elucidate and discriminate the time and temperature dependences of heterogeneous ice nucleation. Freezing rates determined from such refreeze experiments are presented for Hoggar Mountain dust, birch pollen washing water, Arizona test dust (ATD), and also nonadecanol coatings. For the analysis of the experimental data with CNT, we assumed the same active site to be always responsible for freezing. Three different CNT-based parameterizations were used to describe rate coefficients for heterogeneous ice nucleation as a function of temperature, all leading to very similar results: for Hoggar Mountain dust, ATD, and larger nonadecanol-coated water droplets, the experimentally determined increase in freezing rate with decreasing temperature is too shallow to be described properly by CNT using the contact angle α as the only fit parameter. Conversely, birch pollen washing water and small nonadecanol-coated water droplets show temperature dependencies of freezing rates steeper than predicted by all three CNT parameterizations. Good agreement of observations and calculations can be obtained when a pre-factor β is introduced to the rate coefficient as a second fit parameter. Thus, the following microphysical picture emerges: heterogeneous freezing occurs at ice-nucleating sites that need a minimum (critical) surface area to host embryos of critical size to grow into a crystal. Fits based on CNT suggest that the critical active site area is in the range of 10-50 nm2, with the exact value depending on sample, temperature, and CNT-based parameterization. Two fitting parameters are needed to characterize individual active sites. The contact angle α lowers the energy barrier that has to be overcome to form the critical embryo at the site compared to the homogeneous case where the critical embryo develops in the volume of water. The pre-factor β is needed to adjust the calculated slope of freezing rate increase with temperature decrease. When this slope is steep, this can be interpreted as a high frequency of nucleation attempts, so that nucleation occurs immediately when the temperature is low enough for the active site to accommodate a critical embryo. This is the case for active sites of birch pollen washing water and for small droplets coated with nonadecanol. If the pre-factor is low, the frequency of nucleation attempts is low and the increase in freezing rate with decreasing temperature is shallow. This is the case for Hoggar Mountain dust, the large droplets coated with nonadecanol, and ATD. Various hypotheses why the value of the pre-factor depends on the nature of the active sites are discussed.

A methodology to assess the economic impact of power storage technologies.

PubMed

El-Ghandour, Laila; Johnson, Timothy C

2017-08-13

We present a methodology for assessing the economic impact of power storage technologies. The methodology is founded on classical approaches to the optimal stopping of stochastic processes but involves an innovation that circumvents the need to, ex ante , identify the form of a driving process and works directly on observed data, avoiding model risks. Power storage is regarded as a complement to the intermittent output of renewable energy generators and is therefore important in contributing to the reduction of carbon-intensive power generation. Our aim is to present a methodology suitable for use by policy makers that is simple to maintain, adaptable to different technologies and easy to interpret. The methodology has benefits over current techniques and is able to value, by identifying a viable optimal operational strategy, a conceived storage facility based on compressed air technology operating in the UK.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

NASA Technical Reports Server (NTRS)

Sepka, Steve; Vander Kam, Jeremy; McGuire, Kathy

2018-01-01

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bond line temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

NASA Technical Reports Server (NTRS)

Sepka, Steven A.; McGuire, Mary Kathleen; Vander Kam, Jeremy C.

2018-01-01

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bondline temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Helicopter Control Energy Reduction Using Moving Horizontal Tail

PubMed Central

Oktay, Tugrul; Sal, Firat

2015-01-01

Helicopter moving horizontal tail (i.e., MHT) strategy is applied in order to save helicopter flight control system (i.e., FCS) energy. For this intention complex, physics-based, control-oriented nonlinear helicopter models are used. Equations of MHT are integrated into these models and they are together linearized around straight level flight condition. A specific variance constrained control strategy, namely, output variance constrained Control (i.e., OVC) is utilized for helicopter FCS. Control energy savings due to this MHT idea with respect to a conventional helicopter are calculated. Parameters of helicopter FCS and dimensions of MHT are simultaneously optimized using a stochastic optimization method, namely, simultaneous perturbation stochastic approximation (i.e., SPSA). In order to observe improvement in behaviors of classical controls closed loop analyses are done. PMID:26180841

Electronic excitation and quenching of atoms at insulator surfaces

NASA Technical Reports Server (NTRS)

Swaminathan, P. K.; Garrett, Bruce C.; Murthy, C. S.

1988-01-01

A trajectory-based semiclassical method is used to study electronically inelastic collisions of gas atoms with insulator surfaces. The method provides for quantum-mechanical treatment of the internal electronic dynamics of a localized region involving the gas/surface collision, and a classical treatment of all the nuclear degrees of freedom (self-consistently and in terms of stochastic trajectories), and includes accurate simulation of the bath-temperature effects. The method is easy to implement and has a generality that holds promise for many practical applications. The problem of electronically inelastic dynamics is solved by computing a set of stochastic trajectories that on thermal averaging directly provide electronic transition probabilities at a given temperature. The theory is illustrated by a simple model of a two-state gas/surface interaction.

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.

Trapping dynamics of xenon on Pt(111)

NASA Astrophysics Data System (ADS)

Arumainayagam, Christopher R.; Madix, Robert J.; Mcmaster, Mark C.; Suzawa, Valerie M.; Tully, John C.

1990-02-01

The dynamics of Xe trapping on Pt(111) was studied using supersonic atomic beam techniques. Initial trapping probabilities ( S0) were measured directly as a function of incident translational energy ( EinT) and angle of incidence (θ i) at a surface temperature ( Tins) 95 K. The initial trapping probability decreases smoothly with increasing ET cosθ i;, rather than ET cos 2θ i, suggesting participation of parallel momentum in the trapping process. Accordingly, the measured initial trapping probability falls off more slowly with increasing incident translational energy than predicted by one-dimensional theories. This finding is in near agreement with previous mean translational energy measurements for Xe desorbing near the Pt(111) surface normal, assuming detailed balance applies. Three-dimensional stochastic classical trajectory calculations presented herein also exhibit the importance of tangential momentum in trapping and satisfactorily reproduce the experimental initial trapping probabilities.

Option pricing, stochastic volatility, singular dynamics and constrained path integrals

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Hojman, Sergio A.

2014-01-01

Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter ρ which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases ρ=±1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values ρ=±1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac’s method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral.

Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy.

PubMed

Sánchez-Taltavull, Daniel; Vieiro, Arturo; Alarcón, Tomás

2016-10-01

HIV-1 infected patients are effectively treated with highly active anti-retroviral therapy (HAART). Whilst HAART is successful in keeping the disease at bay with average levels of viral load well below the detection threshold of standard clinical assays, it fails to completely eradicate the infection, which persists due to the emergence of a latent reservoir with a half-life time of years and is immune to HAART. This implies that life-long administration of HAART is, at the moment, necessary for HIV-1-infected patients, which is prone to drug resistance and cumulative side effects as well as imposing a considerable financial burden on developing countries, those more afflicted by HIV, and public health systems. The development of therapies which specifically aim at the removal of this latent reservoir has become a focus of much research. A proposal for such therapy consists of elevating the rate of activation of the latently infected cells: by transferring cells from the latently infected reservoir to the active infected compartment, more cells are exposed to the anti-retroviral drugs thus increasing their effectiveness. In this paper, we present a stochastic model of the dynamics of the HIV-1 infection and study the effect of the rate of latently infected cell activation on the average extinction time of the infection. By analysing the model by means of an asymptotic approximation using the semi-classical quasi steady state approximation (QSS), we ascertain that this therapy reduces the average life-time of the infection by many orders of magnitudes. We test the accuracy of our asymptotic results by means of direct simulation of the stochastic process using a hybrid multi-scale Monte Carlo scheme.

Book Review:

NASA Astrophysics Data System (ADS)

Beenakker, C. W. J.

2005-08-01

Quantum Noise is advertised as a handbook, and this is indeed how it functions for me these days: it is a book that I keep within hand's reach, ready to be consulted on the proper use of quantum stochastic methods in the course of my research on quantum dots. I should point out that quantum optics, the target field for this book, is not my field by training. So I have much to learn, and find this handbook to be a reliable and helpful guide. Crispin Gardiner previously wrote the Handbook of Stochastic Methods (also published by Springer), which provides an overview of methods in classical statistical physics. Quantum Noise, written jointly with Peter Zoller, is the counterpart for quantum statistical physics, and indeed the two books rely on each other by frequent cross referencing. The fundamental problem addressed by Quantum Noise is how the quantum dynamics of an open system can be described statistically by treating the environment as a source of noise. This is a general problem in condensed matter physics (in particular in the context of Josephson junctions) and in quantum optics. The emphasis in this book in on the optical applications (for condensed matter applications one could consult Quantum Dissipative Systems by Ulrich Weiss, published by World Scientific). The optical applications centre around the interaction of light with atoms, where the atoms represent the open system and the light is the noisy environment. A complete description of the production and detection of non-classical states of radiation (such as squeezed states) can be obtained using one of the equivalent quantum stochastic formulations: the quantum Langevin equation for the field operators (in either the Ito or the Stratonovich form), the Master equation for the density matrix, or the stochastic Schrödinger equation for the wave functions. Each formulation is fully developed here (as one would expect from a handbook), with detailed instructions on how to go from one to the other. The development of the topic is precise and well-organized. The derivations are written out in sufficient detail, without frustrating comments like `it can be shown that'. The book is not quite self-contained, because it relies on the Handbook of Stochastic Methods for some background material (notably the issue of Ito versus Stratonovich). Still, one could very well use this book as a text for a course, supplying the background material to the students in some other form. Quantum Noise is now in its third edition. The second edition was a major expansion, including applications to laser cooling and quantum information processing. The third edition is a relatively minor upgrade, consisting mainly of pointers to recent literature. If you own the second edition, you might well skip this upgrade. If you do not yet own the book, or are still at edition 1, then I would enthusiastically recommend acquiring this handbook, regardless of whether you work in quantum optics or in another field of quantum physics. As I did, you might well find a new tool to attack your favourite problem.

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Treesearch

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Complete integrability of information processing by biochemical reactions

PubMed Central

Agliari, Elena; Barra, Adriano; Dello Schiavo, Lorenzo; Moro, Antonio

2016-01-01

Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling – based on spin systems – has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis–Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy – based on completely integrable hydrodynamic-type systems of PDEs – which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions. PMID:27812018

Comparative analysis of ArnCl2 (2 ? n ? 30) clusters taking into account molecular relaxation effects

NASA Astrophysics Data System (ADS)

Ferreira, G. G.; Borges, E.; Braga, J. P.; Belchior, J. C.

Cluster structures are discussed in a nonrigid analysis, using a modified minima search method based on stochastic processes and classical dynamics simulations. The relaxation process is taken into account considering the internal motion of the Cl2 molecule. Cluster structures are compared with previous works in which the Cl2 molecule is assumed to be rigid. The interactions are modeled using pair potentials: the Aziz and Lennard-Jones potentials for the Ar==Ar interaction, a Morse potential for the Cl==Cl interaction, and a fully spherical/anisotropic Morse-Spline-van der Waals (MSV) potential for the Ar==Cl interaction. As expected, all calculated energies are lower than those obtained in a rigid approximation; one reason may be attributed to the nonrigid contributions of the internal motion of the Cl2 molecule. Finally, the growing processes in molecular clusters are discussed, and it is pointed out that the growing mechanism can be affected due to the nonrigid initial conditions of smaller clusters such as ArnCl2 (n ? 4 or 5), which are seeds for higher-order clusters.

Complete integrability of information processing by biochemical reactions

NASA Astrophysics Data System (ADS)

Agliari, Elena; Barra, Adriano; Dello Schiavo, Lorenzo; Moro, Antonio

2016-11-01

Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling - based on spin systems - has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis-Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy - based on completely integrable hydrodynamic-type systems of PDEs - which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions.

Complete integrability of information processing by biochemical reactions.

PubMed

Agliari, Elena; Barra, Adriano; Dello Schiavo, Lorenzo; Moro, Antonio

2016-11-04

Statistical mechanics provides an effective framework to investigate information processing in biochemical reactions. Within such framework far-reaching analogies are established among (anti-) cooperative collective behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical mechanics and operational amplifiers/flip-flops in cybernetics. The underlying modeling - based on spin systems - has been proved to be accurate for a wide class of systems matching classical (e.g. Michaelis-Menten, Hill, Adair) scenarios in the infinite-size approximation. However, the current research in biochemical information processing has been focusing on systems involving a relatively small number of units, where this approximation is no longer valid. Here we show that the whole statistical mechanical description of reaction kinetics can be re-formulated via a mechanical analogy - based on completely integrable hydrodynamic-type systems of PDEs - which provides explicit finite-size solutions, matching recently investigated phenomena (e.g. noise-induced cooperativity, stochastic bi-stability, quorum sensing). The resulting picture, successfully tested against a broad spectrum of data, constitutes a neat rationale for a numerically effective and theoretically consistent description of collective behaviors in biochemical reactions.

Fast stochastic algorithm for simulating evolutionary population dynamics

NASA Astrophysics Data System (ADS)

Tsimring, Lev; Hasty, Jeff; Mather, William

2012-02-01

Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.

A stochastic maximum principle for backward control systems with random default time

NASA Astrophysics Data System (ADS)

Shen, Yang; Kuen Siu, Tak

2013-05-01

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Stochastic associative memory

NASA Astrophysics Data System (ADS)

Baumann, Erwin W.; Williams, David L.

1993-08-01

Artificial neural networks capable of learning and recalling stochastic associations between non-deterministic quantities have received relatively little attention to date. One potential application of such stochastic associative networks is the generation of sensory 'expectations' based on arbitrary subsets of sensor inputs to support anticipatory and investigate behavior in sensor-based robots. Another application of this type of associative memory is the prediction of how a scene will look in one spectral band, including noise, based upon its appearance in several other wavebands. This paper describes a semi-supervised neural network architecture composed of self-organizing maps associated through stochastic inter-layer connections. This 'Stochastic Associative Memory' (SAM) can learn and recall non-deterministic associations between multi-dimensional probability density functions. The stochastic nature of the network also enables it to represent noise distributions that are inherent in any true sensing process. The SAM architecture, training process, and initial application to sensor image prediction are described. Relationships to Fuzzy Associative Memory (FAM) are discussed.

Load Balancing in Stochastic Networks: Algorithms, Analysis, and Game Theory

DTIC Science & Technology

2014-04-16

SECURITY CLASSIFICATION OF: The classic randomized load balancing model is the so-called supermarket model, which describes a system in which...P.O. Box 12211 Research Triangle Park, NC 27709-2211 mean-field limits, supermarket model, thresholds, game, randomized load balancing REPORT...balancing model is the so-called supermarket model, which describes a system in which customers arrive to a service center with n parallel servers according

Physical-layer encryption on the public internet: A stochastic approach to the Kish-Sethuraman cipher

NASA Astrophysics Data System (ADS)

Gunn, Lachlan J.; Chappell, James M.; Allison, Andrew; Abbott, Derek

2014-09-01

While information-theoretic security is often associated with the one-time pad and quantum key distribution, noisy transport media leave room for classical techniques and even covert operation. Transit times across the public internet exhibit a degree of randomness, and cannot be determined noiselessly by an eavesdropper. We demonstrate the use of these measurements for information-theoretically secure communication over the public internet.

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise.

PubMed

Paris, Alan; Vosoughi, Azadeh; Berman, Stephen A; Atia, George

2018-07-01

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately [Formula: see text]-type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous [Formula: see text]-type Lorentzian weights, in which the spectral exponent [Formula: see text] is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to [Formula: see text]-type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond [Formula: see text]-type -noise, including applications to animal models and possible impact on quantum foundations.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race.

PubMed

Warnke, Tom; Reinhardt, Oliver; Klabunde, Anna; Willekens, Frans; Uhrmacher, Adelinde M

2017-10-01

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

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.

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.

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.

Comment on Pisarenko et al., "Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory"

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2016-02-01

In this short note, I comment on the research of Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014) regarding the extreme value theory and statistics in the case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic model for the block maxima of a random variable and the generalized Pareto distribution (GPD) as a model for the peaks over threshold (POT) of the same random variable is presented more clearly. Inappropriately, Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014) have neglected to note that the approximations by GEVD and GPD work only asymptotically in most cases. This is particularly the case with truncated exponential distribution (TED), a popular distribution model for earthquake magnitudes. I explain why the classical models and methods of the extreme value theory and statistics do not work well for truncated exponential distributions. Consequently, these classical methods should be used for the estimation of the upper bound magnitude and corresponding parameters. Furthermore, I comment on various issues of statistical inference in Pisarenko et al. and propose alternatives. I argue why GPD and GEVD would work for various types of stochastic earthquake processes in time, and not only for the homogeneous (stationary) Poisson process as assumed by Pisarenko et al. (Pure Appl. Geophys 171:1599-1624, 2014). The crucial point of earthquake magnitudes is the poor convergence of their tail distribution to the GPD, and not the earthquake process over time.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

NASA Astrophysics Data System (ADS)

Zou, Yong; Donner, Reik V.; Kurths, Jürgen

2015-02-01

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm [Liu et al. Phys. Rev. E 89, 032814 (2014), 10.1103/PhysRevE.89.032814] are mainly due to an inappropriate treatment disregarding the intrinsic nonstationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for nonstationary stochastic processes like fBm.

Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory. PMID:19816580

? filtering for stochastic systems driven by Poisson processes

NASA Astrophysics Data System (ADS)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi

2015-04-01

The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be estimated based on the theory of stochastic processes, and it can be applied to the probabilistic risk of flood management.

Stochastic differential equations

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

Sobczyk, K.

1990-01-01

This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshoremore » structures.« less

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Anomalous scaling of stochastic processes and the Moses effect

NASA Astrophysics Data System (ADS)

Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Anomalous scaling of stochastic processes and the Moses effect.

PubMed

Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem.

PubMed

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A; Hazen, Terry C; Tiedje, James M; Arkin, Adam P

2014-03-04

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession.

Theory and applications survey of decentralized control methods

NASA Technical Reports Server (NTRS)

Athans, M.

1975-01-01

A nonmathematical overview is presented of trends in the general area of decentralized control strategies which are suitable for hierarchical systems. Advances in decentralized system theory are closely related to advances in the so-called stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools pertaining to the classical stochastic control problem are outlined. Particular attention is devoted to pitfalls in the mathematical problem formulation for decentralized control. Major conclusions are that any purely deterministic approach to multilevel hierarchical dynamic systems is unlikely to lead to realistic theories or designs, that the flow of measurements and decisions in a decentralized system should not be instantaneous and error-free, and that delays in information exchange in a decentralized system lead to reasonable approaches to decentralized control. A mathematically precise notion of aggregating information is not yet available.

Speckle: tool for diagnosis assistance

NASA Astrophysics Data System (ADS)

Carvalho, O.; Guyot, S.; Roy, L.; Benderitter, M.; Clairac, B.

2006-09-01

In this paper, we present a new approach of the speckle phenomenon. This method is based on the fractal Brownian motion theory and allows the extraction of three stochastic parameters to characterize the speckle pattern. For the first time, we present the results of this method applied to the discrimination of the healthy vs. pathologic skin. We also demonstrate, in case of the scleroderma, than this method is more accurate than the classical frequential approach.

Scalability of Classical Terramechanics Models for Lightweight Vehicle Applications Incorporating Stochastic Modeling and Uncertainty Propagation

DTIC Science & Technology

2013-10-22

Propagation Paramsothy Jayakumar * Daniel Melanz Jamie MacLennan David Gorsich U.S. Army TARDEC Warren, MI, USA Carmine Senatore Karl Iagnemma...Modeling and Uncertainty Propagation 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Paramsothy Jayakumar ; Daniel...of Technology, Cambridge, MA, 2005. [12] C. Senatore, M. Wulfmeier, P. Jayakumar , J. Maclennan, and K. Iagnemma, "Investigation of Stress and

A Markovian event-based framework for stochastic spiking neural networks.

PubMed

Touboul, Jonathan D; Faugeras, Olivier D

2011-11-01

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

Some remarks on quantum physics, stochastic processes, and nonlinear filtering theory

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2016-05-01

The mathematical similarities between quantum mechanics and stochastic processes has been studied in the literature. Some of the major results are reviewed, such as the relationship between the Fokker-Planck equation and the Schrödinger equation. Also reviewed are more recent results that show the mathematical similarities between quantum many particle systems and concepts in other areas of applied science, such as stochastic Petri nets. Some connections to filtering theory are discussed.

A novel model for the chaotic dynamics of superdiffusion

NASA Astrophysics Data System (ADS)

Cushman, J. H.; Park, M.; O'Malley, D.

2009-04-01

Previously we've shown that by modeling the convective velocity in a turbulent flow field as Brownian, one obtains Richardson super diffusion where the expected distance between pairs of particles scales with time cubed. By proving generalized central limit type theorems it's possible to show that modeling the velocity or the acceleration as α-stable Levy gives rise to more general scaling laws that can easily explain other super diffusive regimes. The problem with this latter approach is that the mean square displacement of a particle is infinite. Here we provide an alternate approach that gives a power law mean square displacement of any desired order. We do so by constructing compressed and stretched extensions to Brownian motion. The finite size Lyapunov exponent, the underlying stochastic differential equation and its corresponding Fokker-Planck equations are derived. The fractal dimension of these processes turns out to be the same as that of classical Brownian motion.

Suppression of population transport and control of exciton distributions by entangled photons

PubMed Central

Schlawin, Frank; Dorfman, Konstantin E.; Fingerhut, Benjamin P.; Mukamel, Shaul

2013-01-01

Entangled photons provide an important tool for secure quantum communication, computing and lithography. Low intensity requirements for multi-photon processes make them idealy suited for minimizing damage in imaging applications. Here we show how their unique temporal and spectral features may be used in nonlinear spectroscopy to reveal properties of multiexcitons in chromophore aggregates. Simulations demostrate that they provide unique control tools for two-exciton states in the bacterial reaction centre of Blastochloris viridis. Population transport in the intermediate single-exciton manifold may be suppressed by the absorption of photon pairs with short entanglement time, thus allowing the manipulation of the distribution of two-exciton states. The quantum nature of the light is essential for achieving this degree of control, which cannot be reproduced by stochastic or chirped light. Classical light is fundamentally limited by the frequency-time uncertainty, whereas entangled photons have independent temporal and spectral characteristics not subjected to this uncertainty. PMID:23653194

Connectivity ranking of heterogeneous random conductivity models

NASA Astrophysics Data System (ADS)

Rizzo, C. B.; de Barros, F.

2017-12-01

To overcome the challenges associated with hydrogeological data scarcity, the hydraulic conductivity (K) field is often represented by a spatial random process. The state-of-the-art provides several methods to generate 2D or 3D random K-fields, such as the classic multi-Gaussian fields or non-Gaussian fields, training image-based fields and object-based fields. We provide a systematic comparison of these models based on their connectivity. We use the minimum hydraulic resistance as a connectivity measure, which it has been found to be strictly correlated with early time arrival of dissolved contaminants. A computationally efficient graph-based algorithm is employed, allowing a stochastic treatment of the minimum hydraulic resistance through a Monte-Carlo approach and therefore enabling the computation of its uncertainty. The results show the impact of geostatistical parameters on the connectivity for each group of random fields, being able to rank the fields according to their minimum hydraulic resistance.

A stochastic delay model for pricing debt and equity: Numerical techniques and applications

NASA Astrophysics Data System (ADS)

Tambue, Antoine; Kemajou Brown, Elisabeth; Mohammed, Salah

2015-01-01

Delayed nonlinear models for pricing corporate liabilities and European options were recently developed. Using self-financed strategy and duplication we were able to derive a Random Partial Differential Equation (RPDE) whose solutions describe the evolution of debt and equity values of a corporate in the last delay period interval in the accompanied paper (Kemajou et al., 2012) [14]. In this paper, we provide robust numerical techniques to solve the delayed nonlinear model for the corporate value, along with the corresponding RPDEs modeling the debt and equity values of the corporate. Using financial data from some firms, we forecast and compare numerical solutions from both the nonlinear delayed model and classical Merton model with the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

NASA Astrophysics Data System (ADS)

Küchlin, Stephan; Jenny, Patrick

2018-06-01

Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Memoryless self-reinforcing directionality in endosomal active transport within living cells

NASA Astrophysics Data System (ADS)

Chen, Kejia; Wang, Bo; Granick, Steve

2015-06-01

In contrast to Brownian transport, the active motility of microbes, cells, animals and even humans often follows another random process known as truncated Lévy walk. These stochastic motions are characterized by clustered small steps and intermittent longer jumps that often extend towards the size of the entire system. As there are repeated suggestions, although disagreement, that Lévy walks have functional advantages over Brownian motion in random searching and transport kinetics, their intentional engineering into active materials could be useful. Here, we show experimentally in the classic active matter system of intracellular trafficking that Brownian-like steps self-organize into truncated Lévy walks through an apparent time-independent positive feedback such that directional persistence increases with the distance travelled persistently. A molecular model that allows the maximum output of the active propelling forces to fluctuate slowly fits the experiments quantitatively. Our findings offer design principles for programming efficient transport in active materials.

Use of the Wigner representation in scattering problems

NASA Technical Reports Server (NTRS)

Bemler, E. A.

1975-01-01

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Normalization is a general neural mechanism for context-dependent decision making

PubMed Central

Louie, Kenway; Khaw, Mel W.; Glimcher, Paul W.

2013-01-01

Understanding the neural code is critical to linking brain and behavior. In sensory systems, divisive normalization seems to be a canonical neural computation, observed in areas ranging from retina to cortex and mediating processes including contrast adaptation, surround suppression, visual attention, and multisensory integration. Recent electrophysiological studies have extended these insights beyond the sensory domain, demonstrating an analogous algorithm for the value signals that guide decision making, but the effects of normalization on choice behavior are unknown. Here, we show that choice models using normalization generate significant (and classically irrational) choice phenomena driven by either the value or number of alternative options. In value-guided choice experiments, both monkey and human choosers show novel context-dependent behavior consistent with normalization. These findings suggest that the neural mechanism of value coding critically influences stochastic choice behavior and provide a generalizable quantitative framework for examining context effects in decision making. PMID:23530203

Testing for detailed balance in a financial market

NASA Astrophysics Data System (ADS)

Fiebig, H. R.; Musgrove, D. P.

2015-06-01

We test a historical price-time series in a financial market (the NASDAQ 100 index) for a statistical property known as detailed balance. The presence of detailed balance would imply that the market can be modeled by a stochastic process based on a Markov chain, thus leading to equilibrium. In economic terms, a positive outcome of the test would support the efficient market hypothesis, a cornerstone of neo-classical economic theory. In contrast to the usage in prevalent economic theory the term equilibrium here is tied to the returns, rather than the price-time series. The test is based on an action functional S constructed from the elements of the detailed balance condition and the historical data set, and then analyzing S by means of simulated annealing. Checks are performed to verify the validity of the analysis method. We discuss the outcome of this analysis.

Fickian dispersion is anomalous

DOE PAGES

Cushman, John H.; O’Malley, Dan

2015-06-22

The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion wemore » illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Finally, power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.« less

A Family of Poisson Processes for Use in Stochastic Models of Precipitation

NASA Astrophysics Data System (ADS)

Penland, C.

2013-12-01

Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Markovian limit for a reduced operation-valued stochastic process

NASA Astrophysics Data System (ADS)

Barchielli, Alberto

1987-04-01

Operation-valued stochastic processes give a formalization of the concept of continuous (in time) measurements in quantum mechanics. In this article, a first stage M of a measuring apparatus coupled to the system S is explicitly introduced, and continuous measurement of some observables of M is considered (one can speak of an indirect continuous measurement on S). When the degrees of freedom of the measuring apparatus M are eliminated and the weak coupling limit is taken, it is shown that an operation-valued stochastic process describing a direct continuous observation of the system S is obtained.

Models for interrupted monitoring of a stochastic process

NASA Technical Reports Server (NTRS)

Palmer, E.

1977-01-01

As computers are added to the cockpit, the pilot's job is changing from of manually flying the aircraft, to one of supervising computers which are doing navigation, guidance and energy management calculations as well as automatically flying the aircraft. In this supervisorial role the pilot must divide his attention between monitoring the aircraft's performance and giving commands to the computer. Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies.

Stochastic assembly in a subtropical forest chronosequence: evidence from contrasting changes of species, phylogenetic and functional dissimilarity over succession.

PubMed

Mi, Xiangcheng; Swenson, Nathan G; Jia, Qi; Rao, Mide; Feng, Gang; Ren, Haibao; Bebber, Daniel P; Ma, Keping

2016-09-07

Deterministic and stochastic processes jointly determine the community dynamics of forest succession. However, it has been widely held in previous studies that deterministic processes dominate forest succession. Furthermore, inference of mechanisms for community assembly may be misleading if based on a single axis of diversity alone. In this study, we evaluated the relative roles of deterministic and stochastic processes along a disturbance gradient by integrating species, functional, and phylogenetic beta diversity in a subtropical forest chronosequence in Southeastern China. We found a general pattern of increasing species turnover, but little-to-no change in phylogenetic and functional turnover over succession at two spatial scales. Meanwhile, the phylogenetic and functional beta diversity were not significantly different from random expectation. This result suggested a dominance of stochastic assembly, contrary to the general expectation that deterministic processes dominate forest succession. On the other hand, we found significant interactions of environment and disturbance and limited evidence for significant deviations of phylogenetic or functional turnover from random expectations for different size classes. This result provided weak evidence of deterministic processes over succession. Stochastic assembly of forest succession suggests that post-disturbance restoration may be largely unpredictable and difficult to control in subtropical forests.

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

Multivariate moment closure techniques for stochastic kinetic models

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

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

The critical domain size of stochastic population models.

PubMed

Reimer, Jody R; Bonsall, Michael B; Maini, Philip K

2017-02-01

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

The Two-On-One Stochastic Duel

DTIC Science & Technology

1983-12-01

ACN 67500 TRASANA-TR-43-83 (.0 (v THE TWO-ON-ONE STOCHASTIC DUEL I • Prepared By A.V. Gafarian C.J. Ancker, Jr. DECEMBER 19833D I°"’" " TIC ELECTE...83 M A IL / _ _ 4. TITLE (and Subtitle) TYPE OF REPORT & PERIOD CO\\,ERED The Two-On-One Stochastic Duel Final Report 6. PERFORMING ORG. REPORT NUMBER...Stochastic Duels , Stochastic Processed, and Attrition. 5-14cIa~c fal roLCS-e ss 120. ABSTRACT (C’ntfMte am reverse Ed& if necesemay and idemtitf by block

Importance of vesicle release stochasticity in neuro-spike communication.

PubMed

Ramezani, Hamideh; Akan, Ozgur B

2017-07-01

Aim of this paper is proposing a stochastic model for vesicle release process, a part of neuro-spike communication. Hence, we study biological events occurring in this process and use microphysiological simulations to observe functionality of these events. Since the most important source of variability in vesicle release probability is opening of voltage dependent calcium channels (VDCCs) followed by influx of calcium ions through these channels, we propose a stochastic model for this event, while using a deterministic model for other variability sources. To capture the stochasticity of calcium influx to pre-synaptic neuron in our model, we study its statistics and find that it can be modeled by a distribution defined based on Normal and Logistic distributions.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Using Multi-Objective Genetic Programming to Synthesize Stochastic Processes

NASA Astrophysics Data System (ADS)

Ross, Brian; Imada, Janine

Genetic programming is used to automatically construct stochastic processes written in the stochastic π-calculus. Grammar-guided genetic programming constrains search to useful process algebra structures. The time-series behaviour of a target process is denoted with a suitable selection of statistical feature tests. Feature tests can permit complex process behaviours to be effectively evaluated. However, they must be selected with care, in order to accurately characterize the desired process behaviour. Multi-objective evaluation is shown to be appropriate for this application, since it permits heterogeneous statistical feature tests to reside as independent objectives. Multiple undominated solutions can be saved and evaluated after a run, for determination of those that are most appropriate. Since there can be a vast number of candidate solutions, however, strategies for filtering and analyzing this set are required.

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.

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Soil pH mediates the balance between stochastic and deterministic assembly of bacteria

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

Tripathi, Binu M.; Stegen, James C.; Kim, Mincheol

Little is known about the factors affecting the relative influence of stochastic and deterministic processes that governs the assembly of microbial communities in successional soils. Here, we conducted a meta-analysis of bacterial communities using six different successional soils data sets, scattered across different regions, with different pH conditions in early and late successional soils. We found that soil pH was the best predictor of bacterial community assembly and the relative importance of stochastic and deterministic processes along successional soils. Extreme acidic or alkaline pH conditions lead to assembly of phylogenetically more clustered bacterial communities through deterministic processes, whereas pH conditionsmore » close to neutral lead to phylogenetically less clustered bacterial communities with more stochasticity. We suggest that the influence of pH, rather than successional age, is the main driving force in producing trends in phylogenetic assembly of bacteria, and that pH also influences the relative balance of stochastic and deterministic processes along successional soils. Given that pH had a much stronger association with community assembly than did successional age, we evaluated whether the inferred influence of pH was maintained when studying globally-distributed samples collected without regard for successional age. This dataset confirmed the strong influence of pH, suggesting that the influence of soil pH on community assembly processes occurs globally. Extreme pH conditions likely exert more stringent limits on survival and fitness, imposing strong selective pressures through ecological and evolutionary time. Taken together, these findings suggest that the degree to which stochastic vs. deterministic processes shape soil bacterial community assembly is a consequence of soil pH rather than successional age.« less

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem

PubMed Central

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D.; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A.; Hazen, Terry C.; Tiedje, James M.; Arkin, Adam P.

2014-01-01

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession. PMID:24550501

Data-driven monitoring for stochastic systems and its application on batch process

NASA Astrophysics Data System (ADS)

Yin, Shen; Ding, Steven X.; Haghani Abandan Sari, Adel; Hao, Haiyang

2013-07-01

Batch processes are characterised by a prescribed processing of raw materials into final products for a finite duration and play an important role in many industrial sectors due to the low-volume and high-value products. Process dynamics and stochastic disturbances are inherent characteristics of batch processes, which cause monitoring of batch processes a challenging problem in practice. To solve this problem, a subspace-aided data-driven approach is presented in this article for batch process monitoring. The advantages of the proposed approach lie in its simple form and its abilities to deal with stochastic disturbances and process dynamics existing in the process. The kernel density estimation, which serves as a non-parametric way of estimating the probability density function, is utilised for threshold calculation. An industrial benchmark of fed-batch penicillin production is finally utilised to verify the effectiveness of the proposed approach.

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.

Aboveground and belowground arthropods experience different relative influences of stochastic versus deterministic community assembly processes following disturbance

PubMed Central

Martinez, Alexander S.; Faist, Akasha M.

2016-01-01

Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species) and belowground (species active in organic and mineral soil layers) arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community) and modified Winkler funnels (belowground community) and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity) among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the aboveground arthropod communities and vegetation and soil properties, but no significant association among belowground arthropod communities and environmental factors. Discussion Our results suggest context-dependent influences of stochastic and deterministic community assembly processes across different fractions of a spatially co-occurring ground-dwelling arthropod community following disturbance. This variation in assembly may be linked to contrasting ecological strategies and dispersal rates within above- and below-ground communities. Our findings add to a growing body of evidence indicating concurrent influences of stochastic and deterministic processes in community assembly, and highlight the need to consider potential variation across different fractions of biotic communities when testing community ecology theory and considering conservation strategies. PMID:27761333

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.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Steepest Ascent Low/Non-Low-Frequency Ratio in Empirical Mode Decomposition to Separate Deterministic and Stochastic Velocities From a Single Lagrangian Drifter

NASA Astrophysics Data System (ADS)

Chu, Peter C.

2018-03-01

SOund Fixing And Ranging (RAFOS) floats deployed by the Naval Postgraduate School (NPS) in the California Current system from 1992 to 2001 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) are used to study 2-D turbulent characteristics. Each drifter trajectory is adaptively decomposed using the empirical mode decomposition (EMD) into a series of intrinsic mode functions (IMFs) with corresponding specific scale for each IMF. A new steepest ascent low/non-low-frequency ratio is proposed in this paper to separate a Lagrangian trajectory into low-frequency (nondiffusive, i.e., deterministic) and high-frequency (diffusive, i.e., stochastic) components. The 2-D turbulent (or called eddy) diffusion coefficients are calculated on the base of the classical turbulent diffusion with mixing length theory from stochastic component of a single drifter. Statistical characteristics of the calculated 2-D turbulence length scale, strength, and diffusion coefficients from the NPS RAFOS data are presented with the mean values (over the whole drifters) of the 2-D diffusion coefficients comparable to the commonly used diffusivity tensor method.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

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.

Research in Stochastic Processes.

DTIC Science & Technology

1982-10-31

Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication

Changing contributions of stochastic and deterministic processes in community assembly over a successional gradient.

PubMed

Måren, Inger Elisabeth; Kapfer, Jutta; Aarrestad, Per Arild; Grytnes, John-Arvid; Vandvik, Vigdis

2018-01-01

Successional dynamics in plant community assembly may result from both deterministic and stochastic ecological processes. The relative importance of different ecological processes is expected to vary over the successional sequence, between different plant functional groups, and with the disturbance levels and land-use management regimes of the successional systems. We evaluate the relative importance of stochastic and deterministic processes in bryophyte and vascular plant community assembly after fire in grazed and ungrazed anthropogenic coastal heathlands in Northern Europe. A replicated series of post-fire successions (n = 12) were initiated under grazed and ungrazed conditions, and vegetation data were recorded in permanent plots over 13 years. We used redundancy analysis (RDA) to test for deterministic successional patterns in species composition repeated across the replicate successional series and analyses of co-occurrence to evaluate to what extent species respond synchronously along the successional gradient. Change in species co-occurrences over succession indicates stochastic successional dynamics at the species level (i.e., species equivalence), whereas constancy in co-occurrence indicates deterministic dynamics (successional niche differentiation). The RDA shows high and deterministic vascular plant community compositional change, especially early in succession. Co-occurrence analyses indicate stochastic species-level dynamics the first two years, which then give way to more deterministic replacements. Grazed and ungrazed successions are similar, but the early stage stochasticity is higher in ungrazed areas. Bryophyte communities in ungrazed successions resemble vascular plant communities. In contrast, bryophytes in grazed successions showed consistently high stochasticity and low determinism in both community composition and species co-occurrence. In conclusion, stochastic and individualistic species responses early in succession give way to more niche-driven dynamics in later successional stages. Grazing reduces predictability in both successional trends and species-level dynamics, especially in plant functional groups that are not well adapted to disturbance. © 2017 The Authors. Ecology, published by Wiley Periodicals, Inc., on behalf of the Ecological Society of America.

Research in Stochastic Processes

DTIC Science & Technology

1988-08-31

stationary sequence, Stochastic Proc. Appl. 29, 1988, 155-169 T. Hsing, J. Husler and M.R. Leadbetter, On the exceedance point process for a stationary...Nandagopalan, On exceedance point processes for "regular" sample functions, Proc. Volume, Oberxolfach Conf. on Extreme Value Theory, J. Husler and R. Reiss...exceedance point processes for stationary sequences under mild oscillation restrictions, Apr. 88. Obermotfach Conf. on Extremal Value Theory. Ed. J. HUsler

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.

PubMed

Salis, Howard; Kaznessis, Yiannis

2005-02-01

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Analysis of isothermal and cooling rate dependent immersion freezing by a unifying stochastic ice nucleation model

NASA Astrophysics Data System (ADS)

Alpert, P. A.; Knopf, D. A.

2015-05-01

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature (T) and relative humidity (RH) at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling rate dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nuclei (IN) all have the same IN surface area (ISA), however the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses physically observable parameters including the total number of droplets (Ntot) and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time dependent isothermal frozen fractions exhibiting non-exponential behavior with time can be readily explained by this model considering varying ISA. An apparent cooling rate dependence ofJhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. The model simulations allow for a quantitative experimental uncertainty analysis for parameters Ntot, T, RH, and the ISA variability. In an idealized cloud parcel model applying variability in ISAs for each droplet, the model predicts enhanced immersion freezing temperatures and greater ice crystal production compared to a case when ISAs are uniform in each droplet. The implications of our results for experimental analysis and interpretation of the immersion freezing process are discussed.

Random sex determination: When developmental noise tips the sex balance.

PubMed

Perrin, Nicolas

2016-12-01

Sex-determining factors are usually assumed to be either genetic or environmental. The present paper aims at drawing attention to the potential contribution of developmental noise, an important but often-neglected component of phenotypic variance. Mutual inhibitions between male and female pathways make sex a bistable equilibrium, such that random fluctuations in the expression of genes at the top of the cascade are sufficient to drive individual development toward one or the other stable state. Evolutionary modeling shows that stochastic sex determinants should resist elimination by genetic or environmental sex determinants under ecologically meaningful settings. On the empirical side, many sex-determination systems traditionally considered as environmental or polygenic actually provide evidence for large components of stochasticity. In reviewing the field, I argue that sex-determination systems should be considered within a three-ends continuum, rather than the classical two-ends continuum. © 2016 WILEY Periodicals, Inc.

Stochastic dynamics of genetic broadcasting networks

NASA Astrophysics Data System (ADS)

Potoyan, Davit; Wolynes, Peter

The complex genetic programs of eukaryotic cells are often regulated by key transcription factors occupying or clearing out of a large number of genomic locations. Orchestrating the residence times of these factors is therefore important for the well organized functioning of a large network. The classic models of genetic switches sidestep this timing issue by assuming the binding of transcription factors to be governed entirely by thermodynamic protein-DNA affinities. Here we show that relying on passive thermodynamics and random release times can lead to a ''time-scale crisis'' of master genes that broadcast their signals to large number of binding sites. We demonstrate that this ''time-scale crisis'' can be resolved by actively regulating residence times through molecular stripping. We illustrate these ideas by studying the stochastic dynamics of the genetic network of the central eukaryotic master regulator NFκB which broadcasts its signals to many downstream genes that regulate immune response, apoptosis etc.

Analytical minimization of synchronicity errors in stochastic identification

NASA Astrophysics Data System (ADS)

Bernal, D.

2018-01-01

An approach to minimize error due to synchronicity faults in stochastic system identification is presented. The scheme is based on shifting the time domain signals so the phases of the fundamental eigenvector estimated from the spectral density are zero. A threshold on the mean of the amplitude-weighted absolute value of these phases, above which signal shifting is deemed justified, is derived and found to be proportional to the first mode damping ratio. It is shown that synchronicity faults do not map precisely to phasor multiplications in subspace identification and that the accuracy of spectral density estimated eigenvectors, for inputs with arbitrary spectral density, decrease with increasing mode number. Selection of a corrective strategy based on signal alignment, instead of eigenvector adjustment using phasors, is shown to be the product of the foregoing observations. Simulations that include noise and non-classical damping suggest that the scheme can provide sufficient accuracy to be of practical value.

Importance of Chemical Composition of Ice Nuclei on the Formation of Arctic Ice Clouds

NASA Astrophysics Data System (ADS)

Keita, Setigui Aboubacar; Girard, Eric

2016-09-01

Ice clouds play an important role in the Arctic weather and climate system but interactions between aerosols, clouds and radiation remain poorly understood. Consequently, it is essential to fully understand their properties and especially their formation process. Extensive measurements from ground-based sites and satellite remote sensing reveal the existence of two Types of Ice Clouds (TICs) in the Arctic during the polar night and early spring. TICs-1 are composed by non-precipitating small (radar-unseen) ice crystals of less than 30 μm in diameter. The second type, TICs-2, are detected by radar and are characterized by a low concentration of large precipitating ice crystals ice crystals (>30 μm). To explain these differences, we hypothesized that TIC-2 formation is linked to the acidification of aerosols, which inhibits the ice nucleating properties of ice nuclei (IN). As a result, the IN concentration is reduced in these regions, resulting to a lower concentration of larger ice crystals. Water vapor available for deposition being the same, these crystals reach a larger size. Current weather and climate models cannot simulate these different types of ice clouds. This problem is partly due to the parameterizations implemented for ice nucleation. Over the past 10 years, several parameterizations of homogeneous and heterogeneous ice nucleation on IN of different chemical compositions have been developed. These parameterizations are based on two approaches: stochastic (that is nucleation is a probabilistic process, which is time dependent) and singular (that is nucleation occurs at fixed conditions of temperature and humidity and time-independent). The best approach remains unclear. This research aims to better understand the formation process of Arctic TICs using recently developed ice nucleation parameterizations. For this purpose, we have implemented these ice nucleation parameterizations into the Limited Area version of the Global Multiscale Environmental Model (GEM-LAM) and use them to simulate ice clouds observed during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) in Alaska. Simulation results of the TICs-2 observed on April 15th and 25th (acidic cases) and TICs-1 observed on April 5th (non-acidic cases) are presented. Our results show that the stochastic approach based on the classical nucleation theory with the appropriate contact angle is better. Parameterizations of ice nucleation based on the singular approach tend to overestimate the ice crystal concentration in TICs-1 and TICs-2. The classical nucleation theory using the appropriate contact angle is the best approach to use to simulate the ice clouds investigated in this research.

Optimal Control of Hybrid Systems in Air Traffic Applications

NASA Astrophysics Data System (ADS)

Kamgarpour, Maryam

Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient implementation of the proposed algorithms.

Online POMDP Algorithms for Very Large Observation Spaces

DTIC Science & Technology

2017-06-06

stochastic optimization: From sets to paths." In Advances in Neural Information Processing Systems, pp. 1585- 1593 . 2015. • Luo, Yuanfu, Haoyu Bai...and Wee Sun Lee. "Adaptive stochastic optimization: From sets to paths." In Advances in Neural Information Processing Systems, pp. 1585- 1593 . 2015

An Analysis of Stochastic Duels Involving Fixed Rates of Fire

DTIC Science & Technology

The thesis presents an analysis of stochastic duels involving two opposing weapon systems with constant rates of fire. The duel was developed as a...process stochastic duels . The analysis was then extended to the two versus one duel where the three weapon systems were assumed to have fixed rates of fire.

STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB.

PubMed

Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K

2011-04-15

The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user's models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. The software is open source under the GPL v3 and available at http://www.maths.ox.ac.uk/cmb/STOCHSIMGPU. The web site also contains supplementary information. klingbeil@maths.ox.ac.uk Supplementary data are available at Bioinformatics online.

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.

Effects of Stochastic Traffic Flow Model on Expected System Performance

DTIC Science & Technology

2012-12-01

NSWC-PCD has made considerable improvements to their pedestrian flow modeling . In addition to the linear paths, the 2011 version now includes...using stochastic paths. 2.2 Linear Paths vs. Stochastic Paths 2.2.1 Linear Paths and Direct Maximum Pd Calculation Modeling pedestrian traffic flow...as a stochastic process begins with the linear path model . Let the detec- tion area be R x C voxels. This creates C 2 total linear paths, path(Cs

A unified nonlinear stochastic time series analysis for climate science

PubMed Central

Moon, Woosok; Wettlaufer, John S.

2017-01-01

Earth’s orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability. PMID:28287128

A unified nonlinear stochastic time series analysis for climate science.

PubMed

Moon, Woosok; Wettlaufer, John S

2017-03-13

Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.

A unified nonlinear stochastic time series analysis for climate science

NASA Astrophysics Data System (ADS)

Moon, Woosok; Wettlaufer, John

2017-04-01

Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Niño Southern Oscillation (ENSO), the Atlantic Niño and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some period of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.

Separation of time scales in one-dimensional directed nucleation-growth processes

NASA Astrophysics Data System (ADS)

Pierobon, Paolo; Miné-Hattab, Judith; Cappello, Giovanni; Viovy, Jean-Louis; Lagomarsino, Marco Cosentino

2010-12-01

Proteins involved in homologous recombination such as RecA and hRad51 polymerize on single- and double-stranded DNA according to a nucleation-growth kinetics, which can be monitored by single-molecule in vitro assays. The basic models currently used to extract biochemical rates rely on ensemble averages and are typically based on an underlying process of bidirectional polymerization, in contrast with the often observed anisotropic polymerization of similar proteins. For these reasons, if one considers single-molecule experiments, the available models are useful to understand observations only in some regimes. In particular, recent experiments have highlighted a steplike polymerization kinetics. The classical model of one-dimensional nucleation growth, the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model, predicts the correct polymerization kinetics only in some regimes and fails to predict the steplike behavior. This work illustrates by simulations and analytical arguments the limitation of applicability of the KAMJ description and proposes a minimal model for the statistics of the steps based on the so-called stick-breaking stochastic process. We argue that this insight might be useful to extract information on the time and length scales involved in the polymerization kinetics.

Inter-species competition-facilitation in stochastic riparian vegetation dynamics.

PubMed

Tealdi, Stefano; Camporeale, Carlo; Ridolfi, Luca

2013-02-07

Riparian vegetation is a highly dynamic community that lives on river banks and which depends to a great extent on the fluvial hydrology. The stochasticity of the discharge and erosion/deposition processes in fact play a key role in determining the distribution of vegetation along a riparian transect. These abiotic processes interact with biotic competition/facilitation mechanisms, such as plant competition for light, water, and nutrients. In this work, we focus on the dynamics of plants characterized by three components: (1) stochastic forcing due to river discharges, (2) competition for resources, and (3) inter-species facilitation due to the interplay between vegetation and fluid dynamics processes. A minimalist stochastic bio-hydrological model is proposed for the dynamics of the biomass of two vegetation species: one species is assumed dominant and slow-growing, the other is subdominant, but fast-growing. The stochastic model is solved analytically and the probability density function of the plant biomasses is obtained as a function of both the hydrologic and biologic parameters. The impact of the competition/facilitation processes on the distribution of vegetation species along the riparian transect is investigated and remarkable effects are observed. Finally, a good qualitative agreement is found between the model results and field data. Copyright © 2012 Elsevier Ltd. All rights reserved.

Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

PubMed

Sardar, Tridip; Saha, Bapi

2017-06-01

In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.

Stochastic thermodynamics, fluctuation theorems and molecular machines.

PubMed

Seifert, Udo

2012-12-01

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Research in Stochastic Processes.

DTIC Science & Technology

1983-10-01

increases. A more detailed investigation for the exceedances themselves (rather than Just the cluster centers) was undertaken, together with J. HUsler and...J. HUsler and M.R. Leadbetter, Compoung Poisson limit theorems for high level exceedances by stationary sequences, Center for Stochastic Processes...stability by a random linear operator. C.D. Hardin, General (asymmetric) stable variables and processes. T. Hsing, J. HUsler and M.R. Leadbetter, Compound

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

NASA Astrophysics Data System (ADS)

Samoilov, Michael; Plyasunov, Sergey; Arkin, Adam P.

2005-02-01

Stochastic effects in biomolecular systems have now been recognized as a major physiologically and evolutionarily important factor in the development and function of many living organisms. Nevertheless, they are often thought of as providing only moderate refinements to the behaviors otherwise predicted by the classical deterministic system description. In this work we show by using both analytical and numerical investigation that at least in one ubiquitous class of (bio)chemical-reaction mechanisms, enzymatic futile cycles, the external noise may induce a bistable oscillatory (dynamic switching) behavior that is both quantitatively and qualitatively different from what is predicted or possible deterministically. We further demonstrate that the noise required to produce these distinct properties can itself be caused by a set of auxiliary chemical reactions, making it feasible for biological systems of sufficient complexity to generate such behavior internally. This new stochastic dynamics then serves to confer additional functional modalities on the enzymatic futile cycle mechanism that include stochastic amplification and signaling, the characteristics of which could be controlled by both the type and parameters of the driving noise. Hence, such noise-induced phenomena may, among other roles, potentially offer a novel type of control mechanism in pathways that contain these cycles and the like units. In particular, observations of endogenous or externally driven noise-induced dynamics in regulatory networks may thus provide additional insight into their topology, structure, and kinetics. network motif | signal transduction | chemical reaction | synthetic biology | systems biology

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Wallstrom, Timothy Clarke

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of stochastic mechanics, and it is argued that these difficulties represent fundamental inadequacies in the physical foundation of stochastic mechanics.

Memristor-based neural networks: Synaptic versus neuronal stochasticity

NASA Astrophysics Data System (ADS)

Naous, Rawan; AlShedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled Nabil

2016-11-01

In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

NASA Technical Reports Server (NTRS)

Goad, Clyde C.; Chadwell, C. David

1993-01-01

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

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.

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

PubMed Central

Walpole, J.; Chappell, J.C.; Cluceru, J.G.; Mac Gabhann, F.; Bautch, V.L.; Peirce, S. M.

2015-01-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods. PMID:26158406

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks.

PubMed

Walpole, J; Chappell, J C; Cluceru, J G; Mac Gabhann, F; Bautch, V L; Peirce, S M

2015-09-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

Stochastic flow shop scheduling of overlapping jobs on tandem machines in application to optimizing the US Army's deliberate nuclear, biological, and chemical decontamination process, (final report). Master's thesis

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

Novikov, V.

1991-05-01

The U.S. Army's detailed equipment decontamination process is a stochastic flow shop which has N independent non-identical jobs (vehicles) which have overlapping processing times. This flow shop consists of up to six non-identical machines (stations). With the exception of one station, the processing times of the jobs are random variables. Based on an analysis of the processing times, the jobs for the 56 Army heavy division companies were scheduled according to the best shortest expected processing time - longest expected processing time (SEPT-LEPT) sequence. To assist in this scheduling the Gap Comparison Heuristic was developed to select the best SEPT-LEPTmore » schedule. This schedule was then used in balancing the detailed equipment decon line in order to find the best possible site configuration subject to several constraints. The detailed troop decon line, in which all jobs are independent and identically distributed, was then balanced. Lastly, an NBC decon optimization computer program was developed using the scheduling and line balancing results. This program serves as a prototype module for the ANBACIS automated NBC decision support system.... Decontamination, Stochastic flow shop, Scheduling, Stochastic scheduling, Minimization of the makespan, SEPT-LEPT Sequences, Flow shop line balancing, ANBACIS.« less

Unified picture of strong-coupling stochastic thermodynamics and time reversals

NASA Astrophysics Data System (ADS)

Aurell, Erik

2018-04-01

Strong-coupling statistical thermodynamics is formulated as the Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the log ratio of forward and backward system path probabilities, is in a one-to-one relation with the log ratios of the joint initial conditions of the system and the bath. A version of strong-coupling statistical thermodynamics where the system-bath interaction vanishes at the beginning and at the end of a process is, as is also weak-coupling stochastic thermodynamics, related to the bath initially in equilibrium by itself. The heat is then the change of bath energy over the process, and it is discussed when this heat is a functional of the system history alone. The version of strong-coupling statistical thermodynamics introduced by Seifert and Jarzynski is related to the bath initially in conditional equilibrium with respect to the system. This leads to heat as another functional of the system history which needs to be determined by thermodynamic integration. The log ratio of forward and backward system path probabilities in a stochastic process is finally related to log ratios of the initial conditions of a combined system and bath. It is shown that the entropy production formulas of stochastic processes under a general class of time reversals are given by the differences of bath energies in a larger underlying Hamiltonian system. The paper highlights the centrality of time reversal in stochastic thermodynamics, also in the case of strong coupling.

A stochastic diffusion process for Lochner's generalized Dirichlet distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-10-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle.more » Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.« less

Extension of classical hydrological risk analysis to non-stationary conditions due to climate change - application to the Fulda catchment, Germany

NASA Astrophysics Data System (ADS)

Fink, G.; Koch, M.

2010-12-01

An important aspect in water resources and hydrological engineering is the assessment of hydrological risk, due to the occurrence of extreme events, e.g. droughts or floods. When dealing with the latter - as is the focus here - the classical methods of flood frequency analysis (FFA) are usually being used for the proper dimensioning of a hydraulic structure, for the purpose of bringing down the flood risk to an acceptable level. FFA is based on extreme value statistics theory. Despite the progress of methods in this scientific branch, the development, decision, and fitting of an appropriate distribution function stills remains a challenge, particularly, when certain underlying assumptions of the theory are not met in real applications. This is, for example, the case when the stationarity-condition for a random flood time series is not satisfied anymore, as could be the situation when long-term hydrological impacts of future climate change are to be considered. The objective here is to verify the applicability of classical (stationary) FFA to predicted flood time series in the Fulda catchment in central Germany, as they may occur in the wake of climate change during the 21st century. These discharge time series at the outlet of the Fulda basin have been simulated with a distributed hydrological model (SWAT) that is forced by predicted climate variables of a regional climate model for Germany (REMO). From the simulated future daily time series, annual maximum (extremes) values are computed and analyzed for the purpose of risk evaluation. Although the 21st century estimated extreme flood series of the Fulda river turn out to be only mildly non-stationary, alleviating the need for further action and concern at the first sight, the more detailed analysis of the risk, as quantified, for example, by the return period, shows non-negligent differences in the calculated risk levels. This could be verified by employing a new method, the so-called flood series maximum analysis (FSMA) method, which consists in the stochastic simulation of numerous trajectories of a stochastic process with a given GEV-distribution over a certain length of time (> larger than a desired return period). Then the maximum value for each trajectory is computed, all of which are then used to determine the empirical distribution of this maximum series. Through graphical inversion of this distribution function the size of the design flood for a given risk (quantile) and given life duration can be inferred. The results of numerous simulations show that for stationary flood series, the new FSMA method results, expectedly, in nearly identical risk values as the classical FFA approach. However, once the flood time series becomes slightly non-stationary - for reasons as discussed - and regardless of whether the trend is increasing or decreasing, large differences in the computed risk values for a given design flood occur. Or in other word, for the same risk, the new FSMA method would lead to different values in the design flood for a hydraulic structure than the classical FFA method. This, in turn, could lead to some cost savings in the realization of a hydraulic project.

Definition of the Neutrosophic Probability

NASA Astrophysics Data System (ADS)

Smarandache, Florentin

2014-03-01

Neutrosophic probability (or likelihood) [1995] is a particular case of the neutrosophic measure. It is an estimation of an event (different from indeterminacy) to occur, together with an estimation that some indeterminacy may occur, and the estimation that the event does not occur. The classical probability deals with fair dice, coins, roulettes, spinners, decks of cards, random works, while neutrosophic probability deals with unfair, imperfect such objects and processes. For example, if we toss a regular die on an irregular surface which has cracks, then it is possible to get the die stuck on one of its edges or vertices in a crack (indeterminate outcome). The sample space is in this case: {1, 2, 3, 4, 5, 6, indeterminacy}. So, the probability of getting, for example 1, is less than 1/6. Since there are seven outcomes. The neutrosophic probability is a generalization of the classical probability because, when the chance of determinacy of a stochastic process is zero, these two probabilities coincide. The Neutrosophic Probability that of an event A occurs is NP (A) = (ch (A) , ch (indetA) , ch (A ̲)) = (T , I , F) , where T , I , F are subsets of [0,1], and T is the chance that A occurs, denoted ch(A); I is the indeterminate chance related to A, ch(indetermA) ; and F is the chance that A does not occur, ch (A ̲) . So, NP is a generalization of the Imprecise Probability as well. If T, I, and F are crisp numbers then: - 0 <= T + I + F <=3+ . We used the same notations (T,I,F) as in neutrosophic logic and set.

Hydro-geophysical observations integration in numerical model: case study in Mediterranean karstic unsaturated zone (Larzac, france)

NASA Astrophysics Data System (ADS)

Champollion, Cédric; Fores, Benjamin; Le Moigne, Nicolas; Chéry, Jean

2016-04-01

Karstic hydro-systems are highly non-linear and heterogeneous but one of the main water resource in the Mediterranean area. Neither local measurements in boreholes or analysis at the spring can take into account the variability of the water storage. Since a few years, ground-based geophysical measurements (such as gravity, electrical resistivity or seismological data) allows following water storage in heterogeneous hydrosystems at an intermediate scale between boreholes and basin. Behind classical rigorous monitoring, the integration of geophysical data in hydrological numerical models in needed for both processes interpretation and quantification. Since a few years, a karstic geophysical observatory (GEK: Géodésie de l'Environnement Karstique, OSU OREME, SNO H+) has been setup in the Mediterranean area in the south of France. The observatory is surrounding more than 250m karstified dolomite, with an unsaturated zone of ~150m thickness. At the observatory water level in boreholes, evapotranspiration and rainfall are classical hydro-meteorological observations completed by continuous gravity, resistivity and seismological measurements. The main objective of the study is the modelling of the whole observation dataset by explicit unsaturated numerical model in one dimension. Hydrus software is used for the explicit modelling of the water storage and transfer and links the different observations (geophysics, water level, evapotranspiration) with the water saturation. Unknown hydrological parameters (permeability, porosity) are retrieved from stochastic inversions. The scale of investigation of the different observations are discussed thank to the modelling results. A sensibility study of the measurements against the model is done and key hydro-geological processes of the site are 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.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

Valuation of Capabilities and System Architecture Options to Meet Affordability Requirement

DTIC Science & Technology

2014-04-30

is an extension of the historic volatility and trend of the stock using Brownian motion . In finance , the Black-Scholes equation is used to value...the underlying asset whose value is modeled as a stochastic process. In finance , the underlying asset is a tradeable stock and the stochastic process

On a Result for Finite Markov Chains

ERIC Educational Resources Information Center

Kulathinal, Sangita; Ghosh, Lagnojita

2006-01-01

In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

Stochastic resonance effects reveal the neural mechanisms of transcranial magnetic stimulation

PubMed Central

Schwarzkopf, Dietrich Samuel; Silvanto, Juha; Rees, Geraint

2011-01-01

Transcranial magnetic stimulation (TMS) is a popular method for studying causal relationships between neural activity and behavior. However its mode of action remains controversial, and so far there is no framework to explain its wide range of facilitatory and inhibitory behavioral effects. While some theoretical accounts suggests that TMS suppresses neuronal processing, other competing accounts propose that the effects of TMS result from the addition of noise to neuronal processing. Here we exploited the stochastic resonance phenomenon to distinguish these theoretical accounts and determine how TMS affects neuronal processing. Specifically, we showed that online TMS can induce stochastic resonance in the human brain. At low intensity, TMS facilitated the detection of weak motion signals but with higher TMS intensities and stronger motion signals we found only impairment in detection. These findings suggest that TMS acts by adding noise to neuronal processing, at least in an online TMS protocol. Importantly, such stochastic resonance effects may also explain why TMS parameters that under normal circumstances impair behavior, can induce behavioral facilitations when the stimulated area is in an adapted or suppressed state. PMID:21368025

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

NASA Astrophysics Data System (ADS)

Gao, Peng

2018-06-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

NASA Astrophysics Data System (ADS)

Gao, Peng

2018-04-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

Global climate impacts of stochastic deep convection parameterization in the NCAR CAM5

DOE PAGES

Wang, Yong; Zhang, Guang J.

2016-09-29

In this paper, the stochastic deep convection parameterization of Plant and Craig (PC) is implemented in the Community Atmospheric Model version 5 (CAM5) to incorporate the stochastic processes of convection into the Zhang-McFarlane (ZM) deterministic deep convective scheme. Its impacts on deep convection, shallow convection, large-scale precipitation and associated dynamic and thermodynamic fields are investigated. Results show that with the introduction of the PC stochastic parameterization, deep convection is decreased while shallow convection is enhanced. The decrease in deep convection is mainly caused by the stochastic process and the spatial averaging of input quantities for the PC scheme. More detrainedmore » liquid water associated with more shallow convection leads to significant increase in liquid water and ice water paths, which increases large-scale precipitation in tropical regions. Specific humidity, relative humidity, zonal wind in the tropics, and precipitable water are all improved. The simulation of shortwave cloud forcing (SWCF) is also improved. The PC stochastic parameterization decreases the global mean SWCF from -52.25 W/m 2 in the standard CAM5 to -48.86 W/m 2, close to -47.16 W/m 2 in observations. The improvement in SWCF over the tropics is due to decreased low cloud fraction simulated by the stochastic scheme. Sensitivity tests of tuning parameters are also performed to investigate the sensitivity of simulated climatology to uncertain parameters in the stochastic deep convection scheme.« less

Global climate impacts of stochastic deep convection parameterization in the NCAR CAM5

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

Wang, Yong; Zhang, Guang J.

In this paper, the stochastic deep convection parameterization of Plant and Craig (PC) is implemented in the Community Atmospheric Model version 5 (CAM5) to incorporate the stochastic processes of convection into the Zhang-McFarlane (ZM) deterministic deep convective scheme. Its impacts on deep convection, shallow convection, large-scale precipitation and associated dynamic and thermodynamic fields are investigated. Results show that with the introduction of the PC stochastic parameterization, deep convection is decreased while shallow convection is enhanced. The decrease in deep convection is mainly caused by the stochastic process and the spatial averaging of input quantities for the PC scheme. More detrainedmore » liquid water associated with more shallow convection leads to significant increase in liquid water and ice water paths, which increases large-scale precipitation in tropical regions. Specific humidity, relative humidity, zonal wind in the tropics, and precipitable water are all improved. The simulation of shortwave cloud forcing (SWCF) is also improved. The PC stochastic parameterization decreases the global mean SWCF from -52.25 W/m 2 in the standard CAM5 to -48.86 W/m 2, close to -47.16 W/m 2 in observations. The improvement in SWCF over the tropics is due to decreased low cloud fraction simulated by the stochastic scheme. Sensitivity tests of tuning parameters are also performed to investigate the sensitivity of simulated climatology to uncertain parameters in the stochastic deep convection scheme.« less

Approximation methods for stochastic petri nets

NASA Technical Reports Server (NTRS)

Jungnitz, Hauke Joerg

1992-01-01

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.

Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape

PubMed Central

Aldana, Maximino; Benítez, Mariana; Cortes-Poza, Yuriria; Espinosa-Soto, Carlos; Hartasánchez, Diego A.; Lotto, R. Beau; Malkin, David; Escalera Santos, Gerardo J.; Padilla-Longoria, Pablo

2008-01-01

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5–10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development. PMID:18978941

Auxiliary field loop expansion of the effective action for a class of stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Cooper, Fred; Dawson, John F.

2016-02-01

We present an alternative to the perturbative (in coupling constant) diagrammatic approach for studying stochastic dynamics of a class of reaction diffusion systems. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise induced correlation functions of the fields describing these systems. The systems we consider include Langevin systems describable by the set of self interacting classical fields ϕi(x , t) in the presence of external noise ηi(x , t) , namely (∂t - ν∇2) ϕ - F [ ϕ ] = η, as well as chemical reaction annihilation processes obtained by applying the many-body approach of Doi-Peliti to the Master Equation formulation of these problems. We consider two different effective actions, one based on the Onsager-Machlup (OM) approach, and the other due to Janssen-deGenneris based on the Martin-Siggia-Rose (MSR) response function approach. For the simple models we consider, we determine an analytic expression for the Energy landscape (effective potential) in both formalisms and show how to obtain the more physical effective potential of the Onsager-Machlup approach from the MSR effective potential in leading order in the auxiliary field loop expansion. For the KPZ equation we find that our approximation, which is non-perturbative and obeys broken symmetry Ward identities, does not lead to the appearance of a fluctuation induced symmetry breakdown. This contradicts the results of earlier studies.

Stochastic simulation by image quilting of process-based geological models

NASA Astrophysics Data System (ADS)

Hoffimann, Júlio; Scheidt, Céline; Barfod, Adrian; Caers, Jef

2017-09-01

Process-based modeling offers a way to represent realistic geological heterogeneity in subsurface models. The main limitation lies in conditioning such models to data. Multiple-point geostatistics can use these process-based models as training images and address the data conditioning problem. In this work, we further develop image quilting as a method for 3D stochastic simulation capable of mimicking the realism of process-based geological models with minimal modeling effort (i.e. parameter tuning) and at the same time condition them to a variety of data. In particular, we develop a new probabilistic data aggregation method for image quilting that bypasses traditional ad-hoc weighting of auxiliary variables. In addition, we propose a novel criterion for template design in image quilting that generalizes the entropy plot for continuous training images. The criterion is based on the new concept of voxel reuse-a stochastic and quilting-aware function of the training image. We compare our proposed method with other established simulation methods on a set of process-based training images of varying complexity, including a real-case example of stochastic simulation of the buried-valley groundwater system in Denmark.

A new hybrid model for filling gaps and forecast in sea level: application to the eastern English Channel and the North Atlantic Sea (western France)

NASA Astrophysics Data System (ADS)

Turki, Imen; Laignel, Benoit; Kakeh, Nabil; Chevalier, Laetitia; Costa, Stephane

2015-04-01

This research is carried out in the framework of the program Surface Water and Ocean Topography (SWOT) which is a partnership between NASA and CNES. Here, a new hybrid model is implemented for filling gaps and forecasting the hourly sea level variability by combining classical harmonic analyses to high statistical methods to reproduce the deterministic and stochastic processes, respectively. After simulating the mean trend sea level and astronomical tides, the nontidal residual surges are investigated using an autoregressive moving average (ARMA) methods by two ways: (1) applying a purely statistical approach and (2) introducing the SLP in ARMA as a main physical process driving the residual sea level. The new hybrid model is applied to the western Atlantic sea and the eastern English Channel. Using ARMA model and considering the SLP, results show that the hourly sea level observations of gauges with are well reproduced with a root mean square error (RMSE) ranging between 4.5 and 7 cm for 1 to 30 days of gaps and an explained variance more than 80 %. For larger gaps of months, the RMSE reaches 9 cm. The negative and the positive extreme values of sea levels are also well reproduced with a mean explained variance between 70 and 85 %. The statistical behavior of 1-year modeled residual components shows good agreements with observations. The frequency analysis using the discrete wavelet transform illustrate strong correlations between observed and modeled energy spectrum and the bands of variability. Accordingly, the proposed model presents a coherent, simple, and easy tool to estimate the total sea level at timescales from days to months. The ARMA model seems to be more promising for filling gaps and estimating the sea level at larger scales of years by introducing more physical processes driving its stochastic variability.

Asynchronous Gossip for Averaging and Spectral Ranking

NASA Astrophysics Data System (ADS)

Borkar, Vivek S.; Makhijani, Rahul; Sundaresan, Rajesh

2014-08-01

We consider two variants of the classical gossip algorithm. The first variant is a version of asynchronous stochastic approximation. We highlight a fundamental difficulty associated with the classical asynchronous gossip scheme, viz., that it may not converge to a desired average, and suggest an alternative scheme based on reinforcement learning that has guaranteed convergence to the desired average. We then discuss a potential application to a wireless network setting with simultaneous link activation constraints. The second variant is a gossip algorithm for distributed computation of the Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant draws upon a reinforcement learning algorithm for an average cost controlled Markov decision problem, the second variant draws upon a reinforcement learning algorithm for risk-sensitive control. We then discuss potential applications of the second variant to ranking schemes, reputation networks, and principal component analysis.

Exploring empirical rank-frequency distributions longitudinally through a simple stochastic process.

PubMed

Finley, Benjamin J; Kilkki, Kalevi

2014-01-01

The frequent appearance of empirical rank-frequency laws, such as Zipf's law, in a wide range of domains reinforces the importance of understanding and modeling these laws and rank-frequency distributions in general. In this spirit, we utilize a simple stochastic cascade process to simulate several empirical rank-frequency distributions longitudinally. We focus especially on limiting the process's complexity to increase accessibility for non-experts in mathematics. The process provides a good fit for many empirical distributions because the stochastic multiplicative nature of the process leads to an often observed concave rank-frequency distribution (on a log-log scale) and the finiteness of the cascade replicates real-world finite size effects. Furthermore, we show that repeated trials of the process can roughly simulate the longitudinal variation of empirical ranks. However, we find that the empirical variation is often less that the average simulated process variation, likely due to longitudinal dependencies in the empirical datasets. Finally, we discuss the process limitations and practical applications.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Stochastic scheduling on a repairable manufacturing system

NASA Astrophysics Data System (ADS)

Li, Wei; Cao, Jinhua

1995-08-01

In this paper, we consider some stochastic scheduling problems with a set of stochastic jobs on a manufacturing system with a single machine that is subject to multiple breakdowns and repairs. When the machine processing a job fails, the job processing must restart some time later when the machine is repaired. For this typical manufacturing system, we find the optimal policies that minimize the following objective functions: (1) the weighed sum of the completion times; (2) the weighed number of late jobs having constant due dates; (3) the weighted number of late jobs having random due dates exponentially distributed, which generalize some previous results.

Conference on Stochastic Processes and Their Applications (12th) held at Ithaca, New York on 11-15 Jul 83,

DTIC Science & Technology

1983-07-15

RD- R136 626 CONFERENCE ON STOCHASTIC PROCESSES AND THEIR APPLICATIONS (12TH> JULY 11 15 1983 ITHACA NEW YORK(U) CORNELL UNIV ITHACA NY 15 JUL 83...oscillator phase Instability" 2t53 - 3s15 p.m. M.N. GOPALAN, Indian Institute of Technoloy, Bombay "Cost benefit analysis of systems subject to inspection...p.m. W. KLIEDANN, Univ. Bremen, Fed. Rep. Germany "Controllability of stochastic systems 8sO0 - lOsO0 p.m. RECEPTION Johnson Art Museum ’q % , t

Solving difficult problems creatively: a role for energy optimised deterministic/stochastic hybrid computing

PubMed Central

Palmer, Tim N.; O’Shea, Michael

2015-01-01

How is the brain configured for creativity? What is the computational substrate for ‘eureka’ moments of insight? Here we argue that creative thinking arises ultimately from a synergy between low-energy stochastic and energy-intensive deterministic processing, and is a by-product of a nervous system whose signal-processing capability per unit of available energy has become highly energy optimised. We suggest that the stochastic component has its origin in thermal (ultimately quantum decoherent) noise affecting the activity of neurons. Without this component, deterministic computational models of the brain are incomplete. PMID:26528173

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

NASA Astrophysics Data System (ADS)

Abin, A.; Kalurachchi, J. J.; Kemblowski, M. W.; Chang, C.-M.

1996-08-01

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.

Tsunami hazard assessments with consideration of uncertain earthquakes characteristics

NASA Astrophysics Data System (ADS)

Sepulveda, I.; Liu, P. L. F.; Grigoriu, M. D.; Pritchard, M. E.

2017-12-01

The uncertainty quantification of tsunami assessments due to uncertain earthquake characteristics faces important challenges. First, the generated earthquake samples must be consistent with the properties observed in past events. Second, it must adopt an uncertainty propagation method to determine tsunami uncertainties with a feasible computational cost. In this study we propose a new methodology, which improves the existing tsunami uncertainty assessment methods. The methodology considers two uncertain earthquake characteristics, the slip distribution and location. First, the methodology considers the generation of consistent earthquake slip samples by means of a Karhunen Loeve (K-L) expansion and a translation process (Grigoriu, 2012), applicable to any non-rectangular rupture area and marginal probability distribution. The K-L expansion was recently applied by Le Veque et al. (2016). We have extended the methodology by analyzing accuracy criteria in terms of the tsunami initial conditions. Furthermore, and unlike this reference, we preserve the original probability properties of the slip distribution, by avoiding post sampling treatments such as earthquake slip scaling. Our approach is analyzed and justified in the framework of the present study. Second, the methodology uses a Stochastic Reduced Order model (SROM) (Grigoriu, 2009) instead of a classic Monte Carlo simulation, which reduces the computational cost of the uncertainty propagation. The methodology is applied on a real case. We study tsunamis generated at the site of the 2014 Chilean earthquake. We generate earthquake samples with expected magnitude Mw 8. We first demonstrate that the stochastic approach of our study generates consistent earthquake samples with respect to the target probability laws. We also show that the results obtained from SROM are more accurate than classic Monte Carlo simulations. We finally validate the methodology by comparing the simulated tsunamis and the tsunami records for the 2014 Chilean earthquake. Results show that leading wave measurements fall within the tsunami sample space. At later times, however, there are mismatches between measured data and the simulated results, suggesting that other sources of uncertainty are as relevant as the uncertainty of the studied earthquake characteristics.

Relative Roles of Deterministic and Stochastic Processes in Driving the Vertical Distribution of Bacterial Communities in a Permafrost Core from the Qinghai-Tibet Plateau, China.

PubMed

Hu, Weigang; Zhang, Qi; Tian, Tian; Li, Dingyao; Cheng, Gang; Mu, Jing; Wu, Qingbai; Niu, Fujun; Stegen, James C; An, Lizhe; Feng, Huyuan

2015-01-01

Understanding the processes that influence the structure of biotic communities is one of the major ecological topics, and both stochastic and deterministic processes are expected to be at work simultaneously in most communities. Here, we investigated the vertical distribution patterns of bacterial communities in a 10-m-long soil core taken within permafrost of the Qinghai-Tibet Plateau. To get a better understanding of the forces that govern these patterns, we examined the diversity and structure of bacterial communities, and the change in community composition along the vertical distance (spatial turnover) from both taxonomic and phylogenetic perspectives. Measures of taxonomic and phylogenetic beta diversity revealed that bacterial community composition changed continuously along the soil core, and showed a vertical distance-decay relationship. Multiple stepwise regression analysis suggested that bacterial alpha diversity and phylogenetic structure were strongly correlated with soil conductivity and pH but weakly correlated with depth. There was evidence that deterministic and stochastic processes collectively drived bacterial vertically-structured pattern. Bacterial communities in five soil horizons (two originated from the active layer and three from permafrost) of the permafrost core were phylogenetically random, indicator of stochastic processes. However, we found a stronger effect of deterministic processes related to soil pH, conductivity, and organic carbon content that were structuring the bacterial communities. We therefore conclude that the vertical distribution of bacterial communities was governed primarily by deterministic ecological selection, although stochastic processes were also at work. Furthermore, the strong impact of environmental conditions (for example, soil physicochemical parameters and seasonal freeze-thaw cycles) on these communities underlines the sensitivity of permafrost microorganisms to climate change and potentially subsequent permafrost thaw.

Relative Roles of Deterministic and Stochastic Processes in Driving the Vertical Distribution of Bacterial Communities in a Permafrost Core from the Qinghai-Tibet Plateau, China

PubMed Central

Tian, Tian; Li, Dingyao; Cheng, Gang; Mu, Jing; Wu, Qingbai; Niu, Fujun; Stegen, James C.; An, Lizhe; Feng, Huyuan

2015-01-01

Understanding the processes that influence the structure of biotic communities is one of the major ecological topics, and both stochastic and deterministic processes are expected to be at work simultaneously in most communities. Here, we investigated the vertical distribution patterns of bacterial communities in a 10-m-long soil core taken within permafrost of the Qinghai-Tibet Plateau. To get a better understanding of the forces that govern these patterns, we examined the diversity and structure of bacterial communities, and the change in community composition along the vertical distance (spatial turnover) from both taxonomic and phylogenetic perspectives. Measures of taxonomic and phylogenetic beta diversity revealed that bacterial community composition changed continuously along the soil core, and showed a vertical distance-decay relationship. Multiple stepwise regression analysis suggested that bacterial alpha diversity and phylogenetic structure were strongly correlated with soil conductivity and pH but weakly correlated with depth. There was evidence that deterministic and stochastic processes collectively drived bacterial vertically-structured pattern. Bacterial communities in five soil horizons (two originated from the active layer and three from permafrost) of the permafrost core were phylogenetically random, indicator of stochastic processes. However, we found a stronger effect of deterministic processes related to soil pH, conductivity, and organic carbon content that were structuring the bacterial communities. We therefore conclude that the vertical distribution of bacterial communities was governed primarily by deterministic ecological selection, although stochastic processes were also at work. Furthermore, the strong impact of environmental conditions (for example, soil physicochemical parameters and seasonal freeze-thaw cycles) on these communities underlines the sensitivity of permafrost microorganisms to climate change and potentially subsequent permafrost thaw. PMID:26699734

Simulations of Technology-Induced and Crisis-Led Stochastic and Chaotic Fluctuations in Higher Education Processes: A Model and a Case Study for Performance and Expected Employment

ERIC Educational Resources Information Center

Ahmet, Kara

2015-01-01

This paper presents a simple model of the provision of higher educational services that considers and exemplifies nonlinear, stochastic, and potentially chaotic processes. I use the methods of system dynamics to simulate these processes in the context of a particular sociologically interesting case, namely that of the Turkish higher education…

General Results in Optimal Control of Discrete-Time Nonlinear Stochastic Systems

DTIC Science & Technology

1988-01-01

P. J. McLane, "Optimal Stochastic Control of Linear System. with State- and Control-Dependent Distur- bances," ZEEE Trans. 4uto. Contr., Vol. 16, No...Vol. 45, No. 1, pp. 359-362, 1987 (9] R. R. Mohler and W. J. Kolodziej, "An Overview of Stochastic Bilinear Control Processes," ZEEE Trans. Syst...34 J. of Math. anal. App.:, Vol. 47, pp. 156-161, 1974 [14) E. Yaz, "A Control Scheme for a Class of Discrete Nonlinear Stochastic Systems," ZEEE Trans

Application of quantum master equation for long-term prognosis of asset-prices

NASA Astrophysics Data System (ADS)

Khrennikova, Polina

2016-05-01

This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a ;financial bath;. The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

Study on Stationarity of Random Load Spectrum Based on the Special Road

NASA Astrophysics Data System (ADS)

Yan, Huawen; Zhang, Weigong; Wang, Dong

2017-09-01

In the special road quality assessment method, there is a method using a wheel force sensor, the essence of this method is collecting the load spectrum of the car to reflect the quality of road. According to the definition of stochastic process, it is easy to find that the load spectrum is a stochastic process. However, the analysis method and application range of different random processes are very different, especially in engineering practice, which will directly affect the design and development of the experiment. Therefore, determining the type of a random process has important practical significance. Based on the analysis of the digital characteristics of road load spectrum, this paper determines that the road load spectrum in this experiment belongs to a stationary stochastic process, paving the way for the follow-up modeling and feature extraction of the special road.

Track and vertex reconstruction: From classical to adaptive methods

NASA Astrophysics Data System (ADS)

Strandlie, Are; Frühwirth, Rudolf

2010-04-01

This paper reviews classical and adaptive methods of track and vertex reconstruction in particle physics experiments. Adaptive methods have been developed to meet the experimental challenges at high-energy colliders, in particular, the CERN Large Hadron Collider. They can be characterized by the obliteration of the traditional boundaries between pattern recognition and statistical estimation, by the competition between different hypotheses about what constitutes a track or a vertex, and by a high level of flexibility and robustness achieved with a minimum of assumptions about the data. The theoretical background of some of the adaptive methods is described, and it is shown that there is a close connection between the two main branches of adaptive methods: neural networks and deformable templates, on the one hand, and robust stochastic filters with annealing, on the other hand. As both classical and adaptive methods of track and vertex reconstruction presuppose precise knowledge of the positions of the sensitive detector elements, the paper includes an overview of detector alignment methods and a survey of the alignment strategies employed by past and current experiments.

Comparison of a Classical and Quantum Based Restricted Boltzmann Machine (RBM) for Application to Non-linear Multivariate Regression.

NASA Astrophysics Data System (ADS)

Dorband, J. E.; Tilak, N.; Radov, A.

2016-12-01

In this paper, a classical computer implementation of RBM is compared to a quantum annealing based RBM running on a D-Wave 2X (an adiabatic quantum computer). The codes for both are essentially identical. Only a flag is set to change the activation function from a classically computed logistic function to the D-Wave. To obtain greater understanding of the behavior of the D-Wave, a study of the stochastic properties of a virtual qubit (a 12 qubit chain) and a cell of qubits (an 8 qubit cell) was performed. We will present the results of comparing the D-Wave implementation with a theoretically errorless adiabatic quantum computer. The main purpose of this study is to develop a generic RBM regression tool in order to infer CO2 fluxes from the NASA satellite OCO-2 observed CO2 concentrations and predicted atmospheric states using regression models. The carbon fluxes will then be assimilated into a land surface model to predict the Net Ecosystem Exchange at globally distributed regional sites.

A Stochastic Detection and Retrieval Model for the Study of Metacognition

ERIC Educational Resources Information Center

Jang, Yoonhee; Wallsten, Thomas S.; Huber, David E.

2012-01-01

We present a signal detection-like model termed the stochastic detection and retrieval model (SDRM) for use in studying metacognition. Focusing on paradigms that relate retrieval (e.g., recall or recognition) and confidence judgments, the SDRM measures (1) variance in the retrieval process, (2) variance in the confidence process, (3) the extent to…

Stochastic processes, estimation theory and image enhancement

NASA Technical Reports Server (NTRS)

Assefi, T.

1978-01-01

An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.

Stochastic Multiscale Analysis and Design of Engine Disks

DTIC Science & Technology

2010-07-28

shown recently to fail when used with data-driven non-linear stochastic input models (KPCA, IsoMap, etc.). Need for scalable exascale computing algorithms Materials Process Design and Control Laboratory Cornell University

Transcriptional dynamics with time-dependent reaction rates

NASA Astrophysics Data System (ADS)

Nandi, Shubhendu; Ghosh, Anandamohan

2015-02-01

Transcription is the first step in the process of gene regulation that controls cell response to varying environmental conditions. Transcription is a stochastic process, involving synthesis and degradation of mRNAs, that can be modeled as a birth-death process. We consider a generic stochastic model, where the fluctuating environment is encoded in the time-dependent reaction rates. We obtain an exact analytical expression for the mRNA probability distribution and are able to analyze the response for arbitrary time-dependent protocols. Our analytical results and stochastic simulations confirm that the transcriptional machinery primarily act as a low-pass filter. We also show that depending on the system parameters, the mRNA levels in a cell population can show synchronous/asynchronous fluctuations and can deviate from Poisson statistics.

Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

NASA Astrophysics Data System (ADS)

Jia, Ningning; Y Lam, Edmund

2010-04-01

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

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

Energy loss of ions by electric-field fluctuations in a magnetized plasma.

PubMed

Nersisyan, Hrachya B; Deutsch, Claude

2011-06-01

The results of a theoretical investigation of the energy loss of charged particles in a magnetized classical plasma due to the electric-field fluctuations are reported. The energy loss for a test particle is calculated through the linear-response theory. At vanishing magnetic field, the electric-field fluctuations lead to an energy gain of the charged particle for all velocities. It has been shown that in the presence of strong magnetic field, this effect occurs only at low velocities. In the case of high velocities, the test particle systematically loses its energy due to the interaction with a stochastic electric field. The net effect of the fluctuations is the systematic reduction of the total energy loss (i.e., the sum of the polarization and stochastic energy losses) at vanishing magnetic field and reduction or enhancement at strong field, depending on the velocity of the particle. It is found that the energy loss of the slow heavy ion contains an anomalous term that depends logarithmically on the projectile mass. The physical origin of this anomalous term is the coupling between the cyclotron motion of the plasma electrons and the long-wavelength, low-frequency fluctuations produced by the projectile ion. This effect may strongly enhance the stochastic energy gain of the particle.

Combining Deterministic structures and stochastic heterogeneity for transport modeling

NASA Astrophysics Data System (ADS)

Zech, Alraune; Attinger, Sabine; Dietrich, Peter; Teutsch, Georg

2017-04-01

Contaminant transport in highly heterogeneous aquifers is extremely challenging and subject of current scientific debate. Tracer plumes often show non-symmetric but highly skewed plume shapes. Predicting such transport behavior using the classical advection-dispersion-equation (ADE) in combination with a stochastic description of aquifer properties requires a dense measurement network. This is in contrast to the available information for most aquifers. A new conceptual aquifer structure model is presented which combines large-scale deterministic information and the stochastic approach for incorporating sub-scale heterogeneity. The conceptual model is designed to allow for a goal-oriented, site specific transport analysis making use of as few data as possible. Thereby the basic idea is to reproduce highly skewed tracer plumes in heterogeneous media by incorporating deterministic contrasts and effects of connectivity instead of using unimodal heterogeneous models with high variances. The conceptual model consists of deterministic blocks of mean hydraulic conductivity which might be measured by pumping tests indicating values differing in orders of magnitudes. A sub-scale heterogeneity is introduced within every block. This heterogeneity can be modeled as bimodal or log-normal distributed. The impact of input parameters, structure and conductivity contrasts is investigated in a systematic manor. Furthermore, some first successful implementation of the model was achieved for the well known MADE site.

Exploring Empirical Rank-Frequency Distributions Longitudinally through a Simple Stochastic Process

PubMed Central

Finley, Benjamin J.; Kilkki, Kalevi

2014-01-01

The frequent appearance of empirical rank-frequency laws, such as Zipf’s law, in a wide range of domains reinforces the importance of understanding and modeling these laws and rank-frequency distributions in general. In this spirit, we utilize a simple stochastic cascade process to simulate several empirical rank-frequency distributions longitudinally. We focus especially on limiting the process’s complexity to increase accessibility for non-experts in mathematics. The process provides a good fit for many empirical distributions because the stochastic multiplicative nature of the process leads to an often observed concave rank-frequency distribution (on a log-log scale) and the finiteness of the cascade replicates real-world finite size effects. Furthermore, we show that repeated trials of the process can roughly simulate the longitudinal variation of empirical ranks. However, we find that the empirical variation is often less that the average simulated process variation, likely due to longitudinal dependencies in the empirical datasets. Finally, we discuss the process limitations and practical applications. PMID:24755621

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

NASA Astrophysics Data System (ADS)

González Arenas, Zochil; Barci, Daniel G.

2012-12-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Fiber Breakage Model for Carbon Composite Stress Rupture Phenomenon: Theoretical Development and Applications

NASA Technical Reports Server (NTRS)

Murthy, Pappu L. N.; Phoenix, S. Leigh; Grimes-Ledesma, Lorie

2010-01-01

Stress rupture failure of Carbon Composite Overwrapped Pressure Vessels (COPVs) is of serious concern to Science Mission and Constellation programs since there are a number of COPVs on board space vehicles with stored gases under high pressure for long durations of time. It has become customary to establish the reliability of these vessels using the so called classic models. The classical models are based on Weibull statistics fitted to observed stress rupture data. These stochastic models cannot account for any additional damage due to the complex pressure-time histories characteristic of COPVs being supplied for NASA missions. In particular, it is suspected that the effects of proof test could significantly reduce the stress rupture lifetime of COPVs. The focus of this paper is to present an analytical appraisal of a model that incorporates damage due to proof test. The model examined in the current paper is based on physical mechanisms such as micromechanics based load sharing concepts coupled with creep rupture and Weibull statistics. For example, the classic model cannot accommodate for damage due to proof testing which every flight vessel undergoes. The paper compares current model to the classic model with a number of examples. In addition, several applications of the model to current ISS and Constellation program issues are also examined.

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks

PubMed Central

Li, Yihe; Li, Bofeng; Gao, Yang

2015-01-01

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network. PMID:26633400

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks.

PubMed

Li, Yihe; Li, Bofeng; Gao, Yang

2015-11-30

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network.

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.

Scaling and stochastic cascade properties of NEMO oceanic simulations and their potential value for GCM evaluation and downscaling

NASA Astrophysics Data System (ADS)

Verrier, Sébastien; Crépon, Michel; Thiria, Sylvie

2014-09-01

Spectral scaling properties have already been evidenced on oceanic numerical simulations and have been subject to several interpretations. They can be used to evaluate classical turbulence theories that predict scaling with specific exponents and to evaluate the quality of GCM outputs from a statistical and multiscale point of view. However, a more complete framework based on multifractal cascades is able to generalize the classical but restrictive second-order spectral framework to other moment orders, providing an accurate description of probability distributions of the fields at multiple scales. The predictions of this formalism still needed systematic verification in oceanic GCM while they have been confirmed recently for their atmospheric counterparts by several papers. The present paper is devoted to a systematic analysis of several oceanic fields produced by the NEMO oceanic GCM. Attention is focused to regional, idealized configurations that permit to evaluate the NEMO engine core from a scaling point of view regardless of limitations involved by land masks. Based on classical multifractal analysis tools, multifractal properties were evidenced for several oceanic state variables (sea surface temperature and salinity, velocity components, etc.). While first-order structure functions estimated a different nonconservativity parameter H in two scaling ranges, the multiorder statistics of turbulent fluxes were scaling over almost the whole available scaling range. This multifractal scaling was then parameterized with the help of the universal multifractal framework, providing parameters that are coherent with existing empirical literature. Finally, we argue that the knowledge of these properties may be useful for oceanographers. The framework seems very well suited for the statistical evaluation of OGCM outputs. Moreover, it also provides practical solutions to simulate subpixel variability stochastically for GCM downscaling purposes. As an independent perspective, the existence of multifractal properties in oceanic flows seems also interesting for investigating scale dependencies in remote sensing inversion algorithms.

Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

PubMed

Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

2007-12-01

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

CSI 2264: CHARACTERIZING YOUNG STARS IN NGC 2264 WITH STOCHASTICALLY VARYING LIGHT CURVES

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

Stauffer, John; Rebull, Luisa; Carey, Sean

2016-03-15

We provide CoRoT and Spitzer light curves and other supporting data for 17 classical T Tauri stars in NGC 2264 whose CoRoT light curves exemplify the “stochastic” light curve class as defined in 2014 by Cody et al. The most probable physical mechanism to explain the optical variability within this light curve class is time-dependent mass accretion onto the stellar photosphere, producing transient hot spots. Where we have appropriate spectral data, we show that the veiling variability in these stars is consistent in both amplitude and timescale with the optical light curve morphology. The veiling variability is also well-correlated with the strengthmore » of the He i 6678 Å emission line, predicted by models to arise in accretion shocks on or near the stellar photosphere. Stars with accretion burst light curve morphology also have variable mass accretion. The stochastic and accretion burst light curves can both be explained by a simple model of randomly occurring flux bursts, with the stochastic light curve class having a higher frequency of lower amplitude events. Members of the stochastic light curve class have only moderate mass accretion rates. Their Hα profiles usually have blueshifted absorption features, probably originating in a disk wind. The lack of periodic signatures in the light curves suggests that little of the variability is due to long-lived hot spots rotating into or out of our line of sight; instead, the primary driver of the observed photometric variability is likely to be instabilities in the inner disk that lead to variable mass accretion.« less

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession.

PubMed

Dini-Andreote, Francisco; Stegen, James C; van Elsas, Jan Dirk; Salles, Joana Falcão

2015-03-17

Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages--which provide a larger spatiotemporal scale relative to within stage analyses--revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended--and experimentally testable--conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems.

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession

PubMed Central

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan Dirk; Salles, Joana Falcão

2015-01-01

Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages—which provide a larger spatiotemporal scale relative to within stage analyses—revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended—and experimentally testable—conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems. PMID:25733885

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

Modeling language and cognition with deep unsupervised learning: a tutorial overview

PubMed Central

Zorzi, Marco; Testolin, Alberto; Stoianov, Ivilin P.

2013-01-01

Deep unsupervised learning in stochastic recurrent neural networks with many layers of hidden units is a recent breakthrough in neural computation research. These networks build a hierarchy of progressively more complex distributed representations of the sensory data by fitting a hierarchical generative model. In this article we discuss the theoretical foundations of this approach and we review key issues related to training, testing and analysis of deep networks for modeling language and cognitive processing. The classic letter and word perception problem of McClelland and Rumelhart (1981) is used as a tutorial example to illustrate how structured and abstract representations may emerge from deep generative learning. We argue that the focus on deep architectures and generative (rather than discriminative) learning represents a crucial step forward for the connectionist modeling enterprise, because it offers a more plausible model of cortical learning as well as a way to bridge the gap between emergentist connectionist models and structured Bayesian models of cognition. PMID:23970869

Sanov and central limit theorems for output statistics of quantum Markov chains

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

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

Evidence of Deterministic Components in the Apparent Randomness of GRBs: Clues of a Chaotic Dynamic

PubMed Central

Greco, G.; Rosa, R.; Beskin, G.; Karpov, S.; Romano, L.; Guarnieri, A.; Bartolini, C.; Bedogni, R.

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short – as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration – seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole. PMID:22355609

Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

PubMed

Greco, G; Rosa, R; Beskin, G; Karpov, S; Romano, L; Guarnieri, A; Bartolini, C; Bedogni, R

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short - as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration - seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole.

Solar coronal loop heating by cross-field wave transport

NASA Technical Reports Server (NTRS)

Amendt, Peter; Benford, Gregory

1989-01-01

Solar coronal arches heated by turbulent ion-cyclotron waves may suffer significant cross-field transport by these waves. Nonlinear processes fix the wave-propagation speed at about a tenth of the ion thermal velocity, which seems sufficient to spread heat from a central core into a large cool surrounding cocoon. Waves heat cocoon ions both through classical ion-electron collisions and by turbulent stochastic ion motions. Plausible cocoon sizes set by wave damping are in roughly kilometers, although the wave-emitting core may be only 100 m wide. Detailed study of nonlinear stabilization and energy-deposition rates predicts that nearby regions can heat to values intermediate between the roughly electron volt foot-point temperatures and the about 100 eV core, which is heated by anomalous Ohmic losses. A volume of 100 times the core volume may be affected. This qualitative result may solve a persistent problem with current-driven coronal heating; that it affects only small volumes and provides no way to produce the extended warm structures perceptible to existing instruments.

Modeling language and cognition with deep unsupervised learning: a tutorial overview.

PubMed

Zorzi, Marco; Testolin, Alberto; Stoianov, Ivilin P

2013-01-01

Deep unsupervised learning in stochastic recurrent neural networks with many layers of hidden units is a recent breakthrough in neural computation research. These networks build a hierarchy of progressively more complex distributed representations of the sensory data by fitting a hierarchical generative model. In this article we discuss the theoretical foundations of this approach and we review key issues related to training, testing and analysis of deep networks for modeling language and cognitive processing. The classic letter and word perception problem of McClelland and Rumelhart (1981) is used as a tutorial example to illustrate how structured and abstract representations may emerge from deep generative learning. We argue that the focus on deep architectures and generative (rather than discriminative) learning represents a crucial step forward for the connectionist modeling enterprise, because it offers a more plausible model of cortical learning as well as a way to bridge the gap between emergentist connectionist models and structured Bayesian models of cognition.

An inexact reverse logistics model for municipal solid waste management systems.

PubMed

Zhang, Yi Mei; Huang, Guo He; He, Li

2011-03-01

This paper proposed an inexact reverse logistics model for municipal solid waste management systems (IRWM). Waste managers, suppliers, industries and distributors were involved in strategic planning and operational execution through reverse logistics management. All the parameters were assumed to be intervals to quantify the uncertainties in the optimization process and solutions in IRWM. To solve this model, a piecewise interval programming was developed to deal with Min-Min functions in both objectives and constraints. The application of the model was illustrated through a classical municipal solid waste management case. With different cost parameters for landfill and the WTE, two scenarios were analyzed. The IRWM could reflect the dynamic and uncertain characteristics of MSW management systems, and could facilitate the generation of desired management plans. The model could be further advanced through incorporating methods of stochastic or fuzzy parameters into its framework. Design of multi-waste, multi-echelon, multi-uncertainty reverse logistics model for waste management network would also be preferred. Copyright © 2010 Elsevier Ltd. All rights reserved.

Social selection and peer influence in an online social network.

PubMed

Lewis, Kevin; Gonzalez, Marco; Kaufman, Jason

2012-01-03

Disentangling the effects of selection and influence is one of social science's greatest unsolved puzzles: Do people befriend others who are similar to them, or do they become more similar to their friends over time? Recent advances in stochastic actor-based modeling, combined with self-reported data on a popular online social network site, allow us to address this question with a greater degree of precision than has heretofore been possible. Using data on the Facebook activity of a cohort of college students over 4 years, we find that students who share certain tastes in music and in movies, but not in books, are significantly likely to befriend one another. Meanwhile, we find little evidence for the diffusion of tastes among Facebook friends-except for tastes in classical/jazz music. These findings shed light on the mechanisms responsible for observed network homogeneity; provide a statistically rigorous assessment of the coevolution of cultural tastes and social relationships; and suggest important qualifications to our understanding of both homophily and contagion as generic social processes.

1/f Noise from nonlinear stochastic differential equations.

PubMed

Ruseckas, J; Kaulakys, B

2010-03-01

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

Information transfer with rate-modulated Poisson processes: a simple model for nonstationary stochastic resonance.

PubMed

Goychuk, I

2001-08-01

Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.

Refractory pulse counting processes in stochastic neural computers.

PubMed

McNeill, Dean K; Card, Howard C

2005-03-01

This letter quantitiatively investigates the effect of a temporary refractory period or dead time in the ability of a stochastic Bernoulli processor to record subsequent pulse events, following the arrival of a pulse. These effects can arise in either the input detectors of a stochastic neural network or in subsequent processing. A transient period is observed, which increases with both the dead time and the Bernoulli probability of the dead-time free system, during which the system reaches equilibrium. Unless the Bernoulli probability is small compared to the inverse of the dead time, the mean and variance of the pulse count distributions are both appreciably reduced.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

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…

Mathematics Education. Selected Papers from the Conference on Stochastic Processes and Their Applications. (15th, Nagoya, Japan, July 2-5, 1985).

ERIC Educational Resources Information Center

Hida, Takeyuki; Shimizu, Akinobu

This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical…

Intrinsic Information Processing and Energy Dissipation in Stochastic Input-Output Dynamical Systems

DTIC Science & Technology

2015-07-09

Crutchfield. Information Anatomy of Stochastic Equilibria, Entropy , (08 2014): 0. doi: 10.3390/e16094713 Virgil Griffith, Edwin Chong, Ryan James...Christopher Ellison, James Crutchfield. Intersection Information Based on Common Randomness, Entropy , (04 2014): 0. doi: 10.3390/e16041985 TOTAL: 5 Number...Learning Group Seminar, Complexity Sciences Center, UC Davis. Korana Burke and Greg Wimsatt (UCD), reviewed PRL “Measurement of Stochastic Entropy

Stochastically gated local and occupation times of a Brownian particle

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-01-01

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

The response analysis of fractional-order stochastic system via generalized cell mapping method.

PubMed

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

A large deviations principle for stochastic flows of viscous fluids

NASA Astrophysics Data System (ADS)

Cipriano, Fernanda; Costa, Tiago

2018-04-01

We study the well-posedness of a stochastic differential equation on the two dimensional torus T2, driven by an infinite dimensional Wiener process with drift in the Sobolev space L2 (0 , T ;H1 (T2)) . The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier-Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.

The cardiorespiratory interaction: a nonlinear stochastic model and its synchronization properties

NASA Astrophysics Data System (ADS)

Bahraminasab, A.; Kenwright, D.; Stefanovska, A.; McClintock, P. V. E.

2007-06-01

We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation

PubMed Central

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO2) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms. PMID:29670508

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation.

PubMed

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO 2 ) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms.

Precise Orbit Determination Of Low Earth Satellites At AIUB Using GPS And SLR Data

NASA Astrophysics Data System (ADS)

Jaggi, A.; Bock, H.; Thaller, D.; Sosnica, K.; Meyer, U.; Baumann, C.; Dach, R.

2013-12-01

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Institute of the University of Bern (AIUB) LEO precise orbit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numerical integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to efficiently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circulation Explorer (GOCE).

Stochastic dynamics of genetic broadcasting networks

NASA Astrophysics Data System (ADS)

Potoyan, Davit A.; Wolynes, Peter G.

2017-11-01

The complex genetic programs of eukaryotic cells are often regulated by key transcription factors occupying or clearing out of a large number of genomic locations. Orchestrating the residence times of these factors is therefore important for the well organized functioning of a large network. The classic models of genetic switches sidestep this timing issue by assuming the binding of transcription factors to be governed entirely by thermodynamic protein-DNA affinities. Here we show that relying on passive thermodynamics and random release times can lead to a "time-scale crisis" for master genes that broadcast their signals to a large number of binding sites. We demonstrate that this time-scale crisis for clearance in a large broadcasting network can be resolved by actively regulating residence times through molecular stripping. We illustrate these ideas by studying a model of the stochastic dynamics of the genetic network of the central eukaryotic master regulator NFκ B which broadcasts its signals to many downstream genes that regulate immune response, apoptosis, etc.

A Stochastic Dynamic Programming Model With Fuzzy Storage States Applied to Reservoir Operation Optimization

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Jamshid; Mahdizadeh, Kourosh; Afshar, Abbas

2004-08-01

Application of stochastic dynamic programming (SDP) models to reservoir optimization calls for state variables discretization. As an important variable discretization of reservoir storage volume has a pronounced effect on the computational efforts. The error caused by storage volume discretization is examined by considering it as a fuzzy state variable. In this approach, the point-to-point transitions between storage volumes at the beginning and end of each period are replaced by transitions between storage intervals. This is achieved by using fuzzy arithmetic operations with fuzzy numbers. In this approach, instead of aggregating single-valued crisp numbers, the membership functions of fuzzy numbers are combined. Running a simulated model with optimal release policies derived from fuzzy and non-fuzzy SDP models shows that a fuzzy SDP with a coarse discretization scheme performs as well as a classical SDP having much finer discretized space. It is believed that this advantage in the fuzzy SDP model is due to the smooth transitions between storage intervals which benefit from soft boundaries.

Randomly Sampled-Data Control Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Han, Kuoruey

1990-01-01

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

A stochastic two-scale model for pressure-driven flow between rough surfaces

PubMed Central

Larsson, Roland; Lundström, Staffan; Wall, Peter; Almqvist, Andreas

2016-01-01

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern. PMID:27436975

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.