An Adaptive QSE-reduced Nuclear Reaction Network for Silicon Burning

NASA Astrophysics Data System (ADS)

Parete-Koon, Suzanne; Hix, William Raphael; Thielemann, Friedrich-Karl

2010-02-01

The nuclei of the ``iron peak'' are formed late in the evolution of massive stars and during supernovae. Silicon burning during these events is responsible for the production of a wide range of nuclei with atomic mass numbers from 28 to 64. The large number of nuclei involved make accurate modeling of silicon burning computationally expensive. Examination of the physics of silicon burning reveals that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. We present an improvement on our hybrid equilibrium-network scheme that takes advantage of this quasi-equilibrium (QSE) to reduce the number of independent variables calculated. Because the membership and number of these groups vary as the temperature, density and electron faction change, achieving maximal efficiency requires dynamic adjustment of group number and membership. The resultant QSE-reduced network is up to 20 times faster than the full network it replaces without significant loss of accuracy. These reductions in computational cost and the number of species evolved make QSE-reduced networks well suited for inclusion within hydrodynamic simulations, particularly in multi-dimensional applications. )

The QSE-Reduced Nuclear Reaction Network for Silicon Burning

NASA Astrophysics Data System (ADS)

Hix, W. Raphael; Parete-Koon, Suzanne T.; Freiburghaus, Christian; Thielemann, Friedrich-Karl

2007-09-01

Iron and neighboring nuclei are formed in massive stars shortly before core collapse and during their supernova outbursts, as well as during thermonuclear supernovae. Complete and incomplete silicon burning are responsible for the production of a wide range of nuclei with atomic mass numbers from 28 to 64. Because of the large number of nuclei involved, accurate modeling of silicon burning is computationally expensive. However, examination of the physics of silicon burning has revealed that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. We present a new hybrid equilibrium-network scheme which takes advantage of this quasi-equilibrium in order to reduce the number of independent variables calculated. This allows accurate prediction of the nuclear abundance evolution, deleptonization, and energy generation at a greatly reduced computational cost when compared to a conventional nuclear reaction network. During silicon burning, the resultant QSE-reduced network is approximately an order of magnitude faster than the full network it replaces and requires the tracking of less than a third as many abundance variables, without significant loss of accuracy. These reductions in computational cost and the number of species evolved make QSE-reduced networks well suited for inclusion within hydrodynamic simulations, particularly in multidimensional applications.

The spreading dynamics of sexually transmitted diseases with birth and death on heterogeneous networks

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alsaedi, Ahmed; Hayat, Tasawar

2017-02-01

In this paper, we formulate a deterministic model by including the vacant sites, which represent inactive individuals or potential contacts, to investigate the spreading dynamics of sexually transmitted diseases in heterogeneous networks. We first analytically derive the basic reproduction number R 0, which completely determines global dynamics of the system in the long run. Specifically, if R 0  <  1, the disease-free equilibrium is globally asymptotically stable, i.e. disease disappears from the network irrespective of initial infected numbers and distributions, whereas if R 0  >  1, the system is uniformly persistent around a unique endemic equilibrium, i.e. disease persists in the network. Furthermore, by using a suitable Lyapunov function the global stability of endemic equilibrium for low/high-risk infected individuals only is proved. Finally, the effects of three immunization schemes are studied and compared, and extensive numerical simulations are performed to investigate the effect of network topology and population turnover on disease spread. Our results suggest that population turnover could have great impact on the sexually transmitted disease system in heterogeneous networks, including the basic reproduction number and infection prevalence.

Response to Contradiction: Conflict Resolution Strategies Used by Students in Solving Problems of Chemical Equilibrium.

ERIC Educational Resources Information Center

Niaz, Mansoor

2001-01-01

Illustrates how a novel problem of chemical equilibrium based on a closely related sequence of items can facilitate students' conceptual understanding. Students were presented with a chemical reaction in equilibrium to which a reactant was added as an external effect. Three studies were conducted to assess alternative conceptions. (Author/SAH)

Power allocation for target detection in radar networks based on low probability of intercept: A cooperative game theoretical strategy

NASA Astrophysics Data System (ADS)

Shi, Chenguang; Salous, Sana; Wang, Fei; Zhou, Jianjiang

2017-08-01

Distributed radar network systems have been shown to have many unique features. Due to their advantage of signal and spatial diversities, radar networks are attractive for target detection. In practice, the netted radars in radar networks are supposed to maximize their transmit power to achieve better detection performance, which may be in contradiction with low probability of intercept (LPI). Therefore, this paper investigates the problem of adaptive power allocation for radar networks in a cooperative game-theoretic framework such that the LPI performance can be improved. Taking into consideration both the transmit power constraints and the minimum signal to interference plus noise ratio (SINR) requirement of each radar, a cooperative Nash bargaining power allocation game based on LPI is formulated, whose objective is to minimize the total transmit power by optimizing the power allocation in radar networks. First, a novel SINR-based network utility function is defined and utilized as a metric to evaluate power allocation. Then, with the well-designed network utility function, the existence and uniqueness of the Nash bargaining solution are proved analytically. Finally, an iterative Nash bargaining algorithm is developed that converges quickly to a Pareto optimal equilibrium for the cooperative game. Numerical simulations and theoretic analysis are provided to evaluate the effectiveness of the proposed algorithm.

Three essays on pricing and risk management in electricity markets

NASA Astrophysics Data System (ADS)

Kotsan, Serhiy

2005-07-01

A set of three papers forms this dissertation. In the first paper I analyze an electricity market that does not clear. The system operator satisfies fixed demand at a fixed price, and attempts to minimize "cost" as indicated by independent generators' supply bids. No equilibrium exists in this situation, and the operator lacks information sufficient to minimize actual cost. As a remedy, we propose a simple efficient tax mechanism. With the tax, Nash equilibrium bids still diverge from marginal cost but nonetheless provide sufficient information to minimize actual cost, regardless of the tax rate or number of generators. The second paper examines a price mechanism with one price assigned for each level of bundled real and reactive power. Equilibrium allocation under this pricing approach raises system efficiency via better allocation of the reactive power reserves, neglected in the traditional pricing approach. Pricing reactive power should be considered in the bundle with real power since its cost is highly dependent on real power output. The efficiency of pricing approach is shown in the general case, and tested on the 30-bus IEEE network with piecewise linear cost functions of the generators. Finally the third paper addresses the problem of optimal investment in generation based on mean-variance portfolio analysis. It is assumed the investor can freely create a portfolio of shares in generation located on buses of the electrical network. Investors are risk averse, and seek to minimize the variance of the weighted average Locational Marginal Price (LMP) in their portfolio, and to maximize its expected value. I conduct simulations using a standard IEEE 68-bus network that resembles the New York - New England system and calculate LMPs in accordance with the PJM methodology for a fully optimal AC power flow solution. Results indicate that the network topology is a crucial determinant of the investment decision as line congestion makes it difficult to deliver power to certain nodes at system peak load. Determining those nodes is an important task for an investor in generation as well as the transmission system operator.

Broken Detailed Balance of Filament Dynamics in Active Networks

NASA Astrophysics Data System (ADS)

Schmidt, Christoph F.; Gladrow, Jannes; Fakhri, Nikta; Mackintosh, Fred C.; Broedersz, Chase

Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single- walled carbon nanotubes can be used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in biopolymer networks. We analytically calculated shape fluctuations of semi- flexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under non-equilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

Mass-action equilibrium and non-specific interactions in protein binding networks

NASA Astrophysics Data System (ADS)

Maslov, Sergei

2009-03-01

Large-scale protein binding networks serve as a paradigm of complex properties of living cells. These networks are naturally weighted with edges characterized by binding strength and protein-nodes -- by their concentrations. However, the state-of-the-art high-throughput experimental techniques generate just a binary (yes or no) information about individual interactions. As a result, most of the previous research concentrated just on topology of these networks. In a series of recent publications [1-4] my collaborators and I went beyond purely topological studies and calculated the mass-action equilibrium of a genome-wide binding network using experimentally determined protein concentrations, localizations, and reliable binding interactions in baker's yeast. We then studied how this equilibrium responds to large perturbations [1-2] and noise [3] in concentrations of proteins. We demonstrated that the change in the equilibrium concentration of a protein exponentially decays (and sign-alternates) with its network distance away from the perturbed node. This explains why, despite a globally connected topology, individual functional modules in such networks are able to operate fairly independently. In a separate study [4] we quantified the interplay between specific and non-specific binding interactions under crowded conditions inside living cells. We show how the need to limit the waste of resources constrains the number of types and concentrations of proteins that are present at the same time and at the same place in yeast cells. [1] S Maslov, I. Ispolatov, PNAS 104:13655 (2007). [2] S. Maslov, K. Sneppen, I. Ispolatov, New J. of Phys. 9: 273 (2007). [3] K-K. Yan, D. Walker, S. Maslov, PRL accepted (2008). [4] J. Zhang, S. Maslov, and E. I. Shakhnovich, Mol Syst Biol 4, 210 (2008).

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

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

How-To-Do-It: Multiple Allelic Frequencies in Populations at Equilibrium: Algorithms and Applications.

ERIC Educational Resources Information Center

Nussbaum, Francis, Jr.

1988-01-01

Presents an algorithm for solving problems related to multiple allelic frequencies in populations at equilibrium. Considers sample problems and provides their solution using this tabular algorithm. (CW)

Respondent driven sampling is an effective method for engaging methamphetamine users in HIV prevention research in South Africa

PubMed Central

Kimani, Stephen M.; Watt, Melissa H.; Merli, M. Giovanna; Skinner, Donald; Myers, Bronwyn; Pieterse, Desiree; MacFarlane, Jessica C.; Meade, Christina S.

2014-01-01

Background South Africa, in the midst of the world’s largest HIV epidemic, has a growing methamphetamine problem. Respondent driven sampling (RDS) is a useful tool for recruiting hard-to-reach populations in HIV prevention research, but its use with methamphetamine smokers in South Africa has not been described. This study examined the effectiveness of RDS as a method for engaging methamphetamine users in a Cape Town township into HIV behavioral research. Methods Standard RDS procedures were used to recruit active methamphetamine smokers from a racially diverse peri-urban township in Cape Town. Effectiveness of RDS was determined by examining social network characteristics (network size, homophily, and equilibrium) of recruited participants. Results Beginning with 8 seeds, 345 methamphetamine users were enrolled over 6 months, with a coupon return rate of 67%. The sample included 197 men and 148 women who were racially diverse (73% Coloured, 27% Black African) and had a mean age of 28.8 years (SD=7.2). Social networks were adequate (mean network size >5) and mainly comprised of close social ties. Equilibrium on race was reached after 11 waves of recruitment, and after ≤3 waves for all other variables of interest. There was little to moderate preference for either in- or out-group recruiting in all subgroups. Conclusions Results suggest that RDS is an effective method for engaging methamphetamine users into HIV prevention research in South Africa. Additionally, RDS may be a useful strategy for seeking high-risk methamphetamine users for HIV testing and linkage to HIV care in this and other low resource settings. PMID:25128957

A market-based optimization approach to sensor and resource management

NASA Astrophysics Data System (ADS)

Schrage, Dan; Farnham, Christopher; Gonsalves, Paul G.

2006-05-01

Dynamic resource allocation for sensor management is a problem that demands solutions beyond traditional approaches to optimization. Market-based optimization applies solutions from economic theory, particularly game theory, to the resource allocation problem by creating an artificial market for sensor information and computational resources. Intelligent agents are the buyers and sellers in this market, and they represent all the elements of the sensor network, from sensors to sensor platforms to computational resources. These agents interact based on a negotiation mechanism that determines their bidding strategies. This negotiation mechanism and the agents' bidding strategies are based on game theory, and they are designed so that the aggregate result of the multi-agent negotiation process is a market in competitive equilibrium, which guarantees an optimal allocation of resources throughout the sensor network. This paper makes two contributions to the field of market-based optimization: First, we develop a market protocol to handle heterogeneous goods in a dynamic setting. Second, we develop arbitrage agents to improve the efficiency in the market in light of its dynamic nature.

A stochastic equilibrium model for the North American natural gas market

NASA Astrophysics Data System (ADS)

Zhuang, Jifang

This dissertation is an endeavor in the field of energy modeling for the North American natural gas market using a mixed complementarity formulation combined with the stochastic programming. The genesis of the stochastic equilibrium model presented in this dissertation is the deterministic market equilibrium model developed in [Gabriel, Kiet and Zhuang, 2005]. Based on some improvements that we made to this model, including proving new existence and uniqueness results, we present a multistage stochastic equilibrium model with uncertain demand for the deregulated North American natural gas market using the recourse method of the stochastic programming. The market participants considered by the model are pipeline operators, producers, storage operators, peak gas operators, marketers and consumers. Pipeline operators are described with regulated tariffs but also involve "congestion pricing" as a mechanism to allocate scarce pipeline capacity. Marketers are modeled as Nash-Cournot players in sales to the residential and commercial sectors but price-takers in all other aspects. Consumers are represented by demand functions in the marketers' problem. Producers, storage operators and peak gas operators are price-takers consistent with perfect competition. Also, two types of the natural gas markets are included: the long-term and spot markets. Market participants make both high-level planning decisions (first-stage decisions) in the long-term market and daily operational decisions (recourse decisions) in the spot market subject to their engineering, resource and political constraints, resource constraints as well as market constraints on both the demand and the supply side, so as to simultaneously maximize their expected profits given others' decisions. The model is shown to be an instance of a mixed complementarity problem (MiCP) under minor conditions. The MiCP formulation is derived from applying the Karush-Kuhn-Tucker optimality conditions of the optimization problems faced by the market participants. Some theoretical results regarding the market prices in both markets are shown. We also illustrate the model on a representative, sample network of two production nodes, two consumption nodes with discretely distributed end-user demand and three seasons using four cases.

Systems biology and the origins of life? part II. Are biochemical networks possible ancestors of living systems? networks of catalysed chemical reactions: non-equilibrium, self-organization and evolution.

PubMed

Ricard, Jacques

2010-01-01

The present article discusses the possibility that catalysed chemical networks can evolve. Even simple enzyme-catalysed chemical reactions can display this property. The example studied is that of a two-substrate proteinoid, or enzyme, reaction displaying random binding of its substrates A and B. The fundamental property of such a system is to display either emergence or integration depending on the respective values of the probabilities that the enzyme has bound one of its substrate regardless it has bound the other substrate, or, specifically, after it has bound the other substrate. There is emergence of information if p(A)>p(AB) and p(B)>p(BA). Conversely, if p(A)

Stochastic cycle selection in active flow networks

NASA Astrophysics Data System (ADS)

Woodhouse, Francis; Forrow, Aden; Fawcett, Joanna; Dunkel, Jorn

2016-11-01

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. By connecting concepts from lattice field theory, graph theory and transition rate theory, we show how topology controls dynamics in a generic model for actively driven flow on a network. Through theoretical and numerical analysis we identify symmetry-based rules to classify and predict the selection statistics of complex flow cycles from the network topology. Our conceptual framework is applicable to a broad class of biological and non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models.

Equilibrium problems for Raney densities

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng; Zinn-Justin, Paul

2015-07-01

The Raney numbers are a class of combinatorial numbers generalising the Fuss-Catalan numbers. They are indexed by a pair of positive real numbers (p, r) with p > 1 and 0 < r ⩽ p, and form the moments of a probability density function. For certain (p, r) the latter has the interpretation as the density of squared singular values for certain random matrix ensembles, and in this context equilibrium problems characterising the Raney densities for (p, r) = (θ + 1, 1) and (θ/2 + 1, 1/2) have recently been proposed. Using two different techniques—one based on the Wiener-Hopf method for the solution of integral equations and the other on an analysis of the algebraic equation satisfied by the Green's function—we establish the validity of the equilibrium problems for general θ > 0 and similarly use both methods to identify the equilibrium problem for (p, r) = (θ/q + 1, 1/q), θ > 0 and q \\in Z+ . The Wiener-Hopf method is used to extend the latter to parameters (p, r) = (θ/q + 1, m + 1/q) for m a non-negative integer, and also to identify the equilibrium problem for a family of densities with moments given by certain binomial coefficients.

Optimizing congestion and emissions via tradable credit charge and reward scheme without initial credit allocations

NASA Astrophysics Data System (ADS)

Zhu, Wenlong; Ma, Shoufeng; Tian, Junfang

2017-01-01

This paper investigates the revenue-neutral tradable credit charge and reward scheme without initial credit allocations that can reassign network traffic flow patterns to optimize congestion and emissions. First, we prove the existence of the proposed schemes and further decentralize the minimum emission flow pattern to user equilibrium. Moreover, we design the solving method of the proposed credit scheme for minimum emission problem. Second, we investigate the revenue-neutral tradable credit charge and reward scheme without initial credit allocations for bi-objectives to obtain the Pareto system optimum flow patterns of congestion and emissions; and present the corresponding solutions are located in the polyhedron constituted by some inequalities and equalities system. Last, numerical example based on a simple traffic network is adopted to obtain the proposed credit schemes and verify they are revenue-neutral.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

PubMed

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

PubMed

Liang, X B; Wang, J

2000-01-01

This paper presents a continuous-time recurrent neural-network model for nonlinear optimization with any continuously differentiable objective function and bound constraints. Quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network. The proposed recurrent neural network has the following characteristics. 1) It is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network. If the objective function to be minimized is convex, then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network. 2) The recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region. 3) The recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region. 4) For minimizing any strictly convex quadratic objective function subject to bound constraints, the recurrent neural network is globally exponentially stable for almost any positive network parameters. Simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints.

Comment on "Out-of-plane equilibrium points in the restricted three-body problem with oblateness (Research Note)"

NASA Astrophysics Data System (ADS)

Wu, Nan; Wang, Xuefeng; Zhou, Li-Yong

2018-06-01

Douskos & Markellos (2006, A&A, 446, 357) first reported the existence of the out-of-plane equilibrium points in restricted three-body problem with oblateness. This result deviates significantly from the intuitive physical point of view that there is no other force that can balance the combined gravitation in Z direction. In fact, the out-of-plane equilibrium in that model is illusory and we prove here that such equilibrium points arise from the improper application of the potential function.

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

Mahault, Benoit Alexandre; Saxena, Avadh Behari; Nisoli, Cristiano

We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in the problem of wealth distribution, concentration, and inequality. This framework allows us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from, or lose wealth to, anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity, onlymore » minimally ameliorated by disorder in a non-optimized society. The picture is however dramatically modified when hard constraints are imposed over agents, and they are forced to share wealth with neighbors on a network. We discuss the case of random networks and scale free networks. We then propose an out of equilibrium dynamics of the networks, based on a competition of power and frustration in the decision-making of agents that leads to network evolution. We show that the ratio of power and frustration controls different dynamical regimes separated by kinetic transition and characterized by drastically different values of the indices of equality.« less

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Sitnikov cyclic configuration of N+1-body problem

NASA Astrophysics Data System (ADS)

Shahbaz Ullah, M.; Hassan, M. R.

2014-12-01

This manuscript deals with the generalisation of all previous works on series solutions and linear stability of equilibrium points of the Sitnikov problem. Following Giacaglia (1967), in Sect. 2 we have derived the equation of motion of the infinitesimal mass moving along the z-axis about which the plane of motion is rotating with unit angular velocity. In Sects. 3, 4 and 5 the series solutions of the Sitnikov problem have been developed by the method of MacMillan, Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the three series solutions have been compared graphically by putting N=2, 3, 4. In Sect. 7 the coordinates of equilibrium points have been calculated. In Sect. 8 the linear stability of equilibrium points has been examined by the method of Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) and it was found that the equilibrium points are stable in Sitnikov problem.

Conflict and convention in dynamic networks.

PubMed

Foley, Michael; Forber, Patrick; Smead, Rory; Riedl, Christoph

2018-03-01

An important way to resolve games of conflict (snowdrift, hawk-dove, chicken) involves adopting a convention: a correlated equilibrium that avoids any conflict between aggressive strategies. Dynamic networks allow individuals to resolve conflict via their network connections rather than changing their strategy. Exploring how behavioural strategies coevolve with social networks reveals new dynamics that can help explain the origins and robustness of conventions. Here, we model the emergence of conventions as correlated equilibria in dynamic networks. Our results show that networks have the tendency to break the symmetry between the two conventional solutions in a strongly biased way. Rather than the correlated equilibrium associated with ownership norms (play aggressive at home, not away), we usually see the opposite host-guest norm (play aggressive away, not at home) evolve on dynamic networks, a phenomenon common to human interaction. We also show that learning to avoid conflict can produce realistic network structures in a way different than preferential attachment models. © 2017 The Author(s).

Evaporation in Capillary Porous Media at the Perfect Piston-Like Invasion Limit: Evidence of Nonlocal Equilibrium Effects

NASA Astrophysics Data System (ADS)

Attari Moghaddam, Alireza; Prat, Marc; Tsotsas, Evangelos; Kharaghani, Abdolreza

2017-12-01

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure-saturation relationship classically introduced to obtain the one-equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two-equation model must be considered for improving the continuum modeling of evaporation.

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots.

PubMed

Hess, H; Ross, Jennifer L

2017-09-18

Biological systems have evolved to harness non-equilibrium processes from the molecular to the macro scale. It is currently a grand challenge of chemistry, materials science, and engineering to understand and mimic biological systems that have the ability to autonomously sense stimuli, process these inputs, and respond by performing mechanical work. New chemical systems are responding to the challenge and form the basis for future responsive, adaptive, and active materials. In this article, we describe a particular biochemical-biomechanical network based on the microtubule cytoskeletal filament - itself a non-equilibrium chemical system. We trace the non-equilibrium aspects of the system from molecules to networks and describe how the cell uses this system to perform active work in essential processes. Finally, we discuss how microtubule-based engineered systems can serve as testbeds for autonomous chemical robots composed of biological and synthetic components.

Teaching an Old Dog an Old Trick: FREE-FIX and Free-Boundary Axisymmetric MHD Equilibrium

NASA Astrophysics Data System (ADS)

Guazzotto, Luca

2015-11-01

A common task in plasma physics research is the calculation of an axisymmetric equilibrium for tokamak modeling. The main unknown of the problem is the magnetic poloidal flux ψ. The easiest approach is to assign the shape of the plasma and only solve the equilibrium problem in the plasma / closed-field-lines region (the ``fixed-boundary approach''). Often, one may also need the vacuum fields, i.e. the equilibrium in the open-field-lines region, requiring either coil currents or ψ on some closed curve outside the plasma to be assigned (the ``free-boundary approach''). Going from one approach to the other is a textbook problem, involving the calculation of Green's functions and surface integrals in the plasma. However, no tools are readily available to perform this task. Here we present a code (FREE-FIX) to compute a boundary condition for a free-boundary equilibrium given only the corresponding fixed-boundary equilibrium. An improvement to the standard solution method, allowing for much faster calculations, is presented. Applications are discussed. PPPL fund 245139 and DOE grant G00009102.

Unveiling the molecular mechanism of self-healing in a telechelic, supramolecular polymer network

PubMed Central

Yan, Tingzi; Schröter, Klaus; Herbst, Florian; Binder, Wolfgang H.; Thurn-Albrecht, Thomas

2016-01-01

Reversible polymeric networks can show self-healing properties due to their ability to reassemble after application of stress and fracture, but typically the relation between equilibrium molecular dynamics and self-healing kinetics has been difficult to disentangle. Here we present a well-characterized, self-assembled bulk network based on supramolecular assemblies, that allows a clear distinction between chain dynamics and network relaxation. Small angle x-ray scattering and rheological measurements provide evidence for a structurally well-defined, dense network of interconnected aggregates giving mechanical strength to the material. Different from a covalent network, the dynamic character of the supramolecular bonds enables macroscopic flow on a longer time scale and the establishment of an equilibrium structure. A combination of linear and nonlinear rheological measurements clearly identifies the terminal relaxation process as being responsible for the process of self-healing. PMID:27581380

Modelling inter-supply chain competition with resource limitation and demand disruption

NASA Astrophysics Data System (ADS)

Chen, Zhaobo; Teng, Chunxian; Zhang, Ding; Sun, Jiayi

2016-05-01

This paper proposes a comprehensive model for studying supply chain versus supply chain competition with resource limitation and demand disruption. We assume that there are supply chains with heterogeneous supply network structures that compete at multiple demand markets. Each supply chain is comprised of internal and external firms. The internal firms are coordinated in production and distribution and share some common but limited resources within the supply chain, whereas the external firms are independent and do not share the internal resources. The supply chain managers strive to develop optimal strategies in terms of production level and resource allocation in maximising their profit while facing competition at the end market. The Cournot-Nash equilibrium of this inter-supply chain competition is formulated as a variational inequality problem. We further study the case when there is demand disruption in the plan-execution phase. In such a case, the managers need to revise their planned strategy in order to maximise their profit with the new demand under disruption and minimise the cost of change. We present a bi-criteria decision-making model for supply chain managers and develop the optimal conditions in equilibrium, which again can be formulated by another variational inequality problem. Numerical examples are presented for illustrative purpose.

Spreading dynamics of an e-commerce preferential information model on scale-free networks

NASA Astrophysics Data System (ADS)

Wan, Chen; Li, Tao; Guan, Zhi-Hong; Wang, Yuanmei; Liu, Xiongding

2017-02-01

In order to study the influence of the preferential degree and the heterogeneity of underlying networks on the spread of preferential e-commerce information, we propose a novel susceptible-infected-beneficial model based on scale-free networks. The spreading dynamics of the preferential information are analyzed in detail using the mean-field theory. We determine the basic reproductive number and equilibria. The theoretical analysis indicates that the basic reproductive number depends mainly on the preferential degree and the topology of the underlying networks. We prove the global stability of the information-elimination equilibrium. The permanence of preferential information and the global attractivity of the information-prevailing equilibrium are also studied in detail. Some numerical simulations are presented to verify the theoretical results.

A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks.

PubMed

Faydasicok, Ozlem; Arik, Sabri

2013-08-01

The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition. Copyright © 2013 Elsevier Ltd. All rights reserved.

Non-equilibrium electrokinetic micromixer with 3D nanochannel networks.

PubMed

Choi, Eunpyo; Kwon, Kilsung; Lee, Seung Jun; Kim, Daejoong; Park, Jungyul

2015-04-21

We report an active micromixer which utilizes vortex generation due to non-equilibrium electrokinetics near the interface between a microchannnel and a nanochannel networks membrane (NCNM), constructed from geometrically controlled in situ self-assembled nanoparticles. A large interfacing area where it is possible to generate vortices can be realized, because nano-interstices between the assembled nanoparticles are intrinsically collective three-dimensional nanochannel networks, which may be compared to typical silicon-based 2D nanochannels. The proposed mixer shows a 2-fold shorter mixing time (~0.78 ms) and a 34-fold shorter mixing length (~7.86 μm) compared to conventional 2D nanochannels.

The physics of complex systems in information and biology

NASA Astrophysics Data System (ADS)

Walker, Dylan

Citation networks have re-emerged as a topic intense interest in the complex networks community with the recent availability of large-scale data sets. The ranking of citation networks is a necessary practice as a means to improve information navigability and search. Unlike many information networks, the aging characteristics of citation networks require the development of new ranking methods. To account for strong aging characteristics of citation networks, we modify the PageRank algorithm by initially distributing random surfers exponentially with age, in favor of more recent publications. The output of this algorithm, which we call CiteRank, is interpreted as approximate traffic to individual publications in a simple model of how researchers find new information. We optimize parameters of our algorithm to achieve the best performance. The results are compared for two rather different citation networks: all American Physical Society publications between 1893-2003 and the set of high-energy physics theory (hep-th) preprints. Despite major differences between these two networks, we find that their optimal parameters for the CiteRank algorithm are remarkably similar. The advantages and performance of CiteRank over more conventional methods of ranking publications are discussed. Collaborative voting systems have emerged as an abundant form of real-world, complex information systems that exist in a variety of online applications. These systems are comprised of large populations of users that collectively submit and vote on objects. While the specific properties of these systems vary widely, many of them share a core set of features and dynamical behaviors that govern their evolution. We study a subset of these systems that involve material of a time-critical nature as in the popular example of news items. We consider a general model system in which articles are introduced, voted on by a population of users, and subsequently expire after a proscribed period of time. To study the interaction between popularity and quality, we introduce simple stochastic models of user behavior that approximate differing user quality and susceptibility to the common notion of popularity. We define a metric to quantify user reputation in a manner that is self-consistent, adaptable and content-blind and shows good correlation with the probability that a user behaves in an optimal fashion. We further construct a mechanism for ranking documents that take into account user reputation and provides substantial improvement in the time-critical performance of the system. The structure of complex systems have been well studied in the context of both information and biological systems. More recently, dynamics in complex systems that occur over the background of the underlying network has received a great deal of attention. In particular, the study of fluctuations in complex systems has emerged as an issue central to understanding dynamical behavior. We approach the problem of collective effects of the underlying network on dynamical fluctuations by considering the protein-protein interaction networks for the system of the living cell. We consider two types of fluctuations in the mass-action equilibrium in protein binding networks. The first type is driven by relatively slow changes in total concentrations (copy numbers) of interacting proteins. The second type, to which we refer to as spontaneous, is caused by quickly decaying thermodynamic deviations away from the mass-action equilibrium of the system. As such they are amenable to methods of equilibrium statistical mechanics used in our study. We investigate the effects of network connectivity on these fluctuations by comparing them to different scenarios in which the interacting pair is isolated form the rest of the network. Such comparison allows us to analytically derive upper and lower bounds on network fluctuations. The collective effects are shown to sometimes lead to relatively large amplification of spontaneous fluctuations as compared to the expectation for isolated dimers. As a consequence of this, the strength of both types of fluctuations is positively correlated with the overall network connectivity of proteins forming the complex. On the other hand, the relative amplitude of fluctuations is negatively correlated with the equilibrium concentration of the complex. Our general findings are illustrated using a curated network of protein-protein interactions and multi-protein complexes in bakers yeast with experimentally determined protein concentrations.

Minimizing the Free Energy: A Computer Method for Teaching Chemical Equilibrium Concepts.

ERIC Educational Resources Information Center

Heald, Emerson F.

1978-01-01

Presents a computer method for teaching chemical equilibrium concepts using material balance conditions and the minimization of the free energy. Method for the calculation of chemical equilibrium, the computer program used to solve equilibrium problems and applications of the method are also included. (HM)

Specific non-monotonous interactions increase persistence of ecological networks.

PubMed

Yan, Chuan; Zhang, Zhibin

2014-03-22

The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.

Identifying protein complexes in PPI network using non-cooperative sequential game.

PubMed

Maulik, Ujjwal; Basu, Srinka; Ray, Sumanta

2017-08-21

Identifying protein complexes from protein-protein interaction (PPI) network is an important and challenging task in computational biology as it helps in better understanding of cellular mechanisms in various organisms. In this paper we propose a noncooperative sequential game based model for protein complex detection from PPI network. The key hypothesis is that protein complex formation is driven by mechanism that eventually optimizes the number of interactions within the complex leading to dense subgraph. The hypothesis is drawn from the observed network property named small world. The proposed multi-player game model translates the hypothesis into the game strategies. The Nash equilibrium of the game corresponds to a network partition where each protein either belong to a complex or form a singleton cluster. We further propose an algorithm to find the Nash equilibrium of the sequential game. The exhaustive experiment on synthetic benchmark and real life yeast networks evaluates the structural as well as biological significance of the network partitions.

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Halford, Gary R.

2004-01-01

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Distributed Power Allocation for Wireless Sensor Network Localization: A Potential Game Approach.

PubMed

Ke, Mingxing; Li, Ding; Tian, Shiwei; Zhang, Yuli; Tong, Kaixiang; Xu, Yuhua

2018-05-08

The problem of distributed power allocation in wireless sensor network (WSN) localization systems is investigated in this paper, using the game theoretic approach. Existing research focuses on the minimization of the localization errors of individual agent nodes over all anchor nodes subject to power budgets. When the service area and the distribution of target nodes are considered, finding the optimal trade-off between localization accuracy and power consumption is a new critical task. To cope with this issue, we propose a power allocation game where each anchor node minimizes the square position error bound (SPEB) of the service area penalized by its individual power. Meanwhile, it is proven that the power allocation game is an exact potential game which has one pure Nash equilibrium (NE) at least. In addition, we also prove the existence of an ϵ -equilibrium point, which is a refinement of NE and the better response dynamic approach can reach the end solution. Analytical and simulation results demonstrate that: (i) when prior distribution information is available, the proposed strategies have better localization accuracy than the uniform strategies; (ii) when prior distribution information is unknown, the performance of the proposed strategies outperforms power management strategies based on the second-order cone program (SOCP) for particular agent nodes after obtaining the estimated distribution of agent nodes. In addition, proposed strategies also provide an instructional trade-off between power consumption and localization accuracy.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

NASA Astrophysics Data System (ADS)

Zhao, Hongyong; Zhu, Linhe

2016-06-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

The value of less connected agents in Boolean networks

NASA Astrophysics Data System (ADS)

Epstein, Daniel; Bazzan, Ana L. C.

2013-11-01

In multiagent systems, agents often face binary decisions where one seeks to take either the minority or the majority side. Examples are minority and congestion games in general, i.e., situations that require coordination among the agents in order to depict efficient decisions. In minority games such as the El Farol Bar Problem, previous works have shown that agents may reach appropriate levels of coordination, mostly by looking at the history of past decisions. Not many works consider any kind of structure of the social network, i.e., how agents are connected. Moreover, when structure is indeed considered, it assumes some kind of random network with a given, fixed connectivity degree. The present paper departs from the conventional approach in some ways. First, it considers more realistic network topologies, based on preferential attachments. This is especially useful in social networks. Second, the formalism of random Boolean networks is used to help agents to make decisions given their attachments (for example acquaintances). This is coupled with a reinforcement learning mechanism that allows agents to select strategies that are locally and globally efficient. Third, we use agent-based modeling and simulation, a microscopic approach, which allows us to draw conclusions about individuals and/or classes of individuals. Finally, for the sake of illustration we use two different scenarios, namely the El Farol Bar Problem and a binary route choice scenario. With this approach we target systems that adapt dynamically to changes in the environment, including other adaptive decision-makers. Our results using preferential attachments and random Boolean networks are threefold. First we show that an efficient equilibrium can be achieved, provided agents do experimentation. Second, microscopic analysis show that influential agents tend to consider few inputs in their Boolean functions. Third, we have also conducted measurements related to network clustering and centrality that help to see how agents are organized.

Qualitative analysis of Cohen-Grossberg neural networks with multiple delays

NASA Astrophysics Data System (ADS)

Ye, Hui; Michel, Anthony N.; Wang, Kaining

1995-03-01

It is well known that a class of artificial neural networks with symmetric interconnections and without transmission delays, known as Cohen-Grossberg neural networks, possesses global stability (i.e., all trajectories tend to some equilibrium). We demonstrate in the present paper that many of the qualitative properties of Cohen-Grossberg networks will not be affected by the introduction of sufficiently small delays. Specifically, we establish some bound conditions for the time delays under which a given Cohen-Grossberg network with multiple delays is globally stable and possesses the same asymptotically stable equilibria as the corresponding network without delays. An effective method of determining the asymptotic stability of an equilibrium of a Cohen-Grossberg network with multiple delays is also presented. The present results are motivated by some of the authors earlier work [Phys. Rev. E 50, 4206 (1994)] and by some of the work of Marcus and Westervelt [Phys. Rev. A 39, 347 (1989)]. These works address qualitative analyses of Hopfield neural networks with one time delay. The present work generalizes these results to Cohen-Grossberg neural networks with multiple time delays. Hopfield neural networks constitute special cases of Cohen-Grossberg neural networks.

Students' and Teachers' Misapplication of Le Chatelier's Principle: Implications for the Teaching of Chemical Equilibrium.

ERIC Educational Resources Information Center

Quilez-Pardo, Juan; Solaz-Portoles, Joan Josep

1995-01-01

Study of strategies and procedures of 170 students and 40 teachers when solving chemical equilibrium problems found misconceptions emerging through: misapplication of Le Chatelier's Principle, use of rote-learning recall, incorrect control of variables, limited use of chemical equilibrium law, lack of mastery of chemical equilibrium principles,…

Simplification of reversible Markov chains by removal of states with low equilibrium occupancy.

PubMed

Ullah, Ghanim; Bruno, William J; Pearson, John E

2012-10-21

We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentration. Copyright © 2012 Elsevier Ltd. All rights reserved.

Network-optimized congestion pricing : a parable, model and algorithm

DOT National Transportation Integrated Search

1995-05-31

This paper recites a parable, formulates a model and devises an algorithm for optimizing tolls on a road network. Such tolls induce an equilibrium traffic flow that is at once system-optimal and user-optimal. The parable introduces the network-wide c...

Oligopolistic competition in wholesale electricity markets: Large-scale simulation and policy analysis using complementarity models

NASA Astrophysics Data System (ADS)

Helman, E. Udi

This dissertation conducts research into the large-scale simulation of oligopolistic competition in wholesale electricity markets. The dissertation has two parts. Part I is an examination of the structure and properties of several spatial, or network, equilibrium models of oligopolistic electricity markets formulated as mixed linear complementarity problems (LCP). Part II is a large-scale application of such models to the electricity system that encompasses most of the United States east of the Rocky Mountains, the Eastern Interconnection. Part I consists of Chapters 1 to 6. The models developed in this part continue research into mixed LCP models of oligopolistic electricity markets initiated by Hobbs [67] and subsequently developed by Metzler [87] and Metzler, Hobbs and Pang [88]. Hobbs' central contribution is a network market model with Cournot competition in generation and a price-taking spatial arbitrage firm that eliminates spatial price discrimination by the Cournot firms. In one variant, the solution to this model is shown to be equivalent to the "no arbitrage" condition in a "pool" market, in which a Regional Transmission Operator optimizes spot sales such that the congestion price between two locations is exactly equivalent to the difference in the energy prices at those locations (commonly known as locational marginal pricing). Extensions to this model are presented in Chapters 5 and 6. One of these is a market model with a profit-maximizing arbitrage firm. This model is structured as a mathematical program with equilibrium constraints (MPEC), but due to the linearity of its constraints, can be solved as a mixed LCP. Part II consists of Chapters 7 to 12. The core of these chapters is a large-scale simulation of the U.S. Eastern Interconnection applying one of the Cournot competition with arbitrage models. This is the first oligopolistic equilibrium market model to encompass the full Eastern Interconnection with a realistic network representation (using a DC load flow approximation). Chapter 9 shows the price results. In contrast to prior market power simulations of these markets, much greater variability in price-cost margins is found when using a realistic model of hourly conditions on such a large network. Chapter 10 shows that the conventional concentration indices (HHIs) are poorly correlated with PCMs. Finally, Chapter 11 proposes that the simulation models are applied to merger analysis and provides two large-scale merger examples. (Abstract shortened by UMI.)

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions.

PubMed

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B

2007-06-16

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.

Self-Learning Power Control in Wireless Sensor Networks.

PubMed

Chincoli, Michele; Liotta, Antonio

2018-01-27

Current trends in interconnecting myriad smart objects to monetize on Internet of Things applications have led to high-density communications in wireless sensor networks. This aggravates the already over-congested unlicensed radio bands, calling for new mechanisms to improve spectrum management and energy efficiency, such as transmission power control. Existing protocols are based on simplistic heuristics that often approach interference problems (i.e., packet loss, delay and energy waste) by increasing power, leading to detrimental results. The scope of this work is to investigate how machine learning may be used to bring wireless nodes to the lowest possible transmission power level and, in turn, to respect the quality requirements of the overall network. Lowering transmission power has benefits in terms of both energy consumption and interference. We propose a protocol of transmission power control through a reinforcement learning process that we have set in a multi-agent system. The agents are independent learners using the same exploration strategy and reward structure, leading to an overall cooperative network. The simulation results show that the system converges to an equilibrium where each node transmits at the minimum power while respecting high packet reception ratio constraints. Consequently, the system benefits from low energy consumption and packet delay.

Self-Learning Power Control in Wireless Sensor Networks

PubMed Central

Liotta, Antonio

2018-01-01

Current trends in interconnecting myriad smart objects to monetize on Internet of Things applications have led to high-density communications in wireless sensor networks. This aggravates the already over-congested unlicensed radio bands, calling for new mechanisms to improve spectrum management and energy efficiency, such as transmission power control. Existing protocols are based on simplistic heuristics that often approach interference problems (i.e., packet loss, delay and energy waste) by increasing power, leading to detrimental results. The scope of this work is to investigate how machine learning may be used to bring wireless nodes to the lowest possible transmission power level and, in turn, to respect the quality requirements of the overall network. Lowering transmission power has benefits in terms of both energy consumption and interference. We propose a protocol of transmission power control through a reinforcement learning process that we have set in a multi-agent system. The agents are independent learners using the same exploration strategy and reward structure, leading to an overall cooperative network. The simulation results show that the system converges to an equilibrium where each node transmits at the minimum power while respecting high packet reception ratio constraints. Consequently, the system benefits from low energy consumption and packet delay. PMID:29382072

Modeling, analysis, and simulation of the co-development of road networks and vehicle ownership

NASA Astrophysics Data System (ADS)

Xu, Mingtao; Ye, Zhirui; Shan, Xiaofeng

2016-01-01

A two-dimensional logistic model is proposed to describe the co-development of road networks and vehicle ownership. The endogenous interaction between road networks and vehicle ownership and how natural market forces and policies transformed into their co-development are considered jointly in this model. If the involved parameters satisfy a certain condition, the proposed model can arrive at a steady equilibrium level and the final development scale will be within the maximum capacity of an urban traffic system; otherwise, the co-development process will be unstable and even manifest chaotic behavior. Then sensitivity tests are developed to determine the proper values for a series of parameters in this model. Finally, a case study, using Beijing City as an example, is conducted to explore the applicability of the proposed model to the real condition. Results demonstrate that the proposed model can effectively simulate the co-development of road network and vehicle ownership for Beijing City. Furthermore, we can obtain that their development process will arrive at a stable equilibrium level in the years 2040 and 2045 respectively, and the equilibrium values are within the maximum capacity.

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

NASA Astrophysics Data System (ADS)

Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea

2016-10-01

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables {w_{ij}} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.

Congestion patterns of electric vehicles with limited battery capacity.

PubMed

Jing, Wentao; Ramezani, Mohsen; An, Kun; Kim, Inhi

2018-01-01

The path choice behavior of battery electric vehicle (BEV) drivers is influenced by the lack of public charging stations, limited battery capacity, range anxiety and long battery charging time. This paper investigates the congestion/flow pattern captured by stochastic user equilibrium (SUE) traffic assignment problem in transportation networks with BEVs, where the BEV paths are restricted by their battery capacities. The BEV energy consumption is assumed to be a linear function of path length and path travel time, which addresses both path distance limit problem and road congestion effect. A mathematical programming model is proposed for the path-based SUE traffic assignment where the path cost is the sum of the corresponding link costs and a path specific out-of-energy penalty. We then apply the convergent Lagrangian dual method to transform the original problem into a concave maximization problem and develop a customized gradient projection algorithm to solve it. A column generation procedure is incorporated to generate the path set. Finally, two numerical examples are presented to demonstrate the applicability of the proposed model and the solution algorithm.

Congestion patterns of electric vehicles with limited battery capacity

PubMed Central

2018-01-01

The path choice behavior of battery electric vehicle (BEV) drivers is influenced by the lack of public charging stations, limited battery capacity, range anxiety and long battery charging time. This paper investigates the congestion/flow pattern captured by stochastic user equilibrium (SUE) traffic assignment problem in transportation networks with BEVs, where the BEV paths are restricted by their battery capacities. The BEV energy consumption is assumed to be a linear function of path length and path travel time, which addresses both path distance limit problem and road congestion effect. A mathematical programming model is proposed for the path-based SUE traffic assignment where the path cost is the sum of the corresponding link costs and a path specific out-of-energy penalty. We then apply the convergent Lagrangian dual method to transform the original problem into a concave maximization problem and develop a customized gradient projection algorithm to solve it. A column generation procedure is incorporated to generate the path set. Finally, two numerical examples are presented to demonstrate the applicability of the proposed model and the solution algorithm. PMID:29543875

Perspective: Maximum caliber is a general variational principle for dynamical systems

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

2018-01-01

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

PubMed

Dixit, Purushottam D; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A

2018-01-07

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Predator-prey-subsidy population dynamics on stepping-stone domains.

PubMed

Shen, Lulan; Van Gorder, Robert A

2017-05-07

Predator-prey-subsidy dynamics on stepping-stone domains are examined using a variety of network configurations. Our problem is motivated by the interactions between arctic foxes (predator) and lemmings (prey) in the presence of seal carrion (subsidy) provided by polar bears. We use the n-Patch Model, which considers space explicitly as a "Stepping Stone" system. We consider the role that the carrying capacity, predator migration rate, input subsidy rate, predator mortality rate, and proportion of predators surviving migration play in the predator-prey-subsidy population dynamics. We find that for certain types of networks, added mobility will help predator populations, allowing them to survive or coexist when they would otherwise go extinct if confined to one location, while in other situations (such as when sparsely distributed nodes in the network have few resources available) the added mobility will hurt the predator population. We also find that a combination of favourable conditions for the prey and subsidy can lead to the formation of limit cycles (boom and bust dynamic) from stable equilibrium states. These modifications to the dynamics vary depending on the specific network structure employed, highlighting the fact that network structure can strongly influence the predator-prey-subsidy dynamics in stepping-stone domains. Copyright © 2017 Elsevier Ltd. All rights reserved.

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

DOE PAGES

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

2018-04-27

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

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

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Calculating and Visualizing Thermodynamic Equilibrium: A Tutorial on the Isolated System with an Internal Adiabatic Piston

ERIC Educational Resources Information Center

Ferreira, Joao Paulo M.

2007-01-01

The problem of the equilibrium state of an isolated composite system with a movable internal adiabatic wall is a recurrent one in the literature. Classical equilibrium thermodynamics is unable to predict the equilibrium state, unless supplemented with information about the process taking place. This conclusion is clearly demonstrated in this…

Students' and teachers' misapplication of le chatelier's principle: Implications for the teaching of chemical equilibrium

NASA Astrophysics Data System (ADS)

Quílez-Pardo, Juan; Solaz-Portolés, Joan Josep

The aim of this article was to study the reasons, strategies, and procedures that both students and teachers use to solve some chemical equilibrium questions and problems. Inappropriate conceptions on teaching and a lack of knowledge regarding the limited usefulness of Le Chatelier's principle, with its vague and ambiguous formulation and textbook presentation, may be some of the sources of misconceptions about the prediction of the effect of changing conditions on chemical equilibrium. To diagnose misconceptions and their possible sources, a written test was developed and administered to 170 1st-year university chemistry students. A chemical equilibrium problem, relating to the students' test, was solved by 40 chemistry teachers. First, we ascertained that teacher's conceptions might influence the problem-solving strategies of the learner. Based on this first aspect, our discussion also concerns students' and teachers' misconceptions related to the Le Chatelier's principle. Misconceptions emerged through: (a) misapplication and misunderstanding of Le Chatelier's principle; (b) use of rote-learning recall and algorithmic procedures; (c) incorrect control of the variables involved; (d) limited use of the chemical equilibrium law; (e) a lack of mastery of chemical equilibrium principles and difficulty in transferring such principles to new situations. To avoid chemical equilibrium misconceptions, a specific pattern of conceptual and methodological change may be considered.Received: 16 November 1993; Revised: 21 September 1994;

Equilibrium & Nonequilibrium Fluctuation Effects in Biopolymer Networks

NASA Astrophysics Data System (ADS)

Kachan, Devin Michael

Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. In this dissertation, I explore the role of both thermal and active fluctuations within cross-linked polymer networks. The systems I study are in large part inspired by the amazing physics found within the cytoskeleton of eukaryotic cells. I first predict and verify the existence of a thermal Casimir force between cross-linkers bound to a semi-flexible polymer. The calculation is complicated by the appearance of second order derivatives in the bending Hamiltonian for such polymers, which requires a careful evaluation of the the path integral formulation of the partition function in order to arrive at the physically correct continuum limit and properly address ultraviolet divergences. I find that cross linkers interact along a filament with an attractive logarithmic potential proportional to thermal energy. The proportionality constant depends on whether and how the cross linkers constrain the relative angle between the two filaments to which they are bound. The interaction has important implications for the synthesis of biopolymer bundles within cells. I model the cross-linkers as existing in two phases: bound to the bundle and free in solution. When the cross-linkers are bound, they behave as a one-dimensional gas of particles interacting with the Casimir force, while the free phase is a simple ideal gas. Demanding equilibrium between the two phases, I find a discontinuous transition between a sparsely and a densely bound bundle. This discontinuous condensation transition induced by the long-ranged nature of the Casimir interaction allows for a similarly abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase and a higher cross link density bundle network. This work is supported by the results of finite element Brownian dynamics simulations of semiflexible filaments and transient cross-linkers. I speculate that cells take advantage of this equilibrium effect by tuning near the transition point, where small changes in free cross-linker density will affect large structural rearrangements between free filament networks and networks of bundles. Cells are naturally found far from equilibrium, where the active influx of energy from ATP consumption controls the dynamics. Motor proteins actively generate forces within biopolymer networks, and one may ask how these differ from the random stresses characteristic of equilibrium fluctuations. Besides the trivial observation that the magnitude is independent of temperature, I find that the processive nature of the motors creates a temporally correlated, or colored, noise spectrum. I model the network with a nonlinear scalar elastic theory in the presence of active driving, and study the long distance and large scale properties of the system with renormalization group techniques. I find that there is a new critical point associated with diverging correlation time, and that the colored noise produces novel frequency dependence in the renormalized transport coefficients. Finally, I study marginally elastic solids which have vanishing shear modulus due to the presence of soft modes, modes with zero deformation cost. Although network coordination is a useful metric for determining the mechanical response of random spring networks in mechanical equilibrium, it is insufficient for describing networks under external stress. In particular, under-constrained networks which are fluid-like at zero load will dynamically stiffen at a critical strain, as observed in numerical simulations and experimentally in many biopolymer networks. Drawing upon analogies to the stress induced unjamming of emulsions, I develop a kinetic theory to explain the rigidity transition in spring and filament networks. Describing the dynamic evolution of non-affine deformation via a simple mechanistic picture, I recover the emergent nonlinear strain-stiffening behavior and compare this behavior to the yield stress flow seen in soft glassy fluids. I extend this theory to account for coordination number inhomogeneities and predict a breakdown of universal scaling near the critical point at sufficiently high disorder, and discuss the utility for this type of model in describing biopolymer networks.

Control of stochastic sensitivity in a stabilization problem for gas discharge system

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

Bashkirtseva, Irina

2015-11-30

We consider a nonlinear dynamic stochastic system with control. A problem of stochastic sensitivity synthesis of the equilibrium is studied. A mathematical technique of the solution of this problem is discussed. This technique is applied to the problem of the stabilization of the operating mode for the stochastic gas discharge system. We construct a feedback regulator that reduces the stochastic sensitivity of the equilibrium, suppresses large-amplitude oscillations, and provides a proper operation of this engineering device.

Why are so many networks disassortative?

NASA Astrophysics Data System (ADS)

Johnson, Samuel; Torres, Joaquín J.; Marro, J.; Muñoz, Miguel A.

2011-03-01

A wide range of empirical networks—whether biological, technological, information-related or linguistic—generically exhibit important degree-degree anticorrelations (i.e., they are disassortative), the only exceptions being social ones, which tend to be positively correlated (assortative). Using an information-theory approach, we show that the equilibrium state of highly heterogeneous (scale-free) random networks is disassortative. This not only gives a parsimonious explanation to a long-standing question, but also provides a neutral model against which to compare experimental data and ascertain whether a given system is being driven from equilibrium by correlating mechanisms.

Tidal Amplitude Delta Factors and Phase Shifts for an Oceanic Earth

NASA Astrophysics Data System (ADS)

Spiridonov, E. A.

2017-12-01

M.S. Molodenskiy's problem, which describes the state of an elastic self-gravitating compressible sphere, is generalized to the case of a biaxial hydrostatically equilibrium rotating elliptical inelastic shell. The system of sixth-order equations is supplemented with corrections due to the relative and Coriolis accelerations. The ordinary and load Love numbers of degree 2 are calculated with allowance for their latitude dependence and dissipation for different models of the Earth's structure (the AK135, IASP91, and PREM models). The problem is solved by Love's method. The theoretical amplitude delta factors and phase shifts of second-order tidal waves for an oceanic Earth are compared with their most recent empirical counterparts obtained by the GGP network superconducting gravimeters. In particular, it is shown that a good matching (up to the fourth decimal place) of the theoretical and observed amplitude factors of semidiurnal tides does not require the application of the nonhydrostatic theory.

Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces

NASA Astrophysics Data System (ADS)

Pedesseau, Laurent; Jouanna, Paul

2004-12-01

The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation Ck⇔μk between the concentrations Ck and the chemical potentials μk of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation Ck⇔μk implies in fact two problems: a direct problem Ck⇒μk and an inverse problem μk⇒Ck. Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 Å thick gypsum interface. The major unexpected observation is the repulsion of SO42- ions towards the reference solution and the attraction of Ca2+ ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.

Are equilibrium multichannel networks predictable? The case of the regulated Indus River, Pakistan

NASA Astrophysics Data System (ADS)

Carling, P. A.; Trieu, H.; Hornby, D. D.; Huang, He Qing; Darby, S. E.; Sear, D. A.; Hutton, C.; Hill, C.; Ali, Z.; Ahmed, A.; Iqbal, I.; Hussain, Z.

2018-02-01

Arguably, the current planform behaviour of the Indus River is broadly predictable. Between Chashma and Taunsa, Pakistan, the Indus is a 264-km-long multiple-channel reach. Remote sensing imagery, encompassing major floods in 2007 and 2010, shows that the Indus has a minimum of two and a maximum of nine channels, with on average four active channels during the dry season and five during the annual monsoon. Thus, the network structure, if not detailed planform, remains stable even for the record 2010 flood (27,100 m3 s- 1; recurrence interval > 100 years). Bankline recession is negligible for discharges less than a peak annual discharge of 6000 m3 s- 1 ( 80% of mean annual flood). The Maximum Flow Efficiency (MFE) principle demonstrates that the channel network is insensitive to the monsoon floods, which typically peak at 13,200 m3 s- 1. Rather, the network is in near-equilibrium with the mean annual flood (7530 m3 s- 1). The MFE principle indicates that stable networks have three to four channels, thus the observed stability in the number of active channels accords with the presence of a near-equilibrium reach-scale channel network. Insensitivity to the annual hydrological cycle demonstrates that the timescale for network adjustment is much longer than the timescale of the monsoon hydrograph, with the annual excess water being stored on floodplains rather than being conveyed in an enlarged channel network. The analysis explains the lack of significant channel adjustment following the largest flood in 40 years and the extensive Indus flooding experienced on an annual basis, with its substantial impacts on the populace and agricultural production.

Spatial-temporal modeling of malware propagation in networks.

PubMed

Chen, Zesheng; Ji, Chuanyi

2005-09-01

Network security is an important task of network management. One threat to network security is malware (malicious software) propagation. One type of malware is called topological scanning that spreads based on topology information. The focus of this work is on modeling the spread of topological malwares, which is important for understanding their potential damages, and for developing countermeasures to protect the network infrastructure. Our model is motivated by probabilistic graphs, which have been widely investigated in machine learning. We first use a graphical representation to abstract the propagation of malwares that employ different scanning methods. We then use a spatial-temporal random process to describe the statistical dependence of malware propagation in arbitrary topologies. As the spatial dependence is particularly difficult to characterize, the problem becomes how to use simple (i.e., biased) models to approximate the spatially dependent process. In particular, we propose the independent model and the Markov model as simple approximations. We conduct both theoretical analysis and extensive simulations on large networks using both real measurements and synthesized topologies to test the performance of the proposed models. Our results show that the independent model can capture temporal dependence and detailed topology information and, thus, outperforms the previous models, whereas the Markov model incorporates a certain spatial dependence and, thus, achieves a greater accuracy in characterizing both transient and equilibrium behaviors of malware propagation.

Defense Strategies for Asymmetric Networked Systems with Discrete Components.

PubMed

Rao, Nageswara S V; Ma, Chris Y T; Hausken, Kjell; He, Fei; Yau, David K Y; Zhuang, Jun

2018-05-03

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.

Defense Strategies for Asymmetric Networked Systems with Discrete Components

PubMed Central

Rao, Nageswara S. V.; Ma, Chris Y. T.; Hausken, Kjell; He, Fei; Yau, David K. Y.

2018-01-01

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models. PMID:29751588

Systematic Approach to Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems

ERIC Educational Resources Information Center

Baeza-Baeza, Juan Jose; Garcia-Alvarez-Coque, Maria Celia

2011-01-01

A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the…

A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks.

PubMed

Yang, Liu; Lu, Yinzhi; Xiong, Lian; Tao, Yang; Zhong, Yuanchang

2017-11-17

Clustering is an effective topology control method in wireless sensor networks (WSNs), since it can enhance the network lifetime and scalability. To prolong the network lifetime in clustered WSNs, an efficient cluster head (CH) optimization policy is essential to distribute the energy among sensor nodes. Recently, game theory has been introduced to model clustering. Each sensor node is considered as a rational and selfish player which will play a clustering game with an equilibrium strategy. Then it decides whether to act as the CH according to this strategy for a tradeoff between providing required services and energy conservation. However, how to get the equilibrium strategy while maximizing the payoff of sensor nodes has rarely been addressed to date. In this paper, we present a game theoretic approach for balancing energy consumption in clustered WSNs. With our novel payoff function, realistic sensor behaviors can be captured well. The energy heterogeneity of nodes is considered by incorporating a penalty mechanism in the payoff function, so the nodes with more energy will compete for CHs more actively. We have obtained the Nash equilibrium (NE) strategy of the clustering game through convex optimization. Specifically, each sensor node can achieve its own maximal payoff when it makes the decision according to this strategy. Through plenty of simulations, our proposed game theoretic clustering is proved to have a good energy balancing performance and consequently the network lifetime is greatly enhanced.

A mixed SIR-SIS model to contain a virus spreading through networks with two degrees

NASA Astrophysics Data System (ADS)

Essouifi, Mohamed; Achahbar, Abdelfattah

Due to the fact that the “nodes” and “links” of real networks are heterogeneous, to model computer viruses prevalence throughout the Internet, we borrow the idea of the reduced scale free network which was introduced recently. The purpose of this paper is to extend the previous deterministic two subchains of Susceptible-Infected-Susceptible (SIS) model into a mixed Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible (SIR-SIS) model to contain the computer virus spreading over networks with two degrees. Moreover, we develop its stochastic counterpart. Due to the high protection and security taken for hubs class, we suggest to treat it by using SIR epidemic model rather than the SIS one. The analytical study reveals that the proposed model admits a stable viral equilibrium. Thus, it is shown numerically that the mean dynamic behavior of the stochastic model is in agreement with the deterministic one. Unlike the infection densities i2 and i which both tend to a viral equilibrium for both approaches as in the previous study, i1 tends to the virus-free equilibrium. Furthermore, since a proportion of infectives are recovered, the global infection density i is minimized. Therefore, the permanent presence of viruses in the network due to the lower-degree nodes class. Many suggestions are put forward for containing viruses propagation and minimizing their damages.

The Adverse Effects of Le Châtelier's Principle on Teacher Understanding of Chemical Equilibrium

NASA Astrophysics Data System (ADS)

Cheung, Derek

2009-04-01

Although the scientific inadequacy of Le Châtelier's principle has long been documented in the literature, the principle is still treated as a central concept of chemical equilibrium by textbook writers and teachers in many countries. In the past, researchers' interest has focused on student misconceptions about chemical equilibrium and has neglected teacher misconceptions. This study aimed to determine how Le Châtelier's principle adversely affects teachers' ability to solve chemical equilibrium problems. This area of research is critically important because teachers cannot help their students understand what they themselves do not understand. In this study, a misconception test was developed and administered to a sample of 33 secondary chemistry teachers in Hong Kong. The test consisted of three open-ended chemical equilibrium questions. Analysis of teacher responses revealed that most of the 33 teachers failed the test as they relied on Le Châtelier's principle rather than the equilibrium law to tackle the three chemical equilibrium problems. Teachers' misconceptions about chemical equilibrium were categorized. Implications of these findings for chemistry teacher education and selection of curriculum content for school chemistry are discussed.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

PubMed

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.; Shalymov, Dmitry S.

2017-03-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

PubMed Central

Khantuleva, Tatiana A.

2017-01-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115617

Simulating Chemistry in Star Forming Environments

NASA Astrophysics Data System (ADS)

Gong, Munan

Chemistry plays an important role in the interstellar medium (ISM), regulating the heating and cooling of the gas and determining abundances of molecular species that trace gas properties in observations. One of the most abundant and important molecules in the ISM is CO. CO is a main coolant for the molecular ISM, and the CO(J = 1 - 0) line emission is a widely used observational tracer for molecular clouds. In Chapter 2, we propose a new simplified chemical network for hydrogen and carbon chemistry in the atomic and molecular ISM. We compare results from our chemical network in detail with results from a full photodissociation region (PDR) code, and also with the Nelson & Langer (NL99) network previously adopted in the simulation literature. We show that our chemical network gives similar results to the PDR code in the equilibrium abundances of all species over a wide range of densities, temperature, and metallicities, whereas the NL99 network shows significant disagreement. We also compare with observations of diffuse and translucent clouds. We find that the CO, CHx and OHx abundances are consistent with equilibrium predictions for densities n = 100 - 1000 cm-3, but the predicted equilibrium CI abundance is higher than observations, signaling the potential importance of non-equilibrium/dynamical effects. In Chapter 3, we apply our new chemistry network to a study of the XCO conversion factor, which is used to convert the CO luminosity to the total H2 mass. We use numerical simulations to investigate how XCO depends on numerical resolution, non-equilibrium chemistry, physical environment, and observational beam size. Our study employs 3D magnetohydrodynamics (MHD) simulations of galactic disks with solar neighborhood conditions, where star formation and the three-phase interstellar medium (ISM) is self-consistently generated by the interaction between gravity and stellar feedback. Synthetic CO maps are obtained by post-processing the MHD simulations with chemistry and radiation transfer. We find that CO is only an approximate tracer of H2. Nevertheless, 〈 XCO〉 = 0.7 - 1.0 x 1020 cm-2K-1km-1 s consistent with observations, insensitive to the evolutionary ISM state or the far-ultraviolet (FUV) radiation field strength. Our numerical simulations successfully reproduce the observed variations of X CO on parsec scales, as well as the dependence of X CO on extinction and the CO excitation temperature.

Radiative heat transfer and nonequilibrium Casimir-Lifshitz force in many-body systems with planar geometry

NASA Astrophysics Data System (ADS)

Latella, Ivan; Ben-Abdallah, Philippe; Biehs, Svend-Age; Antezza, Mauro; Messina, Riccardo

2017-05-01

A general theory of photon-mediated energy and momentum transfer in N -body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equilibrium temperatures in such systems. An analogous formulation is introduced to quantify momentum transfer coefficients describing Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal equilibrium are readily obtained as a particular case. As an illustration of this general theoretical framework, we show on three-body systems how the presence of a fourth slab can impact equilibrium temperatures in heat-transfer problems and equilibrium positions resulting from the forces acting on the system.

Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination

NASA Astrophysics Data System (ADS)

Huang, Shouying; Chen, Fengde; Chen, Lijuan

2017-02-01

This paper investigates a new SIQRS epidemic model with demographics and vaccination on complex heterogeneous networks. We analytically derive the basic reproduction number R0, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The permanence of the disease and the globally asymptotical stability of disease-free equilibrium are proved in detail. By using a monotone iterative technique, we show that the unique endemic equilibrium is globally attractive under certain conditions. Our results really improve and enrich the results in Li et al (2014) [14]. Interestingly, the basic reproduction number R0 bears no relation to the degree-dependent birth, but our simulations indicate that the degree-dependent birth does affect the epidemic dynamics. Furthermore, we find that quarantine plays a more active role than vaccination in controlling the disease.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Signal Propagation in Proteins and Relation to Equilibrium Fluctuations

PubMed Central

Chennubhotla, Chakra; Bahar, Ivet

2007-01-01

Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models. PMID:17892319

Multiple μ-stability of neural networks with unbounded time-varying delays.

PubMed

Wang, Lili; Chen, Tianping

2014-05-01

In this paper, we are concerned with a class of recurrent neural networks with unbounded time-varying delays. Based on the geometrical configuration of activation functions, the phase space R(n) can be divided into several Φη-type subsets. Accordingly, a new set of regions Ωη are proposed, and rigorous mathematical analysis is provided to derive the existence of equilibrium point and its local μ-stability in each Ωη. It concludes that the n-dimensional neural networks can exhibit at least 3(n) equilibrium points and 2(n) of them are μ-stable. Furthermore, due to the compatible property, a set of new conditions are presented to address the dynamics in the remaining 3(n)-2(n) subset regions. As direct applications of these results, we can get some criteria on the multiple exponential stability, multiple power stability, multiple log-stability, multiple log-log-stability and so on. In addition, the approach and results can also be extended to the neural networks with K-level nonlinear activation functions and unbounded time-varying delays, in which there can store (2K+1)(n) equilibrium points, (K+1)(n) of them are locally μ-stable. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 Elsevier Ltd. All rights reserved.

Determining the Impact of Personal Mobility Carbon Allowance Schemes in Transportation Networks

DOE PAGES

Aziz, H. M. Abdul; Ukkusuri, Satish V.; Zhan, Xianyuan

2016-10-17

We know that personal mobility carbon allowance (PMCA) schemes are designed to reduce carbon consumption from transportation networks. PMCA schemes influence the travel decision process of users and accordingly impact the system metrics including travel time and greenhouse gas (GHG) emissions. Here, we develop a multi-user class dynamic user equilibrium model to evaluate the transportation system performance when PMCA scheme is implemented. The results using Sioux-Falls test network indicate that PMCA schemes can achieve the emissions reduction goals for transportation networks. Further, users characterized by high value of travel time are found to be less sensitive to carbon budget inmore » the context of work trips. Results also show that PMCA scheme can lead to higher emissions for a path compared with the case without PMCA because of flow redistribution. The developed network equilibrium model allows us to examine the change in system states at different carbon allocation levels and to design parameters of PMCA schemes accounting for population heterogeneity.« less

Determining the Impact of Personal Mobility Carbon Allowance Schemes in Transportation Networks

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

Aziz, H. M. Abdul; Ukkusuri, Satish V.; Zhan, Xianyuan

We know that personal mobility carbon allowance (PMCA) schemes are designed to reduce carbon consumption from transportation networks. PMCA schemes influence the travel decision process of users and accordingly impact the system metrics including travel time and greenhouse gas (GHG) emissions. Here, we develop a multi-user class dynamic user equilibrium model to evaluate the transportation system performance when PMCA scheme is implemented. The results using Sioux-Falls test network indicate that PMCA schemes can achieve the emissions reduction goals for transportation networks. Further, users characterized by high value of travel time are found to be less sensitive to carbon budget inmore » the context of work trips. Results also show that PMCA scheme can lead to higher emissions for a path compared with the case without PMCA because of flow redistribution. The developed network equilibrium model allows us to examine the change in system states at different carbon allocation levels and to design parameters of PMCA schemes accounting for population heterogeneity.« less

Simplifying silicon burning: Application of quasi-equilibrium to (alpha) network nucleosynthesis

NASA Technical Reports Server (NTRS)

Hix, W. R.; Thielemann, F.-K.; Khokhlov, A. M.; Wheeler, J. C.

1997-01-01

While the need for accurate calculation of nucleosynthesis and the resulting rate of thermonuclear energy release within hydrodynamic models of stars and supernovae is clear, the computational expense of these nucleosynthesis calculations often force a compromise in accuracy to reduce the computational cost. To redress this trade-off of accuracy for speed, the authors present an improved nuclear network which takes advantage of quasi- equilibrium in order to reduce the number of independent nuclei, and hence the computational cost of nucleosynthesis, without significant reduction in accuracy. In this paper they will discuss the first application of this method, the further reduction in size of the minimal alpha network. The resultant QSE- reduced alpha network is twice as fast as the conventional alpha network it replaces and requires the tracking of half as many abundance variables, while accurately estimating the rate of energy generation. Such reduction in cost is particularly necessary for future generation of multi-dimensional models for supernovae.

Non-Equlibrium Driven Dynamics of Continuous Attractors in Place Cell Networks

NASA Astrophysics Data System (ADS)

Zhong, Weishun; Kim, Hyun Jin; Schwab, David; Murugan, Arvind

Attractors have found much use in neuroscience as a means of information processing and decision making. Examples include associative memory with point and continuous attractors, spatial navigation and planning using place cell networks, dynamic pattern recognition among others. The functional use of such attractors requires the action of spatially and temporally varying external driving signals and yet, most theoretical work on attractors has been in the limit of small or no drive. We take steps towards understanding the non-equilibrium driven dynamics of continuous attractors in place cell networks. We establish an `equivalence principle' that relates fluctuations under a time-dependent external force to equilibrium fluctuations in a `co-moving' frame with only static forces, much like in Newtonian physics. Consequently, we analytically derive a network's capacity to encode multiple attractors as a function of the driving signal size and rate of change.

Essays on variational approximation techniques for stochastic optimization problems

NASA Astrophysics Data System (ADS)

Deride Silva, Julio A.

This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence of estimators, and a problem for creating probabilistic scenarios on renewable energies estimation. In Chapter 7 we re-visited one of the "folk theorems" in statistics, where a family of Bayes estimators under 0-1 loss functions is claimed to converge to the maximum a posteriori estimator. This assertion is studied under the scope of the hypo-convergence theory, and the density functions are included in the class of upper semicontinuous functions. We conclude this chapter with an example in which the convergence does not hold true, and we provided sufficient conditions that guarantee convergence. The last chapter, Chapter 8, addresses the important topic of creating probabilistic scenarios for solar power generation. Scenarios are a fundamental input for the stochastic optimization problem of energy dispatch, especially when incorporating renewables. We proposed a model designed to capture the constraints induced by physical characteristics of the variables based on the application of an epi-spline density estimation along with a copula estimation, in order to account for partial correlations between variables.

On the stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings

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

Hu, Kun; Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon; Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk

2013-11-15

In this paper, we perform a stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings. Bifurcation diagram of the damping, position and velocity coupling strengths is constructed, which gives insight into how stability boundary curves come into existence and how these curves evolve from small closed loops into open-ended curves. The van der Pol oscillator has been considered by many researchers as the nodes for various networks. It is inherently unstable at the zero equilibrium. Stability control of a network is always an important problem. Currently, the stabilization of the zero equilibriummore » of a pair of van der Pol oscillators can be achieved only for small damping strength by using delayed velocity coupling. An interesting question arises naturally: can the zero equilibrium be stabilized for an arbitrarily large value of the damping strength? We prove that it can be. In addition, a simple condition is given on how to choose the feedback parameters to achieve such goal. We further investigate how the in-phase mode or the out-of-phase mode of a periodic solution is related to the stability boundary curve that it emerges from a Hopf bifurcation. Analytical expression of a periodic solution is derived using an integration method. Some illustrative examples show that the theoretical prediction and numerical simulation are in good agreement.« less

Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong

2017-07-01

A series of online rumours have seriously influenced the normal production and living of people. This paper aims to study the combined impact of psychological factor, propagation delay, network topology and control strategy on rumour diffusion over the online social networks. Based on an online social network, which is seen as a scale-free network, we model the spread of rumours by using a delayed SIS (Susceptible and Infected) epidemic-like model with consideration of psychological factor and network topology. First, through theoretical analysis, we illustrate the boundedness of the density of rumour-susceptible individuals and rumour-infected individuals. Second, we obtain the basic reproduction number R0 and prove the stability of the non-rumour equilibrium point and the rumour-spreading equilibrium point. Third, control strategies, such as uniform immunisation control, proportional immunisation control, targeted immunisation control and optimum control, are put forward to restrain rumour diffusion. Meanwhile, we have compared the differences of these control strategies. Finally, some representative numerical simulations are performed to verify the theoretical analysis results.

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE PAGES

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul; ...

2017-08-28

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

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

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

An improved correlation to predict molecular weight between crosslinks based on equilibrium degree of swelling of hydrogel networks.

PubMed

Jimenez-Vergara, Andrea C; Lewis, John; Hahn, Mariah S; Munoz-Pinto, Dany J

2018-04-01

Accurate characterization of hydrogel diffusional properties is of substantial importance for a range of biotechnological applications. The diffusional capacity of hydrogels has commonly been estimated using the average molecular weight between crosslinks (M c ), which is calculated based on the equilibrium degree of swelling. However, the existing correlation linking M c and equilibrium swelling fails to accurately reflect the diffusional properties of highly crosslinked hydrogel networks. Also, as demonstrated herein, the current model fails to accurately predict the diffusional properties of hydrogels when polymer concentration and molecular weight are varied simultaneously. To address these limitations, we evaluated the diffusional properties of 48 distinct hydrogel formulations using two different photoinitiator systems, employing molecular size exclusion as an alternative methodology to calculate average hydrogel mesh size. The resulting data were then utilized to develop a revised correlation between M c and hydrogel equilibrium swelling that substantially reduces the limitations associated with the current correlation. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 1339-1348, 2018. © 2017 Wiley Periodicals, Inc.

The Lewis Chemical Equilibrium Program with parametric study capability

NASA Technical Reports Server (NTRS)

Sevigny, R.

1981-01-01

The program was developed to determine chemical equilibrium in complex systems. Using a free energy minimization technique, the program permits calculations such as: chemical equilibrium for assigned thermodynamic states; theoretical rocket performance for both equilibrium and frozen compositions during expansion; incident and reflected shock properties; and Chapman-Jouget detonation properties. It is shown that the same program can handle solid coal in an entrained flow coal gasification problem.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Synaptic tagging, evaluation of memories, and the distal reward problem.

PubMed

Päpper, Marc; Kempter, Richard; Leibold, Christian

2011-01-01

Long-term synaptic plasticity exhibits distinct phases. The synaptic tagging hypothesis suggests an early phase in which synapses are prepared, or "tagged," for protein capture, and a late phase in which those proteins are integrated into the synapses to achieve memory consolidation. The synapse specificity of the tags is consistent with conventional neural network models of associative memory. Memory consolidation through protein synthesis, however, is neuron specific, and its functional role in those models has not been assessed. Here, using a theoretical network model, we test the tagging hypothesis on its potential to prolong memory lifetimes in an online-learning paradigm. We find that protein synthesis, though not synapse specific, prolongs memory lifetimes if it is used to evaluate memory items on a cellular level. In our model we assume that only "important" memory items evoke protein synthesis such that these become more stable than "unimportant" items, which do not evoke protein synthesis. The network model comprises an equilibrium distribution of synaptic states that is very susceptible to the storage of new items: Most synapses are in a state in which they are plastic and can be changed easily, whereas only those synapses that are essential for the retrieval of the important memory items are in the stable late phase. The model can solve the distal reward problem, where the initial exposure of a memory item and its evaluation are temporally separated. Synaptic tagging hence provides a viable mechanism to consolidate and evaluate memories on a synaptic basis.

Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems

NASA Astrophysics Data System (ADS)

Dasgupta, Sambarta

Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of sensitivity analysis of power system, subjected to changes or uncertainty in load parameters and network topology, is also studied using the theory of normally hyperbolic manifolds. The sensitivity analysis is used for the identification and rank ordering of the critical interactions and parameters in the power network. The sensitivity analysis is carried out both in finite time and in asymptotic. One of the distinguishing features of the asymptotic sensitivity analysis is that the asymptotic dynamics of the system is assumed to be a periodic orbit. For asymptotic sensitivity analysis we employ combination of tools from ergodic theory and geometric theory of dynamical systems.

The application of statistical mechanics on the study of glassy behaviors in transportation networks and dynamics in models of financial markets

NASA Astrophysics Data System (ADS)

Yeung, Chi Ho

In this thesis, we study two interdisciplinary problems in the framework of statistical physics, which show the broad applicability of physics on problems with various origins. The first problem corresponds to an optimization problem in allocating resources on random regular networks. Frustrations arise from competition for resources. When the initial resources are uniform, different regimes with discrete fractions of satisfied nodes are observed, resembling the Devil's staircase. We apply the spin glass theory in analyses and demonstrate how functional recursions are converted to simple recursions of probabilities. Equilibrium properties such as the average energy and the fraction of free nodes are derived. When the initial resources are bimodally distributed, increases in the fraction of rich nodes induce a glassy transition, entering a glassy phase described by the existence of multiple metastable states, in which we employ the replica symmetry breaking ansatz for analysis. The second problem corresponds to the study of multi-agent systems modeling financial markets. Agents in the system trade among themselves, and self-organize to produce macroscopic trading behaviors resembling the real financial markets. These behaviors include the arbitraging activities, the setting up and the following of price trends. A phase diagram of these behaviors is obtained, as a function of the sensitivity of price and the market impact factor. We finally test the applicability of the models with real financial data including the Hang Seng Index, the Nasdaq Composite and the Dow Jones Industrial Average. A substantial fraction of agents gains faster than the inflation rate of the indices, suggesting the possibility of using multi-agent systems as a tool for real trading.

Solving multi-leader-common-follower games.

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

Leyffer, S.; Munson, T.; Mathematics and Computer Science

Multi-leader-common-follower games arise when modelling two or more competitive firms, the leaders, that commit to their decisions prior to another group of competitive firms, the followers, that react to the decisions made by the leaders. These problems lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We develop a characterization of the solution sets for these problems and examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We demonstrate the practical viability of our approach by solving amore » range of medium-sized test problems.« less

A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks

PubMed Central

Lu, Yinzhi; Xiong, Lian; Tao, Yang; Zhong, Yuanchang

2017-01-01

Clustering is an effective topology control method in wireless sensor networks (WSNs), since it can enhance the network lifetime and scalability. To prolong the network lifetime in clustered WSNs, an efficient cluster head (CH) optimization policy is essential to distribute the energy among sensor nodes. Recently, game theory has been introduced to model clustering. Each sensor node is considered as a rational and selfish player which will play a clustering game with an equilibrium strategy. Then it decides whether to act as the CH according to this strategy for a tradeoff between providing required services and energy conservation. However, how to get the equilibrium strategy while maximizing the payoff of sensor nodes has rarely been addressed to date. In this paper, we present a game theoretic approach for balancing energy consumption in clustered WSNs. With our novel payoff function, realistic sensor behaviors can be captured well. The energy heterogeneity of nodes is considered by incorporating a penalty mechanism in the payoff function, so the nodes with more energy will compete for CHs more actively. We have obtained the Nash equilibrium (NE) strategy of the clustering game through convex optimization. Specifically, each sensor node can achieve its own maximal payoff when it makes the decision according to this strategy. Through plenty of simulations, our proposed game theoretic clustering is proved to have a good energy balancing performance and consequently the network lifetime is greatly enhanced. PMID:29149075

On a numerical solving of random generated hexamatrix games

NASA Astrophysics Data System (ADS)

Orlov, Andrei; Strekalovskiy, Alexander

2016-10-01

In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search Theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.

Green wireless body area nanonetworks: energy management and the game of survival.

PubMed

Misra, Sudip; Islam, Nabiul; Mahapatro, Judhistir; Rodrigues, Joel Jose P C

2014-03-01

In this paper, we envisage the architecture of Green Wireless Body Area Nanonetwork (GBAN) as a collection of nanodevices, in which each device is capable of communicating in both the molecular and wireless electromagnetic communication modes. The term green refers to the fact that the nanodevices in such a network can harvest energy from their surrounding environment, so that no nanodevice gets old solely due to the reasons attributed to energy depletion. However, the residual energy of a nanodevice can deplete substantially with the lapse of time, if the rate of energy consumption is not comparable with the rate of energy harvesting. It is observed that the rate of energy harvesting is nonlinear and sporadic in nature. So, the management of energy of the nanodevices is fundamentally important. We specifically address this problem in a ubiquitous healthcare monitoring scenario and formulate it as a cooperative Nash Bargaining game. The optimal strategy obtained from the Nash equilibrium solution provides improved network performance in terms of throughput and delay.

Dynamical gauge effects in an open quantum network

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

We describe new experimental techniques for simulation of high-energy field theories based on an analogy between open thermodynamic systems and effective dynamical gauge-fields following SU(2) × U(1) Yang-Mills models. By coupling near-resonant laser-modes to atoms moving in a disordered optical environment, we create an open system which exhibits a non-equilibrium phase transition between two steady-state behaviors, exhibiting scale-invariant behavior near the transition. By measuring transport of atoms through the disordered network, we observe two distinct scaling behaviors, corresponding to the classical and quantum limits for the dynamical gauge field. This behavior is loosely analogous to dynamical gauge effects in quantum chromodynamics, and can mapped onto generalized open problems in theoretical understanding of quantized non-Abelian gauge theories. Additional, the scaling behavior can be understood from the geometric structure of the gauge potential and linked to the measure of information in the local disordered potential, reflecting an underlying holographic principle. We acknowledge support from NSF Award No.1068570, and the Charles E. Kaufman Foundation.

Multistability of second-order competitive neural networks with nondecreasing saturated activation functions.

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

Evolutionary dynamics of group interactions on structured populations: a review

PubMed Central

Perc, Matjaž; Gómez-Gardeñes, Jesús; Szolnoki, Attila; Floría, Luis M.; Moreno, Yamir

2013-01-01

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory. PMID:23303223

Microscale Mechanics of Actin Networks During Dynamic Assembly and Dissociation

NASA Astrophysics Data System (ADS)

Gurmessa, Bekele; Robertson-Anderson, Rae; Ross, Jennifer; Nguyen, Dan; Saleh, Omar

Actin is one of the key components of the cytoskeleton, enabling cells to move and divide while maintaining shape by dynamic polymerization, dissociation and crosslinking. Actin polymerization and network formation is driven by ATP hydrolysis and varies depending on the concentrations of actin monomers and crosslinking proteins. The viscoelastic properties of steady-state actin networks have been well-characterized, yet the mechanical properties of these non-equilibrium systems during dynamic assembly and disassembly remain to be understood. We use semipermeable microfluidic devices to induce in situ dissolution and re-polymerization of entangled and crosslinked actin networks, by varying ATP concentrations in real-time, while measuring the mechanical properties during disassembly and re-assembly. We use optical tweezers to sinusoidally oscillate embedded microspheres and measure the resulting force at set time-intervals and in different regions of the network during cyclic assembly/disassembly. We determine the time-dependent viscoelastic properties of non-equilibrium network intermediates and the reproducibility and homogeneity of network formation and dissolution. Results inform the role that cytoskeleton reorganization plays in the dynamic multifunctional mechanics of cells. NSF CAREER Award (DMR-1255446) and a Scialog Collaborative Innovation Award funded by Research Corporation for Scientific Advancement (Grant No. 24192).

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Zeroth Law, Entropy, Equilibrium, and All That

ERIC Educational Resources Information Center

Canagaratna, Sebastian G.

2008-01-01

The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced through the zeroth law. The relation between the zeroth law and the second law in the…

Book Review:

NASA Astrophysics Data System (ADS)

Vespignani, A.

2004-09-01

Networks have been recently recognized as playing a central role in understanding a wide range of systems spanning diverse scientific domains such as physics and biology, economics, computer science and information technology. Specific examples run from the structure of the Internet and the World Wide Web to the interconnections of finance agents and ecological food webs. These networked systems are generally made by many components whose microscopic interactions give rise to global structures characterized by emergent collective behaviour and complex topological properties. In this context the statistical physics approach finds a natural application since it attempts to explain the various large-scale statistical properties of networks in terms of local interactions governing the dynamical evolution of the constituent elements of the system. It is not by chance then that many of the seminal papers in the field have been published in the physics literature, and have nevertheless made a considerable impact on other disciplines. Indeed, a truly interdisciplinary approach is required in order to understand each specific system of interest, leading to a very interesting cross-fertilization between different scientific areas defining the emergence of a new research field sometimes called network science. The book of Dorogovtsev and Mendes is the first comprehensive monograph on this new scientific field. It provides a thorough presentation of the forefront research activities in the area of complex networks, with an extensive sampling of the disciplines involved and the kinds of problems that form the subject of inquiry. The book starts with a short introduction to graphs and network theory that introduces the tools and mathematical background needed for the rest of the book. The following part is devoted to an extensive presentation of the empirical analysis of real-world networks. While for obvious reasons of space the authors cannot analyse in every detail all the various examples, they provide the reader with a general vista that makes clear the relevance of network science to a wide range of natural and man-made systems. Two chapters are then committed to the detailed exposition of the statistical physics approach to equilibrium and non-equilibrium networks. The authors are two leading players in the area of network theory and offer a very careful and complete presentation of the statistical physics theory of evolving networks. Finally, in the last two chapters, the authors focus on various consequences of network topology for dynamical and physical phenomena occurring in these kinds of structures. The book is completed by a very extensive bibliography and some useful appendices containing some technical points arising in the mathematical discussion and data analysis. The book's mathematical level is fairly advanced and allows a coherent and unified framework for the study of networked structure. The book is targeted at mathematicians, physicists and social scientists alike. It will be appreciated by everybody working in the network area, and especially by any researcher or student entering the field that would like to have a reference text on the latest developments in network science.

Global exponential stability of BAM neural networks with time-varying delays and diffusion terms

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-11-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established.

Lysozyme adsorption in pH-responsive hydrogel thin-films: the non-trivial role of acid-base equilibrium.

PubMed

Narambuena, Claudio F; Longo, Gabriel S; Szleifer, Igal

2015-09-07

We develop and apply a molecular theory to study the adsorption of lysozyme on weak polyacid hydrogel films. The theory explicitly accounts for the conformation of the network, the structure of the proteins, the size and shape of all the molecular species, their interactions as well as the chemical equilibrium of each titratable unit of both the protein and the polymer network. The driving forces for adsorption are the electrostatic attractions between the negatively charged network and the positively charged protein. The adsorption is a non-monotonic function of the solution pH, with a maximum in the region between pH 8 and 9 depending on the salt concentration of the solution. The non-monotonic adsorption is the result of increasing negative charge of the network with pH, while the positive charge of the protein decreases. At low pH the network is roughly electroneutral, while at sufficiently high pH the protein is negatively charged. Upon adsorption, the acid-base equilibrium of the different amino acids of the protein shifts in a nontrivial fashion that depends critically on the particular kind of residue and solution composition. Thus, the proteins regulate their charge and enhance adsorption under a wide range of conditions. In particular, adsorption is predicted above the protein isoelectric point where both the solution lysozyme and the polymer network are negatively charged. This behavior occurs because the pH in the interior of the gel is significantly lower than that in the bulk solution and it is also regulated by the adsorption of the protein in order to optimize protein-gel interactions. Under high pH conditions we predict that the protein changes its charge from negative in the solution to positive within the gel. The change occurs within a few nanometers at the interface of the hydrogel film. Our predictions show the non-trivial interplay between acid-base equilibrium, physical interactions and molecular organization under nanoconfined conditions, which leads to non-trivial adsorption behavior that is qualitatively different from what would be predicted from the state of the proteins in the bulk solution.

Interface Control Document for the EMPACT Module that Estimates Electric Power Transmission System Response to EMP-Caused Damage

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

Werley, Kenneth Alan; Mccown, Andrew William

The EPREP code is designed to evaluate the effects of an Electro-Magnetic Pulse (EMP) on the electric power transmission system. The EPREP code embodies an umbrella framework that allows a user to set up analysis conditions and to examine analysis results. The code links to three major physics/engineering modules. The first module describes the EM wave in space and time. The second module evaluates the damage caused by the wave on specific electric power (EP) transmission system components. The third module evaluates the consequence of the damaged network on its (reduced) ability to provide electric power to meet demand. Thismore » third module is the focus of the present paper. The EMPACT code serves as the third module. The EMPACT name denotes EMP effects on Alternating Current Transmission systems. The EMPACT algorithms compute electric power transmission network flow solutions under severely damaged network conditions. Initial solutions are often characterized by unacceptible network conditions including line overloads and bad voltages. The EMPACT code contains algorithms to adjust optimally network parameters to eliminate network problems while minimizing outages. System adjustments include automatically adjusting control equipment (generator V control, variable transformers, and variable shunts), as well as non-automatic control of generator power settings and minimal load shedding. The goal is to evaluate the minimal loss of customer load under equilibrium (steady-state) conditions during peak demand.« less

Characterization and Detection of ϵ-Berge-Zhukovskii Equilibria

PubMed Central

Lung, Rodica Ioana; Suciu, Mihai; Gaskó, Noémi; Dumitrescu, D.

2015-01-01

The Berge-Zhukovskii equilibrium is an alternate solution concept in non-cooperative game theory that formalizes cooperation in a noncooperative setting. In this paper, the ϵ-Berge-Zhukovskii equilibrium is introduced and characterized by using a generative relation. The generative relation also provides a solution to the problem of computing the ϵ-Berge-Zhukovskii equilibrium for large games, by using evolutionary algorithms. Numerical examples illustrate the approach and provide a possible application for this equilibrium concept. PMID:26177217

The diminishing role of hubs in dynamical processes on complex networks.

PubMed

Quax, Rick; Apolloni, Andrea; Sloot, Peter M A

2013-11-06

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein-protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

Game among interdependent networks: The impact of rationality on system robustness

NASA Astrophysics Data System (ADS)

Fan, Yuhang; Cao, Gongze; He, Shibo; Chen, Jiming; Sun, Youxian

2016-12-01

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these entities when designing their own networks. In this paper, we study the game investigating how the rational behaviors of entities impact the system robustness. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium of the game and compare it with the optimal social welfare. We reveal that the cooperation among different entities can be reached to maximize the social welfare in continuous game only when the average degree of each network is constant. Therefore, the huge gap between Nash equilibrium and optimal social welfare generally exists. The rationality of entities makes the system inherently deficient and even renders it extremely vulnerable in some cases. We analyze our model for two concrete systems with continuous strategy space and discrete strategy space, respectively. Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing a suitable topology dependence of the system) that help reduce the gap and the system vulnerability.

Mathematical inference and control of molecular networks from perturbation experiments

NASA Astrophysics Data System (ADS)

Mohammed-Rasheed, Mohammed

One of the main challenges facing biologists and mathematicians in the post genomic era is to understand the behavior of molecular networks and harness this understanding into an educated intervention of the cell. The cell maintains its function via an elaborate network of interconnecting positive and negative feedback loops of genes, RNA and proteins that send different signals to a large number of pathways and molecules. These structures are referred to as genetic regulatory networks (GRNs) or molecular networks. GRNs can be viewed as dynamical systems with inherent properties and mechanisms, such as steady-state equilibriums and stability, that determine the behavior of the cell. The biological relevance of the mathematical concepts are important as they may predict the differentiation of a stem cell, the maintenance of a normal cell, the development of cancer and its aberrant behavior, and the design of drugs and response to therapy. Uncovering the underlying GRN structure from gene/protein expression data, e.g., microarrays or perturbation experiments, is called inference or reverse engineering of the molecular network. Because of the high cost and time consuming nature of biological experiments, the number of available measurements or experiments is very small compared to the number of molecules (genes, RNA and proteins). In addition, the observations are noisy, where the noise is due to the measurements imperfections as well as the inherent stochasticity of genetic expression levels. Intra-cellular activities and extra-cellular environmental attributes are also another source of variability. Thus, the inference of GRNs is, in general, an under-determined problem with a highly noisy set of observations. The ultimate goal of GRN inference and analysis is to be able to intervene within the network, in order to force it away from undesirable cellular states and into desirable ones. However, it remains a major challenge to design optimal intervention strategies in order to affect the time evolution of molecular activity in a desirable manner. In this proposal, we address both the inference and control problems of GRNs. In the first part of the thesis, we consider the control problem. We assume that we are given a general topology network structure, whose dynamics follow a discrete-time Markov chain model. We subsequently develop a comprehensive framework for optimal perturbation control of the network. The aim of the perturbation is to drive the network away from undesirable steady-states and to force it to converge to a unique desirable steady-state. The proposed framework does not make any assumptions about the topology of the initial network (e.g., ergodicity, weak and strong connectivity), and is thus applicable to general topology networks. We define the optimal perturbation as the minimum-energy perturbation measured in terms of the Frobenius norm between the initial and perturbed networks. We subsequently demonstrate that there exists at most one optimal perturbation that forces the network into the desirable steady-state. In the event where the optimal perturbation does not exist, we construct a family of sub-optimal perturbations that approximate the optimal solution arbitrarily closely. In the second part of the thesis, we address the inference problem of GRNs from time series data. We model the dynamics of the molecules using a system of ordinary differential equations corrupted by additive white noise. For large-scale networks, we formulate the inference problem as a constrained maximum likelihood estimation problem. We derive the molecular interactions that maximize the likelihood function while constraining the network to be sparse. We further propose a procedure to recover weak interactions based on the Bayesian information criterion. For small-size networks, we investigated the inference of a globally stable 7-gene melanoma genetic regulatory network from genetic perturbation experiments. We considered five melanoma cell lines, who exhibit different motility/invasion behavior under the same perturbation experiment of gene Wnt5a. The results of the simulations validate both the steady state levels and the experimental data of the perturbation experiments of all five cell lines. The goal of this study is to answer important questions that link the response of the network to perturbations, as measured by the experiments, to its structure, i.e., connectivity. Answers to these questions shed novel insights on the structure of networks and how they react to perturbations.

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

NASA Astrophysics Data System (ADS)

Śloderbach, Zdzisław

2016-05-01

This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337-349, 351-367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.

Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications II. Users Manual and Program Description. 2; Users Manual and Program Description

NASA Technical Reports Server (NTRS)

McBride, Bonnie J.; Gordon, Sanford

1996-01-01

This users manual is the second part of a two-part report describing the NASA Lewis CEA (Chemical Equilibrium with Applications) program. The program obtains chemical equilibrium compositions of complex mixtures with applications to several types of problems. The topics presented in this manual are: (1) details for preparing input data sets; (2) a description of output tables for various types of problems; (3) the overall modular organization of the program with information on how to make modifications; (4) a description of the function of each subroutine; (5) error messages and their significance; and (6) a number of examples that illustrate various types of problems handled by CEA and that cover many of the options available in both input and output. Seven appendixes give information on the thermodynamic and thermal transport data used in CEA; some information on common variables used in or generated by the equilibrium module; and output tables for 14 example problems. The CEA program was written in ANSI standard FORTRAN 77. CEA should work on any system with sufficient storage. There are about 6300 lines in the source code, which uses about 225 kilobytes of memory. The compiled program takes about 975 kilobytes.

Spectrin tetramer-dimer equilibrium and the stability of erythrocyte membrane skeletons

NASA Astrophysics Data System (ADS)

Liu, Shih-Chun; Palek, Jiri

1980-06-01

The inner side of the red-cell membrane is laminated by a two-dimensional network of membrane proteins which include spectrin, actin and some other components1-4. After extraction of lipids and integral proteins from the membrane, this membrane skeleton can be visualized as a ball-shaped network consisting of twisted fibres1-4 and globular protrusions4; however, the assembly of the individual proteins in the membrane skeleton is not well understood. Spectrin can be eluted from the membrane in the form of dimers and tetramers5-8. Electron microscopic study with low-angle shadowing technique shows that spectrin dimers are two parallel strands of twisted fibres presumably representing bands 1 and 2 of spectrin9. Spectrin tetramers presumably formed by head-to-head associations of two dimers are twice as long9. In solution, the spectrin dimer-tetramer equilibrium depends on temperature and salt concentration7,8; however, it is not known whether the same equilibrium exists in the membrane and whether it affects the physical properties of the membrane, such as its structural stability and deformability. We now demonstrate that spectrin dimers and tetramers are in a reversible equilibrium in the membrane and that in physiological conditions this equilibrium favours spectrin tetramers. Furthermore, we show that transformation of spectrin tetramers to dimers, as induced by ghost incubation in hypotonic conditions, diminishes the structural stability of the Triton-insoluble membrane skeletons.

An experimental study of the Online Information Paradox: Does en-route information improve road network performance?

PubMed

Wijayaratna, Kasun P; Dixit, Vinayak V; Denant-Boemont, Laurent; Waller, S Travis

2017-01-01

This study investigates the empirical presence of a theoretical transportation paradox, defined as the "Online Information Paradox" (OIP). The paradox suggests that, for certain road networks, the provision of online information deteriorate travel conditions for all users of that network relative to the situation where no online information is provided to users. The analytical presence of the paradox was derived for a specific network structure by using two equilibrium models, the first being the Expected User Equilibrium (EUE) solution (no information scenario) and the other being the User Equilibrium with Recourse (UER) solution (with information scenario). An incentivised computerised route choice game was designed using the concepts of experimental economics and administered in a controlled laboratory environment to investigate the physical presence of the paradox. Aggregate statistics of path flows and Total System Travel Costs (TSTC) were used to compare the experimental results with the theoretical findings. A total of 12 groups of 12 participants completed the experiment and the OIP and the occurrence of the OIP being significant was observed in 11 of the 12 cases. Though information increased travel costs for users on average, it reduced the volatility of travel costs experienced in the no information scenario indicating that information can achieve a more reliable system. Further replications of similar experiments and more importantly field based identification of the phenomena will force transport professionals to be aware of the emergence of the paradox. In addition, studies such as this emphasise the need for the adoption of adaptive traffic assignment techniques to appropriately model the acquisition of information on a road network.

Structural design using equilibrium programming formulations

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

1995-01-01

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Global analysis of an impulsive delayed Lotka-Volterra competition system

NASA Astrophysics Data System (ADS)

Xia, Yonghui

2011-03-01

In this paper, a retarded impulsive n-species Lotka-Volterra competition system with feedback controls is studied. Some sufficient conditions are obtained to guarantee the global exponential stability and global asymptotic stability of a unique equilibrium for such a high-dimensional biological system. The problem considered in this paper is in many aspects more general and incorporates as special cases various problems which have been extensively studied in the literature. Moreover, applying the obtained results to some special cases, I derive some new criteria which generalize and greatly improve some well known results. A method is proposed to investigate biological systems subjected to the effect of both impulses and delays. The method is based on Banach fixed point theory and matrix's spectral theory as well as Lyapunov function. Moreover, some novel analytic techniques are employed to study GAS and GES. It is believed that the method can be extended to other high-dimensional biological systems and complex neural networks. Finally, two examples show the feasibility of the results.

Hybrid function projective synchronization in complex dynamical networks

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

Wei, Qiang; Wang, Xing-yuan, E-mail: wangxy@dlut.edu.cn; Hu, Xiao-peng

2014-02-15

This paper investigates hybrid function projective synchronization in complex dynamical networks. When the complex dynamical networks could be synchronized up to an equilibrium or periodic orbit, a hybrid feedback controller is designed to realize the different component of vector of node could be synchronized up to different desired scaling function in complex dynamical networks with time delay. Hybrid function projective synchronization (HFPS) in complex dynamical networks with constant delay and HFPS in complex dynamical networks with time-varying coupling delay are researched, respectively. Finally, the numerical simulations show the effectiveness of theoretical analysis.

Out-of-equilibrium dynamical mean-field equations for the perceptron model

NASA Astrophysics Data System (ADS)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

Detection and characterization of nonspecific, sparsely-populated binding modes in the early stages of complexation

PubMed Central

Cardone, A.; Bornstein, A.; Pant, H. C.; Brady, M.; Sriram, R.; Hassan, S. A.

2015-01-01

A method is proposed to study protein-ligand binding in a system governed by specific and non-specific interactions. Strong associations lead to narrow distributions in the proteins configuration space; weak and ultra-weak associations lead instead to broader distributions, a manifestation of non-specific, sparsely-populated binding modes with multiple interfaces. The method is based on the notion that a discrete set of preferential first-encounter modes are metastable states from which stable (pre-relaxation) complexes at equilibrium evolve. The method can be used to explore alternative pathways of complexation with statistical significance and can be integrated into a general algorithm to study protein interaction networks. The method is applied to a peptide-protein complex. The peptide adopts several low-population conformers and binds in a variety of modes with a broad range of affinities. The system is thus well suited to analyze general features of binding, including conformational selection, multiplicity of binding modes, and nonspecific interactions, and to illustrate how the method can be applied to study these problems systematically. The equilibrium distributions can be used to generate biasing functions for simulations of multiprotein systems from which bulk thermodynamic quantities can be calculated. PMID:25782918

Equilibrium expert: an add-in to Microsoft Excel for multiple binding equilibrium simulations and parameter estimations.

PubMed

Raguin, Olivier; Gruaz-Guyon, Anne; Barbet, Jacques

2002-11-01

An add-in to Microsoft Excel was developed to simulate multiple binding equilibriums. A partition function, readily written even when the equilibrium is complex, describes the experimental system. It involves the concentrations of the different free molecular species and of the different complexes present in the experiment. As a result, the software is not restricted to a series of predefined experimental setups but can handle a large variety of problems involving up to nine independent molecular species. Binding parameters are estimated by nonlinear least-square fitting of experimental measurements as supplied by the user. The fitting process allows user-defined weighting of the experimental data. The flexibility of the software and the way it may be used to describe common experimental situations and to deal with usual problems such as tracer reactivity or nonspecific binding is demonstrated by a few examples. The software is available free of charge upon request.

Thermodynamics of Biological Processes

PubMed Central

Garcia, Hernan G.; Kondev, Jane; Orme, Nigel; Theriot, Julie A.; Phillips, Rob

2012-01-01

There is a long and rich tradition of using ideas from both equilibrium thermodynamics and its microscopic partner theory of equilibrium statistical mechanics. In this chapter, we provide some background on the origins of the seemingly unreasonable effectiveness of ideas from both thermodynamics and statistical mechanics in biology. After making a description of these foundational issues, we turn to a series of case studies primarily focused on binding that are intended to illustrate the broad biological reach of equilibrium thinking in biology. These case studies include ligand-gated ion channels, thermodynamic models of transcription, and recent applications to the problem of bacterial chemotaxis. As part of the description of these case studies, we explore a number of different uses of the famed Monod–Wyman–Changeux (MWC) model as a generic tool for providing a mathematical characterization of two-state systems. These case studies should provide a template for tailoring equilibrium ideas to other problems of biological interest. PMID:21333788

An Adaptive QSE-reduced Nuclear Reaction Network for Silicon Burning

NASA Astrophysics Data System (ADS)

Parete-Koon, Suzanne; Hix, W.; Thielemann, F.

2008-03-01

The nuclei of the "iron peak" are formed in massive stars shortly before core collapse and during their supernova outbursts as well as during thermonuclear supernovae. Complete and incomplete silicon burning during these events are responsible for the production of a wide range of nuclei with atomic mass numbers from 28 to 64. Because of the large number of nuclei involved, accurate modeling of silicon burning is computationally expensive. However, examination of the physics of silicon burning has revealed that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. We present an improvement on our hybrid equilibrium-network scheme which takes advantage of this quasi-equilibrium in order to reduce the number of independent variables calculated. Because the size and membership of these groups vary as the temperature, density and electron faction change, achieving maximal efficiency requires dynamic adjustment of group number and membership. Toward this end, we are implementing a scheme beginning with a single QSE (NSE) group at appropriately high temperature, then progressing through 2, 3 and 4 group stages (with successively more independent variables) as temperature declines. This combination allows accurate prediction of the nuclear abundance evolution, deleptonization and energy generation at a further reduced computational cost when compared to a conventional nuclear reaction network or our previous 3 fixed group QSE-reduced network. During silicon burning, the resultant QSE-reduced network is up to 20 times faster than the full network it replaces without significant loss of accuracy. These reductions in computational cost and the number of species evolved make QSE-reduced networks well suited for inclusion within hydrodynamic simulations, particularly in multi-dimensional applications. This work has been supported by the National Science Foundation, by the Department of Energy's Scientic Discovery through Advanced Computing Programs, and by the Joint Institute for Heavy Ion Research at ORNL.

An alternative extragradient projection method for quasi-equilibrium problems.

PubMed

Chen, Haibin; Wang, Yiju; Xu, Yi

2018-01-01

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion property with respect to a given initial point. The global convergence of the method is established under the assumptions of pseudomonotonicity of the equilibrium function and of continuity of the underlying multi-valued mapping. Furthermore, we show that the generated sequence converges to the nearest point in the solution set to the initial point. Numerical experiments show the efficiency of the method.

Existence and Hadamard well-posedness of a system of simultaneous generalized vector quasi-equilibrium problems.

PubMed

Zhang, Wenyan; Zeng, Jing

2017-01-01

An existence result for the solution set of a system of simultaneous generalized vector quasi-equilibrium problems (for short, (SSGVQEP)) is obtained, which improves Theorem 3.1 of the work of Ansari et al. (J. Optim. Theory Appl. 127:27-44, 2005). Moreover, a definition of Hadamard-type well-posedness for (SSGVQEP) is introduced and sufficient conditions for Hadamard well-posedness of (SSGVQEP) are established.

On the Effectiveness of Nature-Inspired Metaheuristic Algorithms for Performing Phase Equilibrium Thermodynamic Calculations

PubMed Central

Fateen, Seif-Eddeen K.; Bonilla-Petriciolet, Adrian

2014-01-01

The search for reliable and efficient global optimization algorithms for solving phase stability and phase equilibrium problems in applied thermodynamics is an ongoing area of research. In this study, we evaluated and compared the reliability and efficiency of eight selected nature-inspired metaheuristic algorithms for solving difficult phase stability and phase equilibrium problems. These algorithms are the cuckoo search (CS), intelligent firefly (IFA), bat (BA), artificial bee colony (ABC), MAKHA, a hybrid between monkey algorithm and krill herd algorithm, covariance matrix adaptation evolution strategy (CMAES), magnetic charged system search (MCSS), and bare bones particle swarm optimization (BBPSO). The results clearly showed that CS is the most reliable of all methods as it successfully solved all thermodynamic problems tested in this study. CS proved to be a promising nature-inspired optimization method to perform applied thermodynamic calculations for process design. PMID:24967430

On the effectiveness of nature-inspired metaheuristic algorithms for performing phase equilibrium thermodynamic calculations.

PubMed

Fateen, Seif-Eddeen K; Bonilla-Petriciolet, Adrian

2014-01-01

The search for reliable and efficient global optimization algorithms for solving phase stability and phase equilibrium problems in applied thermodynamics is an ongoing area of research. In this study, we evaluated and compared the reliability and efficiency of eight selected nature-inspired metaheuristic algorithms for solving difficult phase stability and phase equilibrium problems. These algorithms are the cuckoo search (CS), intelligent firefly (IFA), bat (BA), artificial bee colony (ABC), MAKHA, a hybrid between monkey algorithm and krill herd algorithm, covariance matrix adaptation evolution strategy (CMAES), magnetic charged system search (MCSS), and bare bones particle swarm optimization (BBPSO). The results clearly showed that CS is the most reliable of all methods as it successfully solved all thermodynamic problems tested in this study. CS proved to be a promising nature-inspired optimization method to perform applied thermodynamic calculations for process design.

Calculation of open and closed system elastic coefficients for multicomponent solids

NASA Astrophysics Data System (ADS)

Mishin, Y.

2015-06-01

Thermodynamic equilibrium in multicomponent solids subject to mechanical stresses is a complex nonlinear problem whose exact solution requires extensive computations. A few decades ago, Larché and Cahn proposed a linearized solution of the mechanochemical equilibrium problem by introducing the concept of open system elastic coefficients [Acta Metall. 21, 1051 (1973), 10.1016/0001-6160(73)90021-7]. Using the Ni-Al solid solution as a model system, we demonstrate that open system elastic coefficients can be readily computed by semigrand canonical Monte Carlo simulations in conjunction with the shape fluctuation approach. Such coefficients can be derived from a single simulation run, together with other thermodynamic properties needed for prediction of compositional fields in solid solutions containing defects. The proposed calculation approach enables streamlined solutions of mechanochemical equilibrium problems in complex alloys. Second order corrections to the linear theory are extended to multicomponent systems.

Assortative mating and mutation diffusion in spatial evolutionary systems

NASA Astrophysics Data System (ADS)

Paley, C. J.; Taraskin, S. N.; Elliott, S. R.

2010-04-01

The influence of spatial structure on the equilibrium properties of a sexual population model defined on networks is studied numerically. Using a small-world-like topology of the networks as an investigative tool, the contributions to the fitness of assortative mating and of global mutant spread properties are considered. Simple measures of nearest-neighbor correlations and speed of spread of mutants through the system have been used to confirm that both of these dynamics are important contributory factors to the fitness. It is found that assortative mating increases the fitness of populations. Quick global spread of favorable mutations is shown to be a key factor increasing the equilibrium fitness of populations.

Active DNA gels

NASA Astrophysics Data System (ADS)

Saleh, Omar A.; Fygenson, Deborah K.; Bertrand, Olivier J. N.; Park, Chang Young

2013-02-01

Research into the mechanics and fluctuations of living cells has revealed the key role played by the cytoskeleton, a gel of stiff filaments driven out of equilibrium by force-generating motor proteins. Inspired by the extraordinary mechanical functions that the cytoskeleton imparts to the cell, we sought to create an artificial gel with similar characteristics. We identified DNA, and DNA-based motor proteins, as functional counterparts to the constituents of the cytoskeleton. We used DNA selfassembly to create a gel, and characterized its fluctuations and mechanics both before and after activation by the motor. We found that certain aspects of the DNA gel quantitatively match those of cytoskeletal networks, indicating the universal features of motor-driven, non-equilibrium networks.

Mussel-inspired histidine-based transient network metal coordination hydrogels

PubMed Central

Fullenkamp, Dominic E.; He, Lihong; Barrett, Devin G.; Burghardt, Wesley R.; Messersmith, Phillip B.

2013-01-01

Transient network hydrogels cross-linked through histidine-divalent cation coordination bonds were studied by conventional rheologic methods using histidine-modified star poly(ethylene glycol) (PEG) polymers. These materials were inspired by the mussel, which is thought to use histidine-metal coordination bonds to impart self-healing properties in the mussel byssal thread. Hydrogel viscoelastic mechanical properties were studied as a function of metal, pH, concentration, and ionic strength. The equilibrium metal-binding constants were determined by dilute solution potentiometric titration of monofunctional histidine-modified methoxy-PEG and were found to be consistent with binding constants of small molecule analogs previously studied. pH-dependent speciation curves were then calculated using the equilibrium constants determined by potentiometric titration, providing insight into the pH dependence of histidine-metal ion coordination and guiding the design of metal coordination hydrogels. Gel relaxation dynamics were found to be uncorrelated with the equilibrium constants measured, but were correlated to the expected coordination bond dissociation rate constants. PMID:23441102

Knowledge Management through the Equilibrium Pattern Model for Learning

NASA Astrophysics Data System (ADS)

Sarirete, Akila; Noble, Elizabeth; Chikh, Azeddine

Contemporary students are characterized by having very applied learning styles and methods of acquiring knowledge. This behavior is consistent with the constructivist models where students are co-partners in the learning process. In the present work the authors developed a new model of learning based on the constructivist theory coupled with the cognitive development theory of Piaget. The model considers the level of learning based on several stages and the move from one stage to another requires learners' challenge. At each time a new concept is introduced creates a disequilibrium that needs to be worked out to return back to its equilibrium stage. This process of "disequilibrium/equilibrium" has been analyzed and validated using a course in computer networking as part of Cisco Networking Academy Program at Effat College, a women college in Saudi Arabia. The model provides a theoretical foundation for teaching especially in a complex knowledge domain such as engineering and can be used in a knowledge economy.

The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate

PubMed Central

Dougoud, Michaël; Rohr, Rudolf P.

2018-01-01

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture. PMID:29420532

Broken Detailed Balance of Filament Dynamics in Active Networks

NASA Astrophysics Data System (ADS)

Gladrow, J.; Fakhri, N.; MacKintosh, F. C.; Schmidt, C. F.; Broedersz, C. P.

2016-06-01

Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

Network Aggregation in Transportation Planning : Volume II : A Fixed Point Method for Treating Traffic Equilibria

DOT National Transportation Integrated Search

1978-04-01

Volume 2 defines a new algorithm for the network equilibrium model that works in the space of path flows and is based on the theory of fixed point method. The goals of the study were broadly defined as the identification of aggregation practices and ...

Performance and Fault-Tolerance of Neural Networks for Optimization

DTIC Science & Technology

1991-06-01

initialization to overcome the unstable equilibrium point at uij--O. "’ used the initial values Vij--0.5+6 with small, uniform noise _10-7򔄮 -7 . The...connectionist network: Investigations of acquired dyslexia . Technical Report CRG-TR-89-3, Dept. of Computer Science, University of Toronto, May 1989

Multiagent Reinforcement Learning With Sparse Interactions by Negotiation and Knowledge Transfer.

PubMed

Zhou, Luowei; Yang, Pei; Chen, Chunlin; Gao, Yang

2017-05-01

Reinforcement learning has significant applications for multiagent systems, especially in unknown dynamic environments. However, most multiagent reinforcement learning (MARL) algorithms suffer from such problems as exponential computation complexity in the joint state-action space, which makes it difficult to scale up to realistic multiagent problems. In this paper, a novel algorithm named negotiation-based MARL with sparse interactions (NegoSIs) is presented. In contrast to traditional sparse-interaction-based MARL algorithms, NegoSI adopts the equilibrium concept and makes it possible for agents to select the nonstrict equilibrium-dominating strategy profile (nonstrict EDSP) or meta equilibrium for their joint actions. The presented NegoSI algorithm consists of four parts: 1) the equilibrium-based framework for sparse interactions; 2) the negotiation for the equilibrium set; 3) the minimum variance method for selecting one joint action; and 4) the knowledge transfer of local Q -values. In this integrated algorithm, three techniques, i.e., unshared value functions, equilibrium solutions, and sparse interactions are adopted to achieve privacy protection, better coordination and lower computational complexity, respectively. To evaluate the performance of the presented NegoSI algorithm, two groups of experiments are carried out regarding three criteria: 1) steps of each episode; 2) rewards of each episode; and 3) average runtime. The first group of experiments is conducted using six grid world games and shows fast convergence and high scalability of the presented algorithm. Then in the second group of experiments NegoSI is applied to an intelligent warehouse problem and simulated results demonstrate the effectiveness of the presented NegoSI algorithm compared with other state-of-the-art MARL algorithms.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Meshless method for solving fixed boundary problem of plasma equilibrium

NASA Astrophysics Data System (ADS)

Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi

2015-07-01

This study solves the Grad-Shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time. Previous studies have utilized a finite element method (FEM) to solve an equilibrium inside the fixed separatrix. In order to avoid difficulties of FEM (such as mesh problem, difficulty of coding, expensive calculation cost), this study focuses on the meshless methods, especially RBF-MFS and KANSA's method to solve the fixed boundary problem. The results showed that CPU time of the meshless methods was ten to one hundred times shorter than that of FEM to obtain the same accuracy.

Self-assembly and transformation of hybrid nano-objects and nanostructures under equilibrium and non-equilibrium conditions

NASA Astrophysics Data System (ADS)

Mann, Stephen

2009-10-01

Understanding how chemically derived processes control the construction and organization of matter across extended and multiple length scales is of growing interest in many areas of materials research. Here we review present equilibrium and non-equilibrium self-assembly approaches to the synthetic construction of discrete hybrid (inorganic-organic) nano-objects and higher-level nanostructured networks. We examine a range of synthetic modalities under equilibrium conditions that give rise to integrative self-assembly (supramolecular wrapping, nanoscale incarceration and nanostructure templating) or higher-order self-assembly (programmed/directed aggregation). We contrast these strategies with processes of transformative self-assembly that use self-organizing media, reaction-diffusion systems and coupled mesophases to produce higher-level hybrid structures under non-equilibrium conditions. Key elements of the constructional codes associated with these processes are identified with regard to existing theoretical knowledge, and presented as a heuristic guideline for the rational design of hybrid nano-objects and nanomaterials.

Computational methods for reactive transport modeling: An extended law of mass-action, xLMA, method for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg; Saar, Martin O.

2016-10-01

We present an extended law of mass-action (xLMA) method for multiphase equilibrium calculations and apply it in the context of reactive transport modeling. This extended LMA formulation differs from its conventional counterpart in that (i) it is directly derived from the Gibbs energy minimization (GEM) problem (i.e., the fundamental problem that describes the state of equilibrium of a chemical system under constant temperature and pressure); and (ii) it extends the conventional mass-action equations with Lagrange multipliers from the Gibbs energy minimization problem, which can be interpreted as stability indices of the chemical species. Accounting for these multipliers enables the method to determine all stable phases without presuming their types (e.g., aqueous, gaseous) or their presence in the equilibrium state. Therefore, the here proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium, which can be single-component phases (e.g., pure solids or liquids) or non-ideal multi-component phases (e.g., aqueous, melts, gaseous, solid solutions, adsorption, or ion exchange). Moreover, our xLMA method requires no technique that tentatively adds or removes reactions based on phase stability indices (e.g., saturation indices for minerals), since the extended mass-action equations are valid even when their corresponding reactions involve unstable species. We successfully apply the proposed method to a reactive transport modeling problem in which we use PHREEQC and GEMS as alternative backends for the calculation of thermodynamic properties such as equilibrium constants of reactions, standard chemical potentials of species, and activity coefficients. Our tests show that our algorithm is efficient and robust for demanding applications, such as reactive transport modeling, where it converges within 1-3 iterations in most cases. The proposed xLMA method is implemented in Reaktoro, a unified open-source framework for modeling chemically reactive systems.

Teaching at the edge of knowledge: Non-equilibrium statistical physics

NASA Astrophysics Data System (ADS)

Schmittmann, Beate

2007-03-01

As physicists become increasingly interested in biological problems, we frequently find ourselves confronted with complex open systems, involving many interacting constituents and characterized by non-vanishing fluxes of mass or energy. Faced with the task of predicting macroscopic behaviors from microscopic information for these non-equilibrium systems, the familiar Gibbs-Boltzmann framework fails. The development of a comprehensive theoretical characterization of non-equilibrium behavior is one of the key challenges of modern condensed matter physics. In its absence, several approaches have been developed, from master equations to thermostatted molecular dynamics, which provide key insights into the rich and often surprising phenomenology of systems far from equilibrium. In my talk, I will address some of these methods, selecting those that are most relevant for a broad range of interdisciplinary problems from biology to traffic, finance, and sociology. The ``portability'' of these methods makes them valuable for graduate students from a variety of disciplines. To illustrate how different methods can complement each other when probing a problem from, e.g., the life sciences, I will discuss some recent attempts at modeling translation, i.e., the process by which the genetic information encoded on an mRNA is translated into the corresponding protein.

Zeroth Law, Entropy, Equilibrium, and All That

NASA Astrophysics Data System (ADS)

Canagaratna, Sebastian G.

2008-05-01

The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced through the zeroth law. The relation between the zeroth law and the second law in the traditional approach to thermodynamics is discussed. It is shown that the traditional approach does not need to appeal to the second law to solve with rigor the type of problems discussed by Gislason and Craig: in problems not involving chemical reaction, the zeroth law and the condition for mechanical equilibrium, complemented by the first law and any necessary equations of state, are sufficient to determine the final state. We have to invoke the second law only if we wish to calculate the change of entropy. Since most students are exposed to a traditional approach to thermodynamics, the examples of Gislason and Craig are re-examined in terms of the traditional formulation. The maximization of the entropy in the final state can be verified in the traditional approach quite directly by the use of the fundamental equations of thermodynamics. This approach uses relatively simple mathematics in as general a setting as possible.

Network-scale dynamics of sediment mixtures: how do tectonics affect surface bed texture and channel slope?

NASA Astrophysics Data System (ADS)

Gasparini, N. M.; Bras, R. L.; Tucker, G. E.

2003-04-01

An alluvial channel's slope and bed texture are intimately linked. Along with fluvial discharge, these variables are the key players in setting alluvial transport rates. We know that both channel slope and mean grain size usually decrease downstream, but how sensitive are these variables to tectonic changes? Are basin concavity and downstream fining drastically disrupted during transitions from one tectonic regime to another? We explore these questions using the CHILD numerical landscape evolution model to generate alluvial networks composed of a sand and gravel mixture. The steady-state and transient patterns of both channel slope and sediment texture are investigated. The steady-state patterns in slope and sediment texture are verified independently by solving the erosion equations under equilibrium conditions, i.e. the case when the erosion rate is equal to the uplift rate across the entire landscape. The inclusion of surface texture as a free parameter (as opposed to just channel slope) leads to some surprising results. In all cases, an increase in uplift rate results in channel beds which are finer at equilibrium (for a given drainage area). Higher uplift rates imply larger equilibrium transport rates; this leads to finer channels that have a smaller critical shear stress to entrain material, and therefore more material can be transported for a given discharge (and channel slope). Changes in equilibrium slopes are less intuitive. An increase in uplift rates can cause channel slopes to increase, remain the same, or decrease, depending on model parameter values. In the surprising case in which equilibrium channel slopes decrease with increasing uplift rates, we suggest that surface texture changes more than compensate for the required increase in transport rates, causing channel slopes to decrease. These results highlight the important role of sediment grain size in determining transport rates and caution us against ignoring this important variable in fluvial networks.

An experimental study of the Online Information Paradox: Does en-route information improve road network performance?

PubMed Central

2017-01-01

This study investigates the empirical presence of a theoretical transportation paradox, defined as the “Online Information Paradox” (OIP). The paradox suggests that, for certain road networks, the provision of online information deteriorate travel conditions for all users of that network relative to the situation where no online information is provided to users. The analytical presence of the paradox was derived for a specific network structure by using two equilibrium models, the first being the Expected User Equilibrium (EUE) solution (no information scenario) and the other being the User Equilibrium with Recourse (UER) solution (with information scenario). An incentivised computerised route choice game was designed using the concepts of experimental economics and administered in a controlled laboratory environment to investigate the physical presence of the paradox. Aggregate statistics of path flows and Total System Travel Costs (TSTC) were used to compare the experimental results with the theoretical findings. A total of 12 groups of 12 participants completed the experiment and the OIP and the occurrence of the OIP being significant was observed in 11 of the 12 cases. Though information increased travel costs for users on average, it reduced the volatility of travel costs experienced in the no information scenario indicating that information can achieve a more reliable system. Further replications of similar experiments and more importantly field based identification of the phenomena will force transport professionals to be aware of the emergence of the paradox. In addition, studies such as this emphasise the need for the adoption of adaptive traffic assignment techniques to appropriately model the acquisition of information on a road network. PMID:28902854

Bilevel formulation of a policy design problem considering multiple objectives and incomplete preferences

NASA Astrophysics Data System (ADS)

Hawthorne, Bryant; Panchal, Jitesh H.

2014-07-01

A bilevel optimization formulation of policy design problems considering multiple objectives and incomplete preferences of the stakeholders is presented. The formulation is presented for Feed-in-Tariff (FIT) policy design for decentralized energy infrastructure. The upper-level problem is the policy designer's problem and the lower-level problem is a Nash equilibrium problem resulting from market interactions. The policy designer has two objectives: maximizing the quantity of energy generated and minimizing policy cost. The stakeholders decide on quantities while maximizing net present value and minimizing capital investment. The Nash equilibrium problem in the presence of incomplete preferences is formulated as a stochastic linear complementarity problem and solved using expected value formulation, expected residual minimization formulation, and the Monte Carlo technique. The primary contributions in this article are the mathematical formulation of the FIT policy, the extension of computational policy design problems to multiple objectives, and the consideration of incomplete preferences of stakeholders for policy design problems.

How time delay and network design shape response patterns in biochemical negative feedback systems.

PubMed

Börsch, Anastasiya; Schaber, Jörg

2016-08-24

Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks. We investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not. Our theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.

The effect of non-equilibrium metal cooling on the interstellar medium

NASA Astrophysics Data System (ADS)

Capelo, Pedro R.; Bovino, Stefano; Lupi, Alessandro; Schleicher, Dominik R. G.; Grassi, Tommaso

2018-04-01

By using a novel interface between the modern smoothed particle hydrodynamics code GASOLINE2 and the chemistry package KROME, we follow the hydrodynamical and chemical evolution of an isolated galaxy. In order to assess the relevance of different physical parameters and prescriptions, we constructed a suite of 10 simulations, in which we vary the chemical network (primordial and metal species), how metal cooling is modelled (non-equilibrium versus equilibrium; optically thin versus thick approximation), the initial gas metallicity (from 10 to 100 per cent solar), and how molecular hydrogen forms on dust. This is the first work in which metal injection from supernovae, turbulent metal diffusion, and a metal network with non-equilibrium metal cooling are self-consistently included in a galaxy simulation. We find that properly modelling the chemical evolution of several metal species and the corresponding non-equilibrium metal cooling has important effects on the thermodynamics of the gas, the chemical abundances, and the appearance of the galaxy: the gas is typically warmer, has a larger molecular-gas mass fraction, and has a smoother disc. We also conclude that, at relatively high metallicity, the choice of molecular-hydrogen formation rates on dust is not crucial. Moreover, we confirm that a higher initial metallicity produces a colder gas and a larger fraction of molecular gas, with the low-metallicity simulation best matching the observed molecular Kennicutt-Schmidt relation. Finally, our simulations agree quite well with observations that link star formation rate to metal emission lines.

Leaf hydraulics II: vascularized tissues.

PubMed

Rockwell, Fulton E; Holbrook, N Michele; Stroock, Abraham D

2014-01-07

Current models of leaf hydration employ an Ohm's law analogy of the leaf as an ideal capacitor, neglecting the resistance to flow between cells, or treat the leaf as a plane sheet with a source of water at fixed potential filling the mid-plane, neglecting the discrete placement of veins as well as their resistance. We develop a model of leaf hydration that considers the average conductance of the vascular network to a representative areole (region bounded by the vascular network), and represent the volume of tissue within the areole as a poroelastic composite of cells and air spaces. Solutions to the 3D flow problem are found by numerical simulation, and these results are then compared to 1D models with exact solutions for a range of leaf geometries, based on a survey of temperate woody plants. We then show that the hydration times given by these solutions are well approximated by a sum of the ideal capacitor and plane sheet times, representing the time for transport through the vasculature and tissue respectively. We then develop scaling factors relating this approximate solution to the 3D model, and examine the dependence of these scaling factors on leaf geometry. Finally, we apply a similar strategy to reduce the dimensions of the steady state problem, in the context of peristomatal transpiration, and consider the relation of transpirational gradients to equilibrium leaf water potential measurements. © 2013 Published by Elsevier Ltd. All rights reserved.

Fluxoids behavior in superconducting ladders

NASA Astrophysics Data System (ADS)

Sharon, Omri J.; Haham, Noam; Shaulov, Avner; Yeshurun, Yosef

2018-03-01

The nature of the interaction between fluxoids and between them and the external magnetic field is studied in one-dimensional superconducting networks. An Ising like expression is derived for the energy of a network revealing that fluxoids behave as repulsively interacting objects driven towards the network center by the effective applied field. Competition between these two interactions determines the equilibrium arrangement of fluxoids in the network as a function of the applied field. It is demonstrated that the fluxoids configurations are not always commensurate to the network symmetry. Incommensurate, degenerated configurations may be formed even in networks with an odd number of loops.

Discrete restricted four-body problem: Existence of proof of equilibria and reproducibility of periodic orbits

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

Minesaki, Yukitaka

2015-01-01

We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog thatmore » preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.« less

Broken detailed balance and non-equilibrium dynamics in living systems: a review

NASA Astrophysics Data System (ADS)

Gnesotto, F. S.; Mura, F.; Gladrow, J.; Broedersz, C. P.

2018-06-01

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Broken detailed balance and non-equilibrium dynamics in living systems: a review.

PubMed

Gnesotto, F S; Mura, F; Gladrow, J; Broedersz, C P

2018-06-01

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Modeling Dark Energy Through AN Ising Fluid with Network Interactions

NASA Astrophysics Data System (ADS)

Luongo, Orlando; Tommasini, Damiano

2014-12-01

We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω0, becomes ω0 = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier-Polarsky-Linder (CPL) parametrization.

The dynamics of financial stability in complex networks

NASA Astrophysics Data System (ADS)

da Cruz, J. P.; Lind, P. G.

2012-08-01

We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange `economic energy', forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability.

Oscillatory Protein Expression Dynamics Endows Stem Cells with Robust Differentiation Potential

PubMed Central

Kaneko, Kunihiko

2011-01-01

The lack of understanding of stem cell differentiation and proliferation is a fundamental problem in developmental biology. Although gene regulatory networks (GRNs) for stem cell differentiation have been partially identified, the nature of differentiation dynamics and their regulation leading to robust development remain unclear. Herein, using a dynamical system modeling cell approach, we performed simulations of the developmental process using all possible GRNs with a few genes, and screened GRNs that could generate cell type diversity through cell-cell interactions. We found that model stem cells that both proliferated and differentiated always exhibited oscillatory expression dynamics, and the differentiation frequency of such stem cells was regulated, resulting in a robust number distribution. Moreover, we uncovered the common regulatory motifs for stem cell differentiation, in which a combination of regulatory motifs that generated oscillatory expression dynamics and stabilized distinct cellular states played an essential role. These findings may explain the recently observed heterogeneity and dynamic equilibrium in cellular states of stem cells, and can be used to predict regulatory networks responsible for differentiation in stem cell systems. PMID:22073296

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

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

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

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Network-Theoretic Modeling of Fluid Flow

DTIC Science & Technology

2015-07-29

Final Report STIR: Network-Theoretic Modeling of Fluid Flow ARO Grant W911NF-14-1-0386 Program manager: Dr. Samuel Stanton ( August 1, 2014–April 30...Morzyński, M., and Comte , P., “A finite-time thermodynamics of unsteady fluid flows,” Journal of Non-Equilibrium Thermody- namics, Vol. 33, No. 2

Dynamic pricing of network goods with boundedly rational consumers.

PubMed

Radner, Roy; Radunskaya, Ami; Sundararajan, Arun

2014-01-07

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational and unable either to pay immediate attention to each price change or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller's optimal price trajectory has the following structure: The price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep the user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product's user base evolving over time and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium and are more consistent with the pricing of network goods observed in practice.

Molecular Mechanisms of Stress-Responsive Changes in Collagen and Elastin Networks in Skin.

PubMed

Aziz, Jazli; Shezali, Hafiz; Radzi, Zamri; Yahya, Noor Azlin; Abu Kassim, Noor Hayaty; Czernuszka, Jan; Rahman, Mohammad Tariqur

2016-01-01

Collagen and elastin networks make up the majority of the extracellular matrix in many organs, such as the skin. The mechanisms which are involved in the maintenance of homeostatic equilibrium of these networks are numerous, involving the regulation of genetic expression, growth factor secretion, signalling pathways, secondary messaging systems, and ion channel activity. However, many factors are capable of disrupting these pathways, which leads to an imbalance of homeostatic equilibrium. Ultimately, this leads to changes in the physical nature of skin, both functionally and cosmetically. Although various factors have been identified, including carcinogenesis, ultraviolet exposure, and mechanical stretching of skin, it was discovered that many of them affect similar components of regulatory pathways, such as fibroblasts, lysyl oxidase, and fibronectin. Additionally, it was discovered that the various regulatory pathways intersect with each other at various stages instead of working independently of each other. This review paper proposes a model which elucidates how these molecular pathways intersect with one another, and how various internal and external factors can disrupt these pathways, ultimately leading to a disruption in collagen and elastin networks. © 2016 S. Karger AG, Basel.

Dynamic pricing of network goods with boundedly rational consumers

PubMed Central

Radner, Roy; Radunskaya, Ami; Sundararajan, Arun

2014-01-01

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational and unable either to pay immediate attention to each price change or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller’s optimal price trajectory has the following structure: The price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep the user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product’s user base evolving over time and consumers basing their choices on a mixture of a myopic and a “stubborn” expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium and are more consistent with the pricing of network goods observed in practice. PMID:24367101

River network and watershed morphology analysis with potential implications towards basin classification

NASA Astrophysics Data System (ADS)

Bugaets, Andrey; Gartsman, Boris; Bugaets, Nadezhda

2013-04-01

Generally, the investigation of river network composition and watersheds morphology (fluvial geomorphology), constituting one of the key patterns of land surface, is a fundamental question of Earth Sciences. Recent ideas in this research field are the equilibrium and optimal, in the sense of minimum energy expenditure, river network evolution under constant or slowly varying conditions (Rodriguez-Iturbe, Rinaldo, 1997). It follows to such network behavior as self-similarity, self-affinity and self-organization. That is to say, under relatively stable conditions the river systems tend to some "good composed" form and vice-versa. Lately appearing global free available detailed DEM covers involve new possibilities in this research field. We develop new methodology and program package for river network structure and watershed morphology detailed analysis on the base of ArcMap tools. Different characteristics of river network (e.g. ordering, coefficients of Horton's laws, Shannon entropy, fractal dimension) and basin morphology (e.g. diagrams of average elevation, slope, width and energy index against distance to outlet along streams) could be calculated to find a good indicators of intensity and non-equilibrium of watershed evolution. Watersheds are non-conservative systems in which energy is dissipated by transporting water and sediment in geomorphic adjustment of the slopes and channels. The problem of estimating the amount of energy expenditure associated with overcoming surface and system resistance is extremely complicated to solve. A simplification on a river network scale is to consider energy expenditure to be primarily associated with friction of the fluid. We propose a new technique to analyze the catchment landforms based on so-called "energy function" that is a distribution of total energy index against distance from outlet. As potential energy of water on the hillslopes is transformed into kinetic energy of the flowing fluid-sediment mixture in the runoff process, the energy is dissipated from the system. The rate of energy dissipation is defined as the work that a fluid element needs to perform to overcome friction at the unit area. Appling the product of local slope and watershed area, i.e. calculating the total energy index at the different distance from outlet, one gets the watershed "energy function" E(x). Application results indicate that the proposed method could be used for watersheds classification, regionalization and paleoreconstructions. NASA-SRTM DEM of 3" resolution has been employed to analyze the 24 watersheds within Amur River Basin with area 20-70 thousand km2 (7-8 order). The study was carried out, in particular, to assess the limitation of SRTM DEM data, especially in flat terrains. The study also revealed that some of regularities investigated are described satisfactorily by well-known simplest model of drainage networks, so-called Peano's basin.

Optimal Policy of Cross-Layer Design for Channel Access and Transmission Rate Adaptation in Cognitive Radio Networks

NASA Astrophysics Data System (ADS)

He, Hao; Wang, Jun; Zhu, Jiang; Li, Shaoqian

2010-12-01

In this paper, we investigate the cross-layer design of joint channel access and transmission rate adaptation in CR networks with multiple channels for both centralized and decentralized cases. Our target is to maximize the throughput of CR network under transmission power constraint by taking spectrum sensing errors into account. In centralized case, this problem is formulated as a special constrained Markov decision process (CMDP), which can be solved by standard linear programming (LP) method. As the complexity of finding the optimal policy by LP increases exponentially with the size of action space and state space, we further apply action set reduction and state aggregation to reduce the complexity without loss of optimality. Meanwhile, for the convenience of implementation, we also consider the pure policy design and analyze the corresponding characteristics. In decentralized case, where only local information is available and there is no coordination among the CR users, we prove the existence of the constrained Nash equilibrium and obtain the optimal decentralized policy. Finally, in the case that the traffic load parameters of the licensed users are unknown for the CR users, we propose two methods to estimate the parameters for two different cases. Numerical results validate the theoretic analysis.

Security Investment in Contagious Networks.

PubMed

Hasheminasab, Seyed Alireza; Tork Ladani, Behrouz

2018-01-16

Security of the systems is normally interdependent in such a way that security risks of one part affect other parts and threats spread through the vulnerable links in the network. So, the risks of the systems can be mitigated through investments in the security of interconnecting links. This article takes an innovative look at the problem of security investment of nodes on their vulnerable links in a given contagious network as a game-theoretic model that can be applied to a variety of applications including information systems. In the proposed game model, each node computes its corresponding risk based on the value of its assets, vulnerabilities, and threats to determine the optimum level of security investments on its external links respecting its limited budget. Furthermore, direct and indirect nonlinear influences of a node's security investment on the risks of other nodes are considered. The existence and uniqueness of the game's Nash equilibrium in the proposed game are also proved. Further analysis of the model in a practical case revealed that taking advantage of the investment effects of other players, perfectly rational players (i.e., those who use the utility function of the proposed game model) make more cost-effective decisions than selfish nonrational or semirational players. © 2018 Society for Risk Analysis.

Addition to the Lewis Chemical Equilibrium Program to allow computation from coal composition data

NASA Technical Reports Server (NTRS)

Sevigny, R.

1980-01-01

Changes made to the Coal Gasification Project are reported. The program was developed by equilibrium combustion in rocket engines. It can be applied directly to the entrained flow coal gasification process. The particular problem addressed is the reduction of the coal data into a form suitable to the program, since the manual process is involved and error prone. A similar problem in relating the normal output of the program to parameters meaningful to the coal gasification process is also addressed.

What Can Reinforcement Learning Teach Us About Non-Equilibrium Quantum Dynamics

NASA Astrophysics Data System (ADS)

Bukov, Marin; Day, Alexandre; Sels, Dries; Weinberg, Phillip; Polkovnikov, Anatoli; Mehta, Pankaj

Equilibrium thermodynamics and statistical physics are the building blocks of modern science and technology. Yet, our understanding of thermodynamic processes away from equilibrium is largely missing. In this talk, I will reveal the potential of what artificial intelligence can teach us about the complex behaviour of non-equilibrium systems. Specifically, I will discuss the problem of finding optimal drive protocols to prepare a desired target state in quantum mechanical systems by applying ideas from Reinforcement Learning [one can think of Reinforcement Learning as the study of how an agent (e.g. a robot) can learn and perfect a given policy through interactions with an environment.]. The driving protocols learnt by our agent suggest that the non-equilibrium world features possibilities easily defying intuition based on equilibrium physics.

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

NASA Astrophysics Data System (ADS)

Steenbakkers, Rudi J. A.; Tzoumanekas, Christos; Li, Ying; Liu, Wing Kam; Kröger, Martin; Schieber, Jay D.

2014-01-01

We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi-Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.

A Computational Method for Determining the Equilibrium Composition and Product Temperature in a LH2/LOX Combustor

NASA Technical Reports Server (NTRS)

Sozen, Mehmet

2003-01-01

In what follows, the model used for combustion of liquid hydrogen (LH2) with liquid oxygen (LOX) using chemical equilibrium assumption, and the novel computational method developed for determining the equilibrium composition and temperature of the combustion products by application of the first and second laws of thermodynamics will be described. The modular FORTRAN code developed as a subroutine that can be incorporated into any flow network code with little effort has been successfully implemented in GFSSP as the preliminary runs indicate. The code provides capability of modeling the heat transfer rate to the coolants for parametric analysis in system design.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Stability analysis of an equilibrium position in the photogravitational Sitnikov problem

NASA Astrophysics Data System (ADS)

Bardin, B. S.; Avdushkin, A. N.

2018-05-01

We deal with the so-called photogravitational Sitnikov problem, that is we consider rectilinear motion of a body of infinitesimal mass in a field of two graviting and radiating primaries, which have equal masses and act on the body with equal repulsive forces of radiation pressure. The body has equilibrium position in the barycenter of the system. In this paper the stability of the equilibrium position is investigated in detail. In particular, by the study of the linearized system we have found in the plane of parameter values the regions of instability. It appears that the instability regions alternate with stability regions and become very narrower when the eccentricity of the primaries orbits approaches to 1. Outside the instability regions we have performed non-linear stability analysis and shown that the stability of the equilibrium position in the sense of Lyapunov takes place both in resonant and non-resonant cases. The results of the study are represented in a form of stability diagram.

Unsteady Computational Tests of a Non-Equilibrium

NASA Astrophysics Data System (ADS)

Jirasek, Adam; Hamlington, Peter; Lofthouse, Andrew; Usafa Collaboration; Cu Boulder Collaboration

2017-11-01

A non-equilibrium turbulence model is assessed on simulations of three practically-relevant unsteady test cases; oscillating channel flow, transonic flow around an oscillating airfoil, and transonic flow around the Benchmark Super-Critical Wing. The first case is related to piston-driven flows while the remaining cases are relevant to unsteady aerodynamics at high angles of attack and transonic speeds. Non-equilibrium turbulence effects arise in each of these cases in the form of a lag between the mean strain rate and Reynolds stresses, resulting in reduced kinetic energy production compared to classical equilibrium turbulence models that are based on the gradient transport (or Boussinesq) hypothesis. As a result of the improved representation of unsteady flow effects, the non-equilibrium model provides substantially better agreement with available experimental data than do classical equilibrium turbulence models. This suggests that the non-equilibrium model may be ideally suited for simulations of modern high-speed, high angle of attack aerodynamics problems.

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

PubMed Central

Liebermeister, Wolfram; Klipp, Edda

2006-01-01

Background Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. Results We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. Conclusion Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases. PMID:17173669

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

NASA Astrophysics Data System (ADS)

Tice, Ian

2018-04-01

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

Thermodynamic equilibrium with acceleration and the Unruh effect

NASA Astrophysics Data System (ADS)

Becattini, F.

2018-04-01

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature TU=A /2 π where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.

Computations of ideal and real gas high altitude plume flows

NASA Technical Reports Server (NTRS)

Feiereisen, William J.; Venkatapathy, Ethiraj

1988-01-01

In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

Comparison between different adsorption-desorption kinetics schemes in two dimensional lattice gas

NASA Astrophysics Data System (ADS)

Huespe, V. J.; Belardinelli, R. E.; Pereyra, V. D.; Manzi, S. J.

2017-12-01

Monte Carlo simulation is used to study the adsorption-desorption kinetics in the framework of the kinetic lattice-gas model. Three schemes of the so-called hard dynamics and five schemes of the so called soft dynamics were used for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and non-equilibrium observable, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and non-equilibrium observables have several problems.

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

Cascading Failures as Continuous Phase-Space Transitions

DOE PAGES

Yang, Yang; Motter, Adilson E.

2017-12-14

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. We derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-likemore » function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.« less

Cascading Failures as Continuous Phase-Space Transitions

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

Yang, Yang; Motter, Adilson E.

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. We derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-likemore » function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.« less

Similarities and Dissimilarities in Coauthorship Networks: Gestalt Theory as Explanation for Well-Ordered Collaboration Structures and Production of Scientific Literature.

ERIC Educational Resources Information Center

Kretschmer, Hildrun

2002-01-01

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

Weak turbulence theory for beam-plasma interaction

NASA Astrophysics Data System (ADS)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Opinion diversity and community formation in adaptive networks

NASA Astrophysics Data System (ADS)

Yu, Y.; Xiao, G.; Li, G.; Tay, W. P.; Teoh, H. F.

2017-10-01

It is interesting and of significant importance to investigate how network structures co-evolve with opinions. In this article, we show that, a simple model integrating consensus formation, link rewiring, and opinion change allows complex system dynamics to emerge, driving the system into a dynamic equilibrium with the co-existence of diversified opinions. Specifically, similar opinion holders may form into communities yet with no strict community consensus; and rather than being separated into disconnected communities, different communities are connected by a non-trivial proportion of inter-community links. More importantly, we show that the complex dynamics may lead to different numbers of communities at the steady state with a given tolerance between different opinion holders. We construct a framework for theoretically analyzing the co-evolution process. Theoretical analysis and extensive simulation results reveal some useful insights into the complex co-evolution process, including the formation of dynamic equilibrium, the transition between different steady states with different numbers of communities, and the dynamics between opinion distribution and network modularity.

Modeling quantum cascade lasers: Coupled electron and phonon transport far from equilibrium and across disparate spatial scales

DOE PAGES

Shi, Y. B.; Mei, S.; Jonasson, O.; ...

2016-12-28

Quantum cascade lasers (QCLs) are high-power coherent light sources in the midinfrared and terahertz parts of the electromagnetic spectrum. They are devices in which the electronic and lattice systems are far from equilibrium, strongly coupled to one another, and the problem bridges disparate spatial scales. Here, we present our ongoing work on the multiphysics and multiscale simulation of far-from-equilibrium transport of charge and heat in midinfrared QCLs.

Thermodynamic evolution far from equilibrium

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.

2018-05-01

The presented model of thermodynamic evolution of an open system far from equilibrium is based on the modern results of nonequilibrium statistical mechanics, the nonlocal theory of nonequilibrium transport developed by the author and the Speed Gradient principle introduced in the theory of adaptive control. Transition to a description of the system internal structure evolution at the mesoscopic level allows a new insight at the stability problem of non-equilibrium processes. The new model is used in a number of specific tasks.

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids.

PubMed

Baaske, Philipp; Bataller, Henri; Braibanti, Marco; Carpineti, Marina; Cerbino, Roberto; Croccolo, Fabrizio; Donev, Aleksandar; Köhler, Werner; Ortiz de Zárate, José M; Vailati, Alberto

2016-12-01

Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q -4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.

Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers

NASA Astrophysics Data System (ADS)

Kawai, Soshi; Larsson, Johan

2013-01-01

A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on equilibrium boundary layers and a non-equilibrium shock/boundary-layer interaction problem. The proposed method builds on the prior non-equilibrium wall-models of Balaras et al. [AIAA J. 34, 1111-1119 (1996)], 10.2514/3.13200 and Wang and Moin [Phys. Fluids 14, 2043-2051 (2002)], 10.1063/1.1476668: the failure of these wall-models to accurately predict the skin friction in equilibrium boundary layers is shown and analyzed, and an improved wall-model that solves this issue is proposed. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer, the grid resolution, and the resolution-characteristics of numerical methods. The proposed model yields accurate resolved turbulence, both in terms of structure and statistics for both the equilibrium and non-equilibrium flows without the use of ad hoc corrections. Crucially, the model accurately predicts the skin friction, something that existing non-equilibrium wall-models fail to do robustly.

Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Arik, Sabri

2006-02-01

This Letter presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all bounded continuous non-monotonic neuron activation functions. The results are also compared with the previous results derived in the literature.

Neural network evaluation of tokamak current profiles for real time control

NASA Astrophysics Data System (ADS)

Wróblewski, Dariusz

1997-02-01

Active feedback control of the current profile, requiring real-time determination of the current profile parameters, is envisioned for tokamaks operating in enhanced confinement regimes. The distribution of toroidal current in a tokamak is now routinely evaluated based on external (magnetic probes, flux loops) and internal (motional Stark effect) measurements of the poloidal magnetic field. However, the analysis involves reconstruction of magnetohydrodynamic equilibrium and is too intensive computationally to be performed in real time. In the present study, a neural network is used to provide a mapping from the magnetic measurements (internal and external) to selected parameters of the safety factor profile. The single-pass, feedforward calculation of output of a trained neural network is very fast, making this approach particularly suitable for real-time applications. The network was trained on a large set of simulated equilibrium data for the DIII-D tokamak. The database encompasses a large variety of current profiles including the hollow current profiles important for reversed central shear operation. The parameters of safety factor profile (a quantity related to the current profile through the magnetic field tilt angle) estimated by the neural network include central safety factor, q0, minimum value of q, qmin, and the location of qmin. Very good performance of the trained neural network both for simulated test data and for experimental datais demonstrated.

Neural network evaluation of tokamak current profiles for real time control (abstract)

NASA Astrophysics Data System (ADS)

Wróblewski, Dariusz

1997-01-01

Active feedback control of the current profile, requiring real-time determination of the current profile parameters, is envisioned for tokamaks operating in enhanced confinement regimes. The distribution of toroidal current in a tokamak is now routinely evaluated based on external (magnetic probes, flux loops) and internal (motional Stark effect) measurements of the poloidal magnetic field. However, the analysis involves reconstruction of magnetohydrodynamic equilibrium and is too intensive computationally to be performed in real time. In the present study, a neural network is used to provide a mapping from the magnetic measurements (internal and external) to selected parameters of the safety factor profile. The single-pass, feedforward calculation of output of a trained neural network is very fast, making this approach particularly suitable for real-time applications. The network was trained on a large set of simulated equilibrium data for the DIII-D tokamak. The database encompasses a large variety of current profiles including the hollow current profiles important for reversed central shear operation. The parameters of safety factor profile (a quantity related to the current profile through the magnetic field tilt angle) estimated by the neural network include central safety factor, q0, minimum value of q, qmin, and the location of qmin. Very good performance of the trained neural network both for simulated test data and for experimental data is demonstrated.

Computer program determines chemical composition of physical system at equilibrium

NASA Technical Reports Server (NTRS)

Kwong, S. S.

1966-01-01

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Equilibrium-Staged Separations Using Matlab and Mathematica

ERIC Educational Resources Information Center

Binous, Housam

2008-01-01

We show a new approach, based on the utilization of Matlab and Mathematica, for solving liquid-liquid extraction and binary distillation problems. In addition, the author shares his experience using these two softwares to teach equilibrium staged separations at the National Institute of Applied Sciences and Technology. (Contains 7 figures.)

How Stable Is Stable?

ERIC Educational Resources Information Center

Baehr, Marie

1994-01-01

Provides a problem where students are asked to find the point at which a soda can floating in some liquid changes its equilibrium between stable and unstable as the soda is removed from the can. Requires use of Newton's first law, center of mass, Archimedes' principle, stable and unstable equilibrium, and buoyant force position. (MVL)

Reversible first-order transition in Pauli percolation

NASA Astrophysics Data System (ADS)

Maksymenko, Mykola; Moessner, Roderich; Shtengel, Kirill

2015-06-01

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyze a new percolation problem in which the first-order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight W (n )=n +1 for a cluster of size n . This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle and their reach in practice.

Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis

NASA Astrophysics Data System (ADS)

De Martino, D.

2016-02-01

In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. Coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.

Bistability and delay-induced stability switches in a cancer network with the regulation of microRNA

NASA Astrophysics Data System (ADS)

Song, Yongli; Cao, Xin; Zhang, Tonghua

2018-01-01

In this paper, we are concerned with a cancer network including a protein module and a corresponding microRNA cluster that inhibits the synthesis of proteins. The existence of multiple steady states and their stability depending on the parameters are firstly determined. Bistability and dependency on the parameters, Hopf bifurcations and the corresponding properties like direction and stability of Hopf bifurcations are determined by computing the normal form on the center manifold. Then, the role of the delay in the process of synthesis of the protein is investigated. We show that the delay can stabilize the unstable equilibrium and destabilize the stable equilibrium. Some simulations are carried out to numerically illustrate the obtained theoretical results. Finally, the biological interpretation of the theoretical results is discussed.

Self-Learning Intelligent Agents for Dynamic Traffic Routing on Transportation Networks

NASA Astrophysics Data System (ADS)

Sadek, Add; Basha, Nagi

Intelligent Transportation Systems (ITS) are designed to take advantage of recent advances in communications, electronics, and Information Technology in improving the efficiency and safety of transportation systems. Among the several ITS applications is the notion of Dynamic Traffic Routing (DTR), which involves generating "optimal" routing recommendations to drivers with the aim of maximizing network utilizing. In this paper, we demonstrate the feasibility of using a self-learning intelligent agent to solve the DTR problem to achieve traffic user equilibrium in a transportation network. The core idea is to deploy an agent to a simulation model of a highway. The agent then learns by itself by interacting with the simulation model. Once the agent reaches a satisfactory level of performance, it can then be deployed to the real-world, where it would continue to learn how to refine its control policies over time. To test this concept in this paper, the Cell Transmission Model (CTM) developed by Carlos Daganzo of the University of California at Berkeley is used to simulate a simple highway with two main alternative routes. With the model developed, a Reinforcement Learning Agent (RLA) is developed to learn how to best dynamically route traffic, so as to maximize the utilization of existing capacity. Preliminary results obtained from our experiments are promising. RL, being an adaptive online learning technique, appears to have a great potential for controlling a stochastic dynamic systems such as a transportation system. Furthermore, the approach is highly scalable and applicable to a variety of networks and roadways.

Rheological Predictions of Network Systems Swollen with Entangled Solvent

DTIC Science & Technology

2014-04-01

represent binary entanglements and the crosses represent cross-links. Both of which are fixed in space for Green– Kubo calculations or moved affinely for...Two types of calculations can be performed, equilibrium (or Green– Kubo ) calculations in which the rate of deformation tensor21,22 is set to zero and the...autocorrelation function of stress at equilibrium is followed; or flow calculations in which a specific flow field is applied and the stress as a

Self-Organized Percolation and Critical Sales Fluctuations

NASA Astrophysics Data System (ADS)

Weisbuch, Gérard; Solomon, Sorin

There is a discrepancy between the standard view of equilibrium through price adjustment in economics and the observation of large fluctuations in stock markets. We study here a simple model where agents decisions not only depend upon their individual preferences but also upon information obtained from their neighbors in a social network. The model shows that information diffusion coupled to the adjustment process drives the system to criticality with large fluctuations rather than converging smoothly to equilibrium.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

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

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

Synchrony-induced modes of oscillation of a neural field model

NASA Astrophysics Data System (ADS)

Esnaola-Acebes, Jose M.; Roxin, Alex; Avitabile, Daniele; Montbrió, Ernest

2017-11-01

We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

Synchrony-induced modes of oscillation of a neural field model.

PubMed

Esnaola-Acebes, Jose M; Roxin, Alex; Avitabile, Daniele; Montbrió, Ernest

2017-11-01

We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

Agent-based spin model for financial markets on complex networks: Emergence of two-phase phenomena

NASA Astrophysics Data System (ADS)

Kim, Yup; Kim, Hong-Joo; Yook, Soon-Hyung

2008-09-01

We study a microscopic model for financial markets on complex networks, motivated by the dynamics of agents and their structure of interaction. The model consists of interacting agents (spins) with local ferromagnetic coupling and global antiferromagnetic coupling. In order to incorporate more realistic situations, we also introduce an external field which changes in time. From numerical simulations, we find that the model shows two-phase phenomena. When the local ferromagnetic interaction is balanced with the global antiferromagnetic interaction, the resulting return distribution satisfies a power law having a single peak at zero values of return, which corresponds to the market equilibrium phase. On the other hand, if local ferromagnetic interaction is dominant, then the return distribution becomes double peaked at nonzero values of return, which characterizes the out-of-equilibrium phase. On random networks, the crossover between two phases comes from the competition between two different interactions. However, on scale-free networks, not only the competition between the different interactions but also the heterogeneity of underlying topology causes the two-phase phenomena. Possible relationships between the critical phenomena of spin system and the two-phase phenomena are discussed.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters

NASA Astrophysics Data System (ADS)

Arias, E.; Florez, E.; Pérez-Torres, J. F.

2017-06-01

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported.

Effect of Stellar Wind and Poynting-Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting-Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L 1, L 2 and L 3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov's first method of stability.

Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters.

PubMed

Arias, E; Florez, E; Pérez-Torres, J F

2017-06-28

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu 7 , Cu 9 , and Cu 11 as benchmark systems, and Cu 38 and Ni 9 as novel systems. New equilibrium structures for Cu 9 , Cu 11 , Cu 38 , and Ni 9 are reported.

Global robust stability of bidirectional associative memory neural networks with multiple time delays.

PubMed

Senan, Sibel; Arik, Sabri

2007-10-01

This correspondence presents a sufficient condition for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point for bidirectional associative memory neural networks with discrete time delays. The results impose constraint conditions on the network parameters of the neural system independently of the delay parameter, and they are applicable to all bounded continuous nonmonotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.

Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

NASA Astrophysics Data System (ADS)

Tallury, Syamal S.; Mineart, Kenneth P.; Woloszczuk, Sebastian; Williams, David N.; Thompson, Russell B.; Pasquinelli, Melissa A.; Banaszak, Michal; Spontak, Richard J.

2014-09-01

Molecularly asymmetric triblock copolymers progressively grown from a parent diblock copolymer can be used to elucidate the phase and property transformation from diblock to network-forming triblock copolymer. In this study, we use several theoretical formalisms and simulation methods to examine the molecular-level characteristics accompanying this transformation, and show that reported macroscopic-level transitions correspond to the onset of an equilibrium network. Midblock conformational fractions and copolymer morphologies are provided as functions of copolymer composition and temperature.

Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

PubMed

Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

2011-01-28

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks.

PubMed

Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia

2018-07-14

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

Fixed and equilibrium endpoint problems in uneven-aged stand management

Treesearch

Robert G. Haight; Wayne M. Getz

1987-01-01

Studies in uneven-aged management have concentrated on the determination of optimal steady-state diameter distribution harvest policies for single and mixed species stands. To find optimal transition harvests for irregular stands, either fixed endpoint or equilibrium endpoint constraints can be imposed after finite transition periods. Penalty function and gradient...

University Policies under Varying Market Conditions: The Training of Electrical Engineers.

ERIC Educational Resources Information Center

Eckstein, Zvi; And Others

1988-01-01

Analyzes an Israeli university's problem in optimizing the quality and quantity of electrical engineers in response to fluctuating enrollment. An equilibrium model considers the effect of students' occupation choice and the university's decision on the current and future demand and supply of engineers, in order to predict the equilibrium number of…

Ergodicity in natural earthquake fault networks

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

Tiampo, K. F.; Rundle, J. B.; Holliday, J.

2007-06-15

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F.more » Tiampo, J. B. Rundle, W. Klein, J. S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal evolution.« less

Equilibrium point control of a monkey arm simulator by a fast learning tree structured artificial neural network.

PubMed

Dornay, M; Sanger, T D

1993-01-01

A planar 17 muscle model of the monkey's arm based on realistic biomechanical measurements was simulated on a Symbolics Lisp Machine. The simulator implements the equilibrium point hypothesis for the control of arm movements. Given initial and final desired positions, it generates a minimum-jerk desired trajectory of the hand and uses the backdriving algorithm to determine an appropriate sequence of motor commands to the muscles (Flash 1987; Mussa-Ivaldi et al. 1991; Dornay 1991b). These motor commands specify a temporal sequence of stable (attractive) equilibrium positions which lead to the desired hand movement. A strong disadvantage of the simulator is that it has no memory of previous computations. Determining the desired trajectory using the minimum-jerk model is instantaneous, but the laborious backdriving algorithm is slow, and can take up to one hour for some trajectories. The complexity of the required computations makes it a poor model for biological motor control. We propose a computationally simpler and more biologically plausible method for control which achieves the benefits of the backdriving algorithm. A fast learning, tree-structured network (Sanger 1991c) was trained to remember the knowledge obtained by the backdriving algorithm. The neural network learned the nonlinear mapping from a 2-dimensional cartesian planar hand position (x,y) to a 17-dimensional motor command space (u1, . . ., u17). Learning 20 training trajectories, each composed of 26 sample points [[x,y], [u1, . . ., u17] took only 20 min on a Sun-4 Sparc workstation. After the learning stage, new, untrained test trajectories as well as the original trajectories of the hand were given to the neural network as input. The network calculated the required motor commands for these movements. The resulting movements were close to the desired ones for both the training and test cases.

One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet.

PubMed

Harrison, Michael G; Neukirch, Thomas

2009-04-03

In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.

Congestion schemes and Nash equilibrium in complex networks

NASA Astrophysics Data System (ADS)

Almendral, Juan A.; López, Luis; Cholvi, Vicent; Sanjuán, Miguel A. F.

2005-09-01

Whenever a common resource is scarce, a set of rules are needed to share it in a fairly way. However, most control schemes assume that users will behave in a cooperative way, without taking care of guaranteeing that they will not act in a selfish manner. Then, a fundamental issue is to evaluate the impact of cheating. From the point of view of game theory, a Nash equilibrium implies that nobody can take advantage by unilaterally deviating from this stable state, even in the presence of selfish users. In this paper we prove that any efficient Nash equilibrium strongly depends on the number of users, if the control scheme policy does not record their previous behavior. Since this is a common pattern in real situations, this implies that the system would be always out of equilibrium. Consequently, this result proves that, in practice, oblivious control schemes must be improved to cope with selfish users.

Transportation Network Analysis and Decomposition Methods

DOT National Transportation Integrated Search

1978-03-01

The report outlines research in transportation network analysis using decomposition techniques as a basis for problem solutions. Two transportation network problems were considered in detail: a freight network flow problem and a scheduling problem fo...

How do video-based demonstration assessment tasks affect problem-solving process, test anxiety, chemistry anxiety and achievement in general chemistry students?

NASA Astrophysics Data System (ADS)

Terrell, Rosalind Stephanie

2001-12-01

Because paper-and-pencil testing provides limited knowledge about what students know about chemical phenomena, we have developed video-based demonstrations to broaden measurement of student learning. For example, students might be shown a video demonstrating equilibrium shifts. Two methods for viewing equilibrium shifts are changing the concentration of the reactants and changing the temperature of the system. The students are required to combine the data collected from the video and their knowledge of chemistry to determine which way the equilibrium shifts. Video-based demonstrations are important techniques for measuring student learning because they require students to apply conceptual knowledge learned in class to a specific chemical problem. This study explores how video-based demonstration assessment tasks affect problem-solving processes, test anxiety, chemistry anxiety and achievement in general chemistry students. Several instruments were used to determine students' knowledge about chemistry, students' test and chemistry anxiety before and after treatment. Think-aloud interviews were conducted to determine students' problem-solving processes after treatment. The treatment group was compared to a control group and a group watching video demonstrations. After treatment students' anxiety increased and achievement decreased. There were also no significant differences found in students' problem-solving processes following treatment. These negative findings may be attributed to several factors that will be explored in this study.

Equilibrium Propagation: Bridging the Gap between Energy-Based Models and Backpropagation

PubMed Central

Scellier, Benjamin; Bengio, Yoshua

2017-01-01

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal “back-propagated” during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task. PMID:28522969

Network planning under uncertainties

NASA Astrophysics Data System (ADS)

Ho, Kwok Shing; Cheung, Kwok Wai

2008-11-01

One of the main focuses for network planning is on the optimization of network resources required to build a network under certain traffic demand projection. Traditionally, the inputs to this type of network planning problems are treated as deterministic. In reality, the varying traffic requirements and fluctuations in network resources can cause uncertainties in the decision models. The failure to include the uncertainties in the network design process can severely affect the feasibility and economics of the network. Therefore, it is essential to find a solution that can be insensitive to the uncertain conditions during the network planning process. As early as in the 1960's, a network planning problem with varying traffic requirements over time had been studied. Up to now, this kind of network planning problems is still being active researched, especially for the VPN network design. Another kind of network planning problems under uncertainties that has been studied actively in the past decade addresses the fluctuations in network resources. One such hotly pursued research topic is survivable network planning. It considers the design of a network under uncertainties brought by the fluctuations in topology to meet the requirement that the network remains intact up to a certain number of faults occurring anywhere in the network. Recently, the authors proposed a new planning methodology called Generalized Survivable Network that tackles the network design problem under both varying traffic requirements and fluctuations of topology. Although all the above network planning problems handle various kinds of uncertainties, it is hard to find a generic framework under more general uncertainty conditions that allows a more systematic way to solve the problems. With a unified framework, the seemingly diverse models and algorithms can be intimately related and possibly more insights and improvements can be brought out for solving the problem. This motivates us to seek a generic framework for solving the network planning problem under uncertainties. In addition to reviewing the various network planning problems involving uncertainties, we also propose that a unified framework based on robust optimization can be used to solve a rather large segment of network planning problem under uncertainties. Robust optimization is first introduced in the operations research literature and is a framework that incorporates information about the uncertainty sets for the parameters in the optimization model. Even though robust optimization is originated from tackling the uncertainty in the optimization process, it can serve as a comprehensive and suitable framework for tackling generic network planning problems under uncertainties. In this paper, we begin by explaining the main ideas behind the robust optimization approach. Then we demonstrate the capabilities of the proposed framework by giving out some examples of how the robust optimization framework can be applied to the current common network planning problems under uncertain environments. Next, we list some practical considerations for solving the network planning problem under uncertainties with the proposed framework. Finally, we conclude this article with some thoughts on the future directions for applying this framework to solve other network planning problems.

Spreading dynamics of a SIQRS epidemic model on scale-free networks

NASA Astrophysics Data System (ADS)

Li, Tao; Wang, Yuanmei; Guan, Zhi-Hong

2014-03-01

In order to investigate the influence of heterogeneity of the underlying networks and quarantine strategy on epidemic spreading, a SIQRS epidemic model on the scale-free networks is presented. Using the mean field theory the spreading dynamics of the virus is analyzed. The spreading critical threshold and equilibria are derived. Theoretical results indicate that the critical threshold value is significantly dependent on the topology of the underlying networks and quarantine rate. The existence of equilibria is determined by threshold value. The stability of disease-free equilibrium and the permanence of the disease are proved. Numerical simulations confirmed the analytical results.

The analysis of HIV/AIDS drug-resistant on networks

NASA Astrophysics Data System (ADS)

Liu, Maoxing

2014-01-01

In this paper, we present an Human Immunodeficiency Virus (HIV)/Acquired Immune Deficiency Syndrome (AIDS) drug-resistant model using an ordinary differential equation (ODE) model on scale-free networks. We derive the threshold for the epidemic to be zero in infinite scale-free network. We also prove the stability of disease-free equilibrium (DFE) and persistence of HIV/AIDS infection. The effects of two immunization schemes, including proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy compare favorably to a proportional condom using has prominent effect to control HIV/AIDS spread on scale-free networks.

Social Interactions under Incomplete Information: Games, Equilibria, and Expectations

NASA Astrophysics Data System (ADS)

Yang, Chao

My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter "A Tobit Model with Social Interactions under Incomplete Information", is an application of the first chapter to censored outcomes, corresponding to the situation when agents" behaviors are subjected to some binding restrictions. In an interesting empirical analysis for property tax rates set by North Carolina municipal governments, it is found that there is a significant positive correlation among near-by municipalities. Additionally, some private information about its own residents is used by a municipal government to predict others' tax rates, which enriches current empirical work about tax competition. The third chapter, "Social Interactions under Incomplete Information with Multiple Equilibria", extends the first chapter by investigating effective estimation methods when the condition for a unique equilibrium may not be satisfied. With multiple equilibria, the previous model is incomplete due to the unobservable equilibrium selection. Neither conventional likelihoods nor moment conditions can be used to estimate parameters without further specifications. Although there are some solutions to this issue in the current literature, they are based on strong assumptions such as agents with the same observable characteristics play the same strategy. This paper relaxes those assumptions and extends the all-solution method used to estimate discrete choice games to a setting with both discrete and continuous choices, bounded and unbounded outcomes, and a general form of incomplete information, where the existence of a pure strategy equilibrium has been an open question for a long time. By the use of differential topology and functional analysis, it is found that when all exogenous characteristics are public information, there are a finite number of equilibria. With privately known exogenous characteristics, the equilbria can be represented by a compact set in a Banach space and be approximated by a finite set. As a result, a finite-state probability mass function can be used to specify a probability measure for equilibrium selection, which completes the model. From Monte Carlo experiments about two types of binary choice models, it is found that assuming equilibrium uniqueness can bring in estimation biases when the true value of interaction intensity is large and there are multiple equilibria in the data generating process.

Non-additive dissipation in open quantum networks out of equilibrium

NASA Astrophysics Data System (ADS)

Mitchison, Mark T.; Plenio, Martin B.

2018-03-01

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

Chemical reaction networks as a model to describe UVC- and radiolytically-induced reactions of simple compounds.

PubMed

Dondi, Daniele; Merli, Daniele; Albini, Angelo; Zeffiro, Alberto; Serpone, Nick

2012-05-01

When a chemical system is submitted to high energy sources (UV, ionizing radiation, plasma sparks, etc.), as is expected to be the case of prebiotic chemistry studies, a plethora of reactive intermediates could form. If oxygen is present in excess, carbon dioxide and water are the major products. More interesting is the case of reducing conditions where synthetic pathways are also possible. This article examines the theoretical modeling of such systems with random-generated chemical networks. Four types of random-generated chemical networks were considered that originated from a combination of two connection topologies (viz., Poisson and scale-free) with reversible and irreversible chemical reactions. The results were analyzed taking into account the number of the most abundant products required for reaching 50% of the total number of moles of compounds at equilibrium, as this may be related to an actual problem of complex mixture analysis. The model accounts for multi-component reaction systems with no a priori knowledge of reacting species and the intermediates involved if system components are sufficiently interconnected. The approach taken is relevant to an earlier study on reactions that may have occurred in prebiotic systems where only a few compounds were detected. A validation of the model was attained on the basis of results of UVC and radiolytic reactions of prebiotic mixtures of low molecular weight compounds likely present on the primeval Earth.

Region stability analysis and tracking control of memristive recurrent neural network.

PubMed

Bao, Gang; Zeng, Zhigang; Shen, Yanjun

2018-02-01

Memristor is firstly postulated by Leon Chua and realized by Hewlett-Packard (HP) laboratory. Research results show that memristor can be used to simulate the synapses of neurons. This paper presents a class of recurrent neural network with HP memristors. Firstly, it shows that memristive recurrent neural network has more compound dynamics than the traditional recurrent neural network by simulations. Then it derives that n dimensional memristive recurrent neural network is composed of [Formula: see text] sub neural networks which do not have a common equilibrium point. By designing the tracking controller, it can make memristive neural network being convergent to the desired sub neural network. At last, two numerical examples are given to verify the validity of our result. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the stability, storage capacity, and design of nonlinear continuous neural networks

NASA Technical Reports Server (NTRS)

Guez, Allon; Protopopsecu, Vladimir; Barhen, Jacob

1988-01-01

The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the post synaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3N equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. Moreover, it is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.

Fokker-Planck description of conductance-based integrate-and-fire neuronal networks

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

Kovacic, Gregor; Tao, Louis; Rangan, Aaditya V.

2009-08-15

Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and verified via direct numerical simulations.

Degradable transportation network with the addition of electric vehicles: Network equilibrium analysis

PubMed Central

Zhang, Rui; Yao, Enjian; Yang, Yang

2017-01-01

Introducing electric vehicles (EVs) into urban transportation network brings higher requirement on travel time reliability and charging reliability. Specifically, it is believed that travel time reliability is a key factor influencing travelers’ route choice. Meanwhile, due to the limited cruising range, EV drivers need to better learn about the required energy for the whole trip to make decisions about whether charging or not and where to charge (i.e., charging reliability). Since EV energy consumption is highly related to travel speed, network uncertainty affects travel time and charging demand estimation significantly. Considering the network uncertainty resulted from link degradation, which influences the distribution of travel demand on transportation network and the energy demand on power network, this paper aims to develop a reliability-based network equilibrium framework for accommodating degradable road conditions with the addition of EVs. First, based on the link travel time distribution, the mean and variance of route travel time and monetary expenses related to energy consumption are deduced, respectively. And the charging time distribution of EVs with charging demand is also estimated. Then, a nested structure is considered to deal with the difference of route choice behavior derived by the different uncertainty degrees between the routes with and without degradable links. Given the expected generalized travel cost and a psychological safety margin, a traffic assignment model with the addition of EVs is formulated. Subsequently, a heuristic solution algorithm is developed to solve the proposed model. Finally, the effects of travelers’ risk attitude, network degradation degree, and EV penetration rate on network performance are illustrated through an example network. The numerical results show that the difference of travelers’ risk attitudes does have impact on the route choice, and the widespread adoption of EVs can cut down the total system travel cost effectively when the transportation network is more reliable. PMID:28886167

Degradable transportation network with the addition of electric vehicles: Network equilibrium analysis.

PubMed

Zhang, Rui; Yao, Enjian; Yang, Yang

2017-01-01

Introducing electric vehicles (EVs) into urban transportation network brings higher requirement on travel time reliability and charging reliability. Specifically, it is believed that travel time reliability is a key factor influencing travelers' route choice. Meanwhile, due to the limited cruising range, EV drivers need to better learn about the required energy for the whole trip to make decisions about whether charging or not and where to charge (i.e., charging reliability). Since EV energy consumption is highly related to travel speed, network uncertainty affects travel time and charging demand estimation significantly. Considering the network uncertainty resulted from link degradation, which influences the distribution of travel demand on transportation network and the energy demand on power network, this paper aims to develop a reliability-based network equilibrium framework for accommodating degradable road conditions with the addition of EVs. First, based on the link travel time distribution, the mean and variance of route travel time and monetary expenses related to energy consumption are deduced, respectively. And the charging time distribution of EVs with charging demand is also estimated. Then, a nested structure is considered to deal with the difference of route choice behavior derived by the different uncertainty degrees between the routes with and without degradable links. Given the expected generalized travel cost and a psychological safety margin, a traffic assignment model with the addition of EVs is formulated. Subsequently, a heuristic solution algorithm is developed to solve the proposed model. Finally, the effects of travelers' risk attitude, network degradation degree, and EV penetration rate on network performance are illustrated through an example network. The numerical results show that the difference of travelers' risk attitudes does have impact on the route choice, and the widespread adoption of EVs can cut down the total system travel cost effectively when the transportation network is more reliable.

Stochastic geometry in disordered systems, applications to quantum Hall transitions

NASA Astrophysics Data System (ADS)

Gruzberg, Ilya

2012-02-01

A spectacular success in the study of random fractal clusters and their boundaries in statistical mechanics systems at or near criticality using Schramm-Loewner Evolutions (SLE) naturally calls for extensions in various directions. Can this success be repeated for disordered and/or non-equilibrium systems? Naively, when one thinks about disordered systems and their average correlation functions one of the very basic assumptions of SLE, the so called domain Markov property, is lost. Also, in some lattice models of Anderson transitions (the network models) there are no natural clusters to consider. Nevertheless, in this talk I will argue that one can apply the so called conformal restriction, a notion of stochastic conformal geometry closely related to SLE, to study the integer quantum Hall transition and its variants. I will focus on the Chalker-Coddington network model and will demonstrate that its average transport properties can be mapped to a classical problem where the basic objects are geometric shapes (loosely speaking, the current paths) that obey an important restriction property. At the transition point this allows to use the theory of conformal restriction to derive exact expressions for point contact conductances in the presence of various non-trivial boundary conditions.

Quantitative dissection of hydrogen bond-mediated proton transfer in the ketosteroid isomerase active site

PubMed Central

Sigala, Paul A.; Fafarman, Aaron T.; Schwans, Jason P.; Fried, Stephen D.; Fenn, Timothy D.; Caaveiro, Jose M. M.; Pybus, Brandon; Ringe, Dagmar; Petsko, Gregory A.; Boxer, Steven G.; Herschlag, Daniel

2013-01-01

Hydrogen bond networks are key elements of protein structure and function but have been challenging to study within the complex protein environment. We have carried out in-depth interrogations of the proton transfer equilibrium within a hydrogen bond network formed to bound phenols in the active site of ketosteroid isomerase. We systematically varied the proton affinity of the phenol using differing electron-withdrawing substituents and incorporated site-specific NMR and IR probes to quantitatively map the proton and charge rearrangements within the network that accompany incremental increases in phenol proton affinity. The observed ionization changes were accurately described by a simple equilibrium proton transfer model that strongly suggests the intrinsic proton affinity of one of the Tyr residues in the network, Tyr16, does not remain constant but rather systematically increases due to weakening of the phenol–Tyr16 anion hydrogen bond with increasing phenol proton affinity. Using vibrational Stark spectroscopy, we quantified the electrostatic field changes within the surrounding active site that accompany these rearrangements within the network. We were able to model these changes accurately using continuum electrostatic calculations, suggesting a high degree of conformational restriction within the protein matrix. Our study affords direct insight into the physical and energetic properties of a hydrogen bond network within a protein interior and provides an example of a highly controlled system with minimal conformational rearrangements in which the observed physical changes can be accurately modeled by theoretical calculations. PMID:23798390

Magnetospheric equilibrium configurations and slow adiabatic convection

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1986-01-01

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.

Emergent inequality and self-organized social classes in a network of power and frustration

DOE PAGES

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

2017-02-17

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution ofmore » wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.« less

Emergent inequality and self-organized social classes in a network of power and frustration

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

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution ofmore » wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.« less

Emergent inequality and self-organized social classes in a network of power and frustration

PubMed Central

Mahault, Benoit; Saxena, Avadh

2017-01-01

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes. PMID:28212440

Emergent inequality and self-organized social classes in a network of power and frustration.

PubMed

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

2017-01-01

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.

A Graphical Simulation of Vapor-Liquid Equilibrium for Use as an Undergraduate Laboratory Experiment and to Demonstrate the Concept of Mathematical Modeling.

ERIC Educational Resources Information Center

Whitman, David L.; Terry, Ronald E.

1985-01-01

Demonstrating petroleum engineering concepts in undergraduate laboratories often requires expensive and time-consuming experiments. To eliminate these problems, a graphical simulation technique was developed for junior-level laboratories which illustrate vapor-liquid equilibrium and the use of mathematical modeling. A description of this…

User's manual for the FLORA equilibrium and stability code

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

Freis, R.P.; Cohen, B.I.

1985-04-01

This document provides a user's guide to the content and use of the two-dimensional axisymmetric equilibrium and stability code FLORA. FLORA addresses the low-frequency MHD stability of long-thin axisymmetric tandem mirror systems with finite pressure and finite-larmor-radius effects. FLORA solves an initial-value problem for interchange, rotational, and ballooning stability.

Quantum gambling based on Nash-equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Pei; Zhou, Xiao-Qi; Wang, Yun-Long; Liu, Bi-Heng; Shadbolt, Pete; Zhang, Yong-Sheng; Gao, Hong; Li, Fu-Li; O'Brien, Jeremy L.

2017-06-01

The problem of establishing a fair bet between spatially separated gambler and casino can only be solved in the classical regime by relying on a trusted third party. By combining Nash-equilibrium theory with quantum game theory, we show that a secure, remote, two-party game can be played using a quantum gambling machine which has no classical counterpart. Specifically, by modifying the Nash-equilibrium point we can construct games with arbitrary amount of bias, including a game that is demonstrably fair to both parties. We also report a proof-of-principle experimental demonstration using linear optics.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Spinel cataclasites in 15445 and 72435 - Petrology and criteria for equilibrium

NASA Technical Reports Server (NTRS)

Baker, M. B.; Herzberg, C. T.

1980-01-01

The problem of establishing the existence of equilibrium among the coexisting phases in the rock is addressed by presenting petrographic and mineral chemistry data on a new spinel cataclasite from 15445 (clast H) and data more extensive than those previously available on two clasts in 72435. Criteria useful in reconstructing the original petrology of these and other spinel cataclasites are analyzed by considering equilibrium among the different phases, that is, the mono- or polymict nature of these cataclasized samples. Finally, the role of impact processes in disturbing the equilibria is discussed.

NetFlow Dynamics

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

Corbet Jr., Thomas F; Beyeler, Walter E; Vanwestrienen, Dirk

NetFlow Dynamics is a web-accessible analysis environment for simulating dynamic flows of materials on model networks. Performing a simulation requires both the NetFlow Dynamics application and a network model which is a description of the structure of the nodes and edges of a network including the flow capacity of each edge and the storage capacity of each node, and the sources and sinks of the material flowing on the network. NetFlow Dynamics consists of databases for storing network models, algorithms to calculate flows on networks, and a GIS-based graphical interface for performing simulations and viewing simulation results. Simulated flows aremore » dynamic in the sense that flows on each edge of the network and inventories at each node change with time and can be out of equilibrium with boundary conditions. Any number of network models could be simulated using Net Flow Dynamics. To date, the models simulated have been models of petroleum infrastructure. The main model has been the National Transportation Fuels Model (NTFM), a network of U.S. oil fields, transmission pipelines, rail lines, refineries, tank farms, and distribution terminals. NetFlow Dynamics supports two different flow algorithms, the Gradient Flow algorithm and the Inventory Control algorithm, that were developed specifically for the NetFlow Dynamics application. The intent is to add additional algorithms in the future as needed. The ability to select from multiple algorithms is desirable because a single algorithm never covers all analysis needs. The current algorithms use a demand-driven capacity-constrained formulation which means that the algorithms strive to use all available capacity and stored inventory to meet desired flows to sinks, subject to the capacity constraints of each network component. The current flow algorithms are best suited for problems in which a material flows on a capacity-constrained network representing a supply chain in which the material supplied can be stored at each node of the network. In the petroleum models, the flowing materials are crude oil and refined products that can be stored at tank farms, refineries, or terminals (i.e. the nodes of the network). Examples of other network models that could be simulated are currency flowing in a financial network, agricultural products moving to market, or natural gas flowing on a pipeline network.« less

Dynamics analysis of epidemic and information spreading in overlay networks.

PubMed

Liu, Guirong; Liu, Zhimei; Jin, Zhen

2018-05-07

We establish an SIS-UAU model to present the dynamics of epidemic and information spreading in overlay networks. The overlay network is represented by two layers: one where the dynamics of the epidemic evolves and another where the information spreads. We theoretically derive the explicit formulas for the basic reproduction number of awareness R 0 a by analyzing the self-consistent equation and the basic reproduction number of disease R 0 d by using the next generation matrix. The formula of R 0 d shows that the effect of awareness can reduce the basic reproduction number of disease. In particular, when awareness does not affect epidemic spreading, R 0 d is shown to match the existing theoretical results. Furthermore, we demonstrate that the disease-free equilibrium is globally asymptotically stable if R 0 d <1; and the endemic equilibrium is globally asymptotically stable if R 0 d >1. Finally, numerical simulations show that information plays a vital role in preventing and controlling disease and effectively reduces the final disease scale. Copyright © 2018 Elsevier Ltd. All rights reserved.

Intrinsic limits to gene regulation by global crosstalk

PubMed Central

Friedlander, Tamar; Prizak, Roshan; Guet, Călin C.; Barton, Nicholas H.; Tkačik, Gašper

2016-01-01

Gene regulation relies on the specificity of transcription factor (TF)–DNA interactions. Limited specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to noncognate TF–DNA interactions or remains erroneously inactive. As each TF can have numerous interactions with noncognate cis-regulatory elements, crosstalk is inherently a global problem, yet has previously not been studied as such. We construct a theoretical framework to analyse the effects of global crosstalk on gene regulation. We find that crosstalk presents a significant challenge for organisms with low-specificity TFs, such as metazoans. Crosstalk is not easily mitigated by known regulatory schemes acting at equilibrium, including variants of cooperativity and combinatorial regulation. Our results suggest that crosstalk imposes a previously unexplored global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints that act at the level of individual gene regulatory elements. PMID:27489144

Modeling the propagation of mobile malware on complex networks

NASA Astrophysics Data System (ADS)

Liu, Wanping; Liu, Chao; Yang, Zheng; Liu, Xiaoyang; Zhang, Yihao; Wei, Zuxue

2016-08-01

In this paper, the spreading behavior of malware across mobile devices is addressed. By introducing complex networks to model mobile networks, which follows the power-law degree distribution, a novel epidemic model for mobile malware propagation is proposed. The spreading threshold that guarantees the dynamics of the model is calculated. Theoretically, the asymptotic stability of the malware-free equilibrium is confirmed when the threshold is below the unity, and the global stability is further proved under some sufficient conditions. The influences of different model parameters as well as the network topology on malware propagation are also analyzed. Our theoretical studies and numerical simulations show that networks with higher heterogeneity conduce to the diffusion of malware, and complex networks with lower power-law exponents benefit malware spreading.

Newly developed double neural network concept for reliable fast plasma position control

NASA Astrophysics Data System (ADS)

Jeon, Young-Mu; Na, Yong-Su; Kim, Myung-Rak; Hwang, Y. S.

2001-01-01

Neural network is considered as a parameter estimation tool in plasma controls for next generation tokamak such as ITER. The neural network has been reported to be so accurate and fast for plasma equilibrium identification that it may be applied to the control of complex tokamak plasmas. For this application, the reliability of the conventional neural network needs to be improved. In this study, a new idea of double neural network is developed to achieve this. The new idea has been applied to simple plasma position identification of KSTAR tokamak for feasibility test. Characteristics of the concept show higher reliability and fault tolerance even in severe faulty conditions, which may make neural network applicable to plasma control reliably and widely in future tokamaks.

Wireless Networks under a Backoff Attack: A Game Theoretical Perspective.

PubMed

Parras, Juan; Zazo, Santiago

2018-01-30

We study a wireless sensor network using CSMA/CA in the MAC layer under a backoff attack: some of the sensors of the network are malicious and deviate from the defined contention mechanism. We use Bianchi's network model to study the impact of the malicious sensors on the total network throughput, showing that it causes the throughput to be unfairly distributed among sensors. We model this conflict using game theory tools, where each sensor is a player. We obtain analytical solutions and propose an algorithm, based on Regret Matching, to learn the equilibrium of the game with an arbitrary number of players. Our approach is validated via simulations, showing that our theoretical predictions adjust to reality.

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

Identifying apparent local stable isotope equilibrium in a complex non-equilibrium system.

PubMed

He, Yuyang; Cao, Xiaobin; Wang, Jianwei; Bao, Huiming

2018-02-28

Although being out of equilibrium, biomolecules in organisms have the potential to approach isotope equilibrium locally because enzymatic reactions are intrinsically reversible. A rigorous approach that can describe isotope distribution among biomolecules and their apparent deviation from equilibrium state is lacking, however. Applying the concept of distance matrix in graph theory, we propose that apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference (|Δα|) matrix, in which the differences between the observed isotope composition (δ') and the calculated equilibrium fractionation factor (1000lnβ) can be more rigorously evaluated than by using a previous approach for multiple biomolecules. We tested our |Δα| matrix approach by re-analyzing published data of different amino acids (AAs) in potato and in green alga. Our re-analysis shows that biosynthesis pathways could be the reason for an apparently close-to-equilibrium relationship inside AA families in potato leaves. Different biosynthesis/degradation pathways in tubers may have led to the observed isotope distribution difference between potato leaves and tubers. The analysis of data from green algae does not support the conclusion that AAs are further from equilibrium in glucose-cultured green algae than in the autotrophic ones. Application of the |Δα| matrix can help us to locate potential reversible reactions or reaction networks in a complex system such as a metabolic system. The same approach can be broadly applied to all complex systems that have multiple components, e.g. geochemical or atmospheric systems of early Earth or other planets. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamics of quality as a strategic variable in complex food supply chain network competition: The case of fresh produce

NASA Astrophysics Data System (ADS)

Nagurney, Anna; Besik, Deniz; Yu, Min

2018-04-01

In this paper, we construct a competitive food supply chain network model in which the profit-maximizing producers decide not only as to the volume of fresh produce produced and distributed using various supply chain network pathways, but they also decide, with the associated costs, on the initial quality of the fresh produce. Consumers, in turn, respond to the various producers' product outputs through the prices that they are willing to pay, given also the average quality associated with each producer or brand at the retail outlets. The quality of the fresh produce is captured through explicit formulae that incorporate time, temperature, and other link characteristics with links associated with processing, shipment, storage, etc. Capacities on links are also incorporated as well as upper bounds on the initial product quality of the firms at their production/harvesting sites. The governing concept of the competitive supply chain network model is that of Nash Equilibrium, for which alternative variational inequality formulations are derived, along with existence results. An algorithmic procedure, which can be interpreted as a discrete-time tatonnement process, is then described and applied to compute the equilibrium produce flow patterns and accompanying link Lagrange multipliers in a realistic case study, focusing on peaches, which includes disruptions.

A multidimensional framework of conceptual change for developing chemical equilibrium learning

NASA Astrophysics Data System (ADS)

Chanyoo, Wassana; Suwannoi, Paisan; Treagust, David F.

2018-01-01

The purposes of this research is to investigate the existing chemical equilibrium lessons in Thailand based on the multidimensional framework of conceptual change, to determine how the existing lessons could enhance students' conceptual change. This research was conducted based on qualitative perspective. Document, observations and interviews were used to collect data. To comprehend all students conceptions, diagnostic tests were applied comprised of The Chemical Equilibrium Diagnostic Test (the CEDT) and The Chemical Equilibrium Test for Reveal Conceptual Change (the CETforRCC). In addition, to study students' motivations, the Motivated Strategies for Learning Questionnaire (the MSLQ) and students' task engagement were applied. Following each perspective of conceptual change - ontological, epistemological, and social/affective - the result showed that the existing chemical equilibrium unit did not enhance students' conceptual change, and some issues were found. The problems obstructed students conceptual change should be remedy under the multidimensional framework of conceptual change. Finally, some suggestions were provided to enhance students' conceptual change in chemical equilibrium effectively

Non-equilibrium phase transitions in a driven-dissipative system of interacting bosons

NASA Astrophysics Data System (ADS)

Young, Jeremy T.; Foss-Feig, Michael; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-04-01

Atomic, molecular, and optical systems provide unique opportunities to study simple models of driven-dissipative many-body quantum systems. Typically, one is interested in the resultant steady state, but the non-equilibrium nature of the physics involved presents several problems in understanding its behavior theoretically. Recently, it has been shown that in many of these models, it is possible to map the steady-state phase transitions onto classical equilibrium phase transitions. In the language of Keldysh field theory, this relation typically only becomes apparent after integrating out massive fields near the critical point, leaving behind a single massless field undergoing near-equilibrium dynamics. In this talk, we study a driven-dissipative XXZ bosonic model and discover critical points at which two fields become gapless. Each critical point separates three different possible phases: a uniform phase, an anti-ferromagnetic phase, and a limit cycle phase. Furthermore, a description in terms of an equilibrium phase transition does not seem possible, so the associated phase transitions appear to be inherently non-equilibrium.

The Effect of Cooperative Learning Approach Based on Conceptual Change Condition on Students' Understanding of Chemical Equilibrium Concepts

ERIC Educational Resources Information Center

Bilgin, Ibrahim; Geban, Omer

2006-01-01

The purpose of this study is to investigate the effects of the cooperative learning approach based on conceptual change conditions over traditional instruction on 10th grade students' conceptual understanding and achievement of computational problems related to chemical equilibrium concepts. The subjects of this study consisted of 87 tenth grade…

The Stability of Tidal Equilibrium for Hierarchical Star-Planet-Moon Systems

NASA Astrophysics Data System (ADS)

Adams, Fred C.

2018-04-01

Motivated by the current search for exomoons, this talk considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets include contributions from the planetary orbit, lunar orbit, stellar spin, planetary spin, and lunar spin. The goal is to determine the optimized energy state of the system subject to the constraint of constant angular momentum. Due to the lack of a closed form solution for the full three-body problem, however, we must use use an approximate description of the orbits. We first consider the Keplerian limit and find that the critical energy states are saddle points, rather than minima, so that these hierarchical systems have no stable tidal equilibrium states. We then generalize the calculation so that the lunar orbit is described by a time-averaged version of the circular restricted three-body problem. In this latter case, the critical energy state is a shallow minimum, so that a tidal equilibrium state exists. In both cases, however, the lunar orbit for the critical point lies outside the boundary (roughly half the Hill radius) where (previous) numerical simulations indicate dynamical instability.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

Influence of network topology on the swelling of polyelectrolyte nanogels.

PubMed

Rizzi, L G; Levin, Y

2016-03-21

It is well-known that the swelling behavior of ionic nanogels depends on their cross-link density; however, it is unclear how different topologies should affect the response of the polyelectrolyte network. Here we perform Monte Carlo simulations to obtain the equilibrium properties of ionic nanogels as a function of salt concentration Cs and the fraction f of ionizable groups in a polyelectrolyte network formed by cross-links of functionality z. Our results indicate that the network with cross-links of low connectivity result in nanogel particles with higher swelling ratios. We also confirm a de-swelling effect of salt on nanogel particles.

A Study on Standard Competition with Network Effect Based on Evolutionary Game Model

NASA Astrophysics Data System (ADS)

Wang, Ye; Wang, Bingdong; Li, Kangning

Owing to networks widespread in modern society, standard competition with network effect is now endowed with new connotation. This paper aims to study the impact of network effect on standard competition; it is organized in the mode of "introduction-model setup-equilibrium analysis-conclusion". Starting from a well-structured model of evolutionary game, it is then extended to a dynamic analysis. This article proves both theoretically and empirically that whether or not a standard can lead the market trends depends on the utility it would bring, and the author also discusses some advisable strategies revolving around the two factors of initial position and border break.

Equilibrium paths analysis of materials with rheological properties by using the chaos theory

NASA Astrophysics Data System (ADS)

Bednarek, Paweł; Rządkowski, Jan

2018-01-01

The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.

Collaborative learning in networks.

PubMed

Mason, Winter; Watts, Duncan J

2012-01-17

Complex problems in science, business, and engineering typically require some tradeoff between exploitation of known solutions and exploration for novel ones, where, in many cases, information about known solutions can also disseminate among individual problem solvers through formal or informal networks. Prior research on complex problem solving by collectives has found the counterintuitive result that inefficient networks, meaning networks that disseminate information relatively slowly, can perform better than efficient networks for problems that require extended exploration. In this paper, we report on a series of 256 Web-based experiments in which groups of 16 individuals collectively solved a complex problem and shared information through different communication networks. As expected, we found that collective exploration improved average success over independent exploration because good solutions could diffuse through the network. In contrast to prior work, however, we found that efficient networks outperformed inefficient networks, even in a problem space with qualitative properties thought to favor inefficient networks. We explain this result in terms of individual-level explore-exploit decisions, which we find were influenced by the network structure as well as by strategic considerations and the relative payoff between maxima. We conclude by discussing implications for real-world problem solving and possible extensions.

Collaborative learning in networks

PubMed Central

Mason, Winter; Watts, Duncan J.

2012-01-01

Complex problems in science, business, and engineering typically require some tradeoff between exploitation of known solutions and exploration for novel ones, where, in many cases, information about known solutions can also disseminate among individual problem solvers through formal or informal networks. Prior research on complex problem solving by collectives has found the counterintuitive result that inefficient networks, meaning networks that disseminate information relatively slowly, can perform better than efficient networks for problems that require extended exploration. In this paper, we report on a series of 256 Web-based experiments in which groups of 16 individuals collectively solved a complex problem and shared information through different communication networks. As expected, we found that collective exploration improved average success over independent exploration because good solutions could diffuse through the network. In contrast to prior work, however, we found that efficient networks outperformed inefficient networks, even in a problem space with qualitative properties thought to favor inefficient networks. We explain this result in terms of individual-level explore-exploit decisions, which we find were influenced by the network structure as well as by strategic considerations and the relative payoff between maxima. We conclude by discussing implications for real-world problem solving and possible extensions. PMID:22184216

Construction of road network vulnerability evaluation index based on general travel cost

NASA Astrophysics Data System (ADS)

Leng, Jun-qiang; Zhai, Jing; Li, Qian-wen; Zhao, Lin

2018-03-01

With the development of China's economy and the continuous improvement of her urban road network, the vulnerability of the urban road network has attracted increasing attention. Based on general travel cost, this work constructs the vulnerability evaluation index for the urban road network, and evaluates the vulnerability of the urban road network from the perspective of user generalised travel cost. Firstly, the generalised travel cost model is constructed based on vehicle cost, travel time, and traveller comfort. Then, the network efficiency index is selected as an evaluation index of vulnerability: the network efficiency index is composed of the traffic volume and the generalised travel cost, which are obtained from the equilibrium state of the network. In addition, the research analyses the influence of traffic capacity decrease, road section attribute value, and location of road section, on vulnerability. Finally, the vulnerability index is used to analyse the local area network of Harbin and verify its applicability.

Control and instanton trajectories for random transitions in turbulent flows

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

Many turbulent systems exhibit random switches between qualitatively different attractors. The transition between these bistable states is often an extremely rare event, that can not be computed through DNS, due to complexity limitations. We present results for the calculation of instanton trajectories (a control problem) between non-equilibrium stationary states (attractors) in the 2D stochastic Navier-Stokes equations. By representing the transition probability between two states using a path integral formulation, we can compute the most probable trajectory (instanton) joining two non-equilibrium stationary states. Technically, this is equivalent to the minimization of an action, which can be related to a fluid mechanics control problem.

Equilibrium polymerization on the equivalent-neighbor lattice

NASA Technical Reports Server (NTRS)

Kaufman, Miron

1989-01-01

The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.

Disk in a groove with friction: An analysis of static equilibrium and indeterminacy

NASA Astrophysics Data System (ADS)

Donolato, Cesare

2018-05-01

This note studies the statics of a rigid disk placed in a V-shaped groove with frictional walls and subjected to gravity and a torque. The two-dimensional equilibrium problem is formulated in terms of the angles that contact forces form with the normal to the walls. This approach leads to a single trigonometric equation in two variables whose domain is determined by Coulomb's law of friction. The properties of solutions (existence, uniqueness, or indeterminacy) as functions of groove angle, friction coefficient and applied torque are derived by a simple geometric representation. The results modify some of the conclusions by other authors on the same problem.

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

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

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

A general equilibrium model of guest-worker migration: the source-country perspective.

PubMed

Djajic, S; Milbourne, R

1988-11-01

"This paper examines the problem of guest-worker migration from an economy populated by identical, utility-maximizing individuals with finite working lives. The decision to migrate, the rate of saving while abroad, as well as the length of a migrant's stay in the foreign country, are all viewed as part of a solution to an intertemporal optimization problem. In addition to studying the microeconomic aspects of temporary migration, the paper analyses the determinants of the equilibrium flow of migrants, the corresponding domestic wage, and the level of welfare enjoyed by a typical worker. Effects of an emigration tax are also investigated." excerpt

A comparative analysis of numerical approaches to the mechanics of elastic sheets

NASA Astrophysics Data System (ADS)

Taylor, Michael; Davidovitch, Benny; Qiu, Zhanlong; Bertoldi, Katia

2015-06-01

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

Mur-Petit, J; Relaño, A; Molina, R A; Jaksch, D

2018-05-22

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

What Mathematical Competencies Are Needed for Success in College.

ERIC Educational Resources Information Center

Garofalo, Joe

1990-01-01

Identifies requisite math skills for a microeconomics course, offering samples of supply curves, demand curves, equilibrium prices, elasticity, and complex graph problems. Recommends developmental mathematics competencies, including problem solving, reasoning, connections, communication, number and operation sense, algebra, relationships,…

Distributed Nash Equilibrium Seeking for Generalized Convex Games with Shared Constraints

NASA Astrophysics Data System (ADS)

Sun, Chao; Hu, Guoqiang

2018-05-01

In this paper, we deal with the problem of finding a Nash equilibrium for a generalized convex game. Each player is associated with a convex cost function and multiple shared constraints. Supposing that each player can exchange information with its neighbors via a connected undirected graph, the objective of this paper is to design a Nash equilibrium seeking law such that each agent minimizes its objective function in a distributed way. Consensus and singular perturbation theories are used to prove the stability of the system. A numerical example is given to show the effectiveness of the proposed algorithms.

Metacognitive skills and students' motivation toward chemical equilibrium problem solving ability: A correlational study on students of XI IPA SMAN 2 Banjarmasin

NASA Astrophysics Data System (ADS)

Muna, Khairiatul; Sanjaya, Rahmat Eko; Syahmani, Bakti, Iriani

2017-12-01

The demand for students to have metacognitive skills and problem solving ability can be seen in the core competencies of the 2013 curriculum. Metacognitive skills are the skills which affect students' success in solving problems depending on students' motivation. This explains the possibility of the relationship between metacognition and motivation in affecting students' achievement including problem solving. Due to the importance of metacognitive skills to solve problems and the possible relationship between metacognition and motivation, a study to find the relationship among the variables is necessary to conduct, particularly on chemistry problem solving. This one shot case study using quantitative method aimed to investigate the correlation between metacognitive skills and motivation toward problem solving ability focusing on chemical equilibrium. The research population was students of grade XI of majoring Science of Banjarmasin Public High Scool 2 (XI IPA SMAN 2 Banjarmasin) with the samples of 33 students obtained by using purposive sampling technique. The research data were collected using test and non-test and analyzed using multiple regression in SPSS 21. The results of this study showed that (1) the students' metacognitive skills and motivation correlated positively with coefficient of +0.450 to problem solving ability on chemical equilibrium: (2) inter-variables of students' motivation (self-efficacy, active learning strategies, science/chemistry learning value, performance goal, achievement goal, and learning environment stimulations) correlated positively to metacognitive skills with the correlation coefficients of +0.580, +0.537, +0.363, +0.241, +0.516, and +0.271, respectively. Based on the results, it is necessary for teachers to implement learning which develops students' metacognitive skills and motivation, such as learning with scientific approach. The implementation of the learning is also supposed to be complemented with the use of learning device, such as student worksheet, to help students use their metacognitive skills in solving problems, particularly on chemistry subject.

Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching

NASA Astrophysics Data System (ADS)

Liu, Cheng-Wei

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

NASA Astrophysics Data System (ADS)

Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.

2017-12-01

It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82, 905820306, 2016 2. O. Allanson, S. Troscheit & T. Neukirch: The inverse problem for collisionless plasma equilibria (invited paper for IMA Journal of Applied Mathematics, under review)

Distributed Synchronization in Communication Networks

DTIC Science & Technology

2018-01-24

synchronization. Secondly, it is known that identical oscillators with sin() coupling functions are guaranteed to synchronize in phase on a complete...provide sufficient conditions for phase- locking , i.e., convergence to a stable equilibrium almost surely. We additionally find conditions when the

Crossing the Technology Adoption Chasm: Implications for DoD

DTIC Science & Technology

2008-06-30

technologies (where, given uncertainty of evaluation, adoption is driven by mimicry processes) and those technologies that exhibit network...Total Capital per Farm Dependent Variable = Long-run Equilibrium Percentage of Acreage Planted to Hybrid Seed Average Corn Acre per

Equilibium and Stability of Spherical Vlasov Systems

NASA Astrophysics Data System (ADS)

Barnes, D. C.; Chacon, L.; Finn, J. M.

2002-04-01

Collisionless systems with inverse square interaction potentials and possible background confining potentials are considered for the case of spherical symmetry and in the Vlasov limit. The equilibrium is the most general, with single-particle distribution function dependence on both total energy E and total angular momentum L. A new formulation of the full integral-equation stability problem is developed. For a general spherical harmonic perturbation potential, the 3D stability problem is reduced to a 2D problem in an arbitrary central plane of motion, then to a small number of coupled 1D problems involving only the radius. Normal modes depend only on the total mode number l, as is shown directly by this new formulation, with all m degenerate. This method has been used for the Coulomb (repulsive) case.[1] An equilibrium family with uniform central (electron) density is found, and the low-frequency response computed to show that these solutions may provide stable confinement of a massive second (ion) species. These methods may be applied to a particle bunch in the beam frame, and some stability results appropriate to this case are presented. Application to the gravitational (attractive) case is also described, and some initial analytic results are presented. [1] D. C. Barnes, L. Chacón, J. M. Finn, “Equilibrium and Low-frequency Stability of a Uniform Density, Collisionless, Spherical Vlasov System,” submitted to Phys. of Plasmas (2002).

Real-tiem Adaptive Control Scheme for Superior Plasma Confinement

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

Alexander Trunov, Ph.D.

2001-06-01

During this Phase I project, IOS, in collaboration with our subcontractors at General Atomics, Inc., acquired and analyzed measurement data on various plasma equilibrium modes. We developed a Matlab-based toolbox consisting of linear and neural network approximators that are capable of learning and predicting, with accuracy, the behavior of plasma parameters. We also began development of the control algorithm capable of using the model of the plasma obtained by the neural network approximator.

Current-flow efficiency of networks

NASA Astrophysics Data System (ADS)

Liu, Kai; Yan, Xiaoyong

2018-02-01

Many real-world networks, from infrastructure networks to social and communication networks, can be formulated as flow networks. How to realistically measure the transport efficiency of these networks is of fundamental importance. The shortest-path-based efficiency measurement has limitations, as it assumes that flow travels only along those shortest paths. Here, we propose a new metric named current-flow efficiency, in which we calculate the average reciprocal effective resistance between all pairs of nodes in the network. This metric takes the multipath effect into consideration and is more suitable for measuring the efficiency of many real-world flow equilibrium networks. Moreover, this metric can handle a disconnected graph and can thus be used to identify critical nodes and edges from the efficiency-loss perspective. We further analyze how the topological structure affects the current-flow efficiency of networks based on some model and real-world networks. Our results enable a better understanding of flow networks and shed light on the design and improvement of such networks with higher transport efficiency.

SEIR Model of Rumor Spreading in Online Social Network with Varying Total Population Size

NASA Astrophysics Data System (ADS)

Dong, Suyalatu; Deng, Yan-Bin; Huang, Yong-Chang

2017-10-01

Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network. Supported by National Natural Science Foundation of China under Grant Nos. 11275017 and 11173028

Energy optimization in mobile sensor networks

NASA Astrophysics Data System (ADS)

Yu, Shengwei

Mobile sensor networks are considered to consist of a network of mobile robots, each of which has computation, communication and sensing capabilities. Energy efficiency is a critical issue in mobile sensor networks, especially when mobility (i.e., locomotion control), routing (i.e., communications) and sensing are unique characteristics of mobile robots for energy optimization. This thesis focuses on the problem of energy optimization of mobile robotic sensor networks, and the research results can be extended to energy optimization of a network of mobile robots that monitors the environment, or a team of mobile robots that transports materials from stations to stations in a manufacturing environment. On the energy optimization of mobile robotic sensor networks, our research focuses on the investigation and development of distributed optimization algorithms to exploit the mobility of robotic sensor nodes for network lifetime maximization. In particular, the thesis studies these five problems: 1. Network-lifetime maximization by controlling positions of networked mobile sensor robots based on local information with distributed optimization algorithms; 2. Lifetime maximization of mobile sensor networks with energy harvesting modules; 3. Lifetime maximization using joint design of mobility and routing; 4. Optimal control for network energy minimization; 5. Network lifetime maximization in mobile visual sensor networks. In addressing the first problem, we consider only the mobility strategies of the robotic relay nodes in a mobile sensor network in order to maximize its network lifetime. By using variable substitutions, the original problem is converted into a convex problem, and a variant of the sub-gradient method for saddle-point computation is developed for solving this problem. An optimal solution is obtained by the method. Computer simulations show that mobility of robotic sensors can significantly prolong the lifetime of the whole robotic sensor network while consuming negligible amount of energy for mobility cost. For the second problem, the problem is extended to accommodate mobile robotic nodes with energy harvesting capability, which makes it a non-convex optimization problem. The non-convexity issue is tackled by using the existing sequential convex approximation method, based on which we propose a novel procedure of modified sequential convex approximation that has fast convergence speed. For the third problem, the proposed procedure is used to solve another challenging non-convex problem, which results in utilizing mobility and routing simultaneously in mobile robotic sensor networks to prolong the network lifetime. The results indicate that joint design of mobility and routing has an edge over other methods in prolonging network lifetime, which is also the justification for the use of mobility in mobile sensor networks for energy efficiency purpose. For the fourth problem, we include the dynamics of the robotic nodes in the problem by modeling the networked robotic system using hybrid systems theory. A novel distributed method for the networked hybrid system is used to solve the optimal moving trajectories for robotic nodes and optimal network links, which are not answered by previous approaches. Finally, the fact that mobility is more effective in prolonging network lifetime for a data-intensive network leads us to apply our methods to study mobile visual sensor networks, which are useful in many applications. We investigate the joint design of mobility, data routing, and encoding power to help improving the video quality while maximizing the network lifetime. This study leads to a better understanding of the role mobility can play in data-intensive surveillance sensor networks.

Wireless Networks under a Backoff Attack: A Game Theoretical Perspective

PubMed Central

Zazo, Santiago

2018-01-01

We study a wireless sensor network using CSMA/CA in the MAC layer under a backoff attack: some of the sensors of the network are malicious and deviate from the defined contention mechanism. We use Bianchi’s network model to study the impact of the malicious sensors on the total network throughput, showing that it causes the throughput to be unfairly distributed among sensors. We model this conflict using game theory tools, where each sensor is a player. We obtain analytical solutions and propose an algorithm, based on Regret Matching, to learn the equilibrium of the game with an arbitrary number of players. Our approach is validated via simulations, showing that our theoretical predictions adjust to reality. PMID:29385752

Self-organization and solution of shortest-path optimization problems with memristive networks

NASA Astrophysics Data System (ADS)

Pershin, Yuriy V.; Di Ventra, Massimiliano

2013-07-01

We show that memristive networks, namely networks of resistors with memory, can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time nonlocality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.

Reviewing Some Crucial Concepts of Gibbs Energy in Chemical Equilibrium Using a Computer-Assisted, Guided-Problem-Solving Approach

ERIC Educational Resources Information Center

Borge, Javier

2015-01-01

G, G°, [delta][subscript r]G, [delta][subscript r]G°, [delta]G, and [delta]G° are essential quantities to master the chemical equilibrium. Although the number of publications devoted to explaining these items is extremely high, it seems that they do not produce the desired effect because some articles and textbooks are still being written with…

Modeling Misbehavior in Cooperative Diversity: A Dynamic Game Approach

NASA Astrophysics Data System (ADS)

Dehnie, Sintayehu; Memon, Nasir

2009-12-01

Cooperative diversity protocols are designed with the assumption that terminals always help each other in a socially efficient manner. This assumption may not be valid in commercial wireless networks where terminals may misbehave for selfish or malicious intentions. The presence of misbehaving terminals creates a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a suboptimal Nash equilibrium where wireless terminals opt out of cooperation. Hence, without establishing a mechanism to detect and mitigate effects of misbehavior, it is difficult to maintain a socially optimal cooperation. In this paper, we first examine effects of misbehavior assuming static game model and show that cooperation under existing cooperative protocols is characterized by a noncooperative Nash equilibrium. Using evolutionary game dynamics we show that a small number of mutants can successfully invade a population of cooperators, which indicates that misbehavior is an evolutionary stable strategy (ESS). Our main goal is to design a mechanism that would enable wireless terminals to select reliable partners in the presence of uncertainty. To this end, we formulate cooperative diversity as a dynamic game with incomplete information. We show that the proposed dynamic game formulation satisfied the conditions for the existence of perfect Bayesian equilibrium.

Tax Evasion and Nonequilibrium Model on Apollonian Networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2012-11-01

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

Mental Health, School Problems, and Social Networks: Modeling Urban Adolescent Substance Use

ERIC Educational Resources Information Center

Mason, Michael J.

2010-01-01

This study tested a mediation model of the relationship with school problems, social network quality, and substance use with a primary care sample of 301 urban adolescents. It was theorized that social network quality (level of risk or protection in network) would mediate the effects of school problems, accounting for internalizing problems and…

Algorithms for Data Sharing, Coordination, and Communication in Dynamic Network Settings

DTIC Science & Technology

2007-12-03

problems in dynamic networks, focusing on mobile networks with wireless communication. Problems studied include data management, time synchronization ...The discovery of a fundamental limitation in capabilities for time synchronization in large networks. (2) The identification and development of the...Problems studied include data management, time synchronization , communication problems (broadcast, geocast, and point-to-point routing), distributed

A new class of problems in the calculus of variations

NASA Astrophysics Data System (ADS)

Ekeland, Ivar; Long, Yiming; Zhou, Qinglong

2013-11-01

This paper investigates an infinite-horizon problem in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak.

Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A

1949-01-01

Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

Kolkata Paise Restaurant Problem and the Cyclically Fair Norm

NASA Astrophysics Data System (ADS)

Banerjee, Priyodorshi; Mitra, Manipushpak; Mukherjee, Conan

In this paper we revisit the Kolkata Paise Restaurant problem by allowing for a more general (but common) preference of the n customers defined over the set of n restaurants. This generalization allows for the possibility that each pure strategy Nash equilibrium differs from the Pareto efficient allocation. By assuming that n is small and by allowing for mutual interaction across all customers we design strategies to sustain cyclically fair norm as a sub-game perfect equilibrium of the Kolkata Paise Restaurant problem. We have a cyclically fair norm if n strategically different Pareto efficient strategies are sequentially sustained in a way such that each customer gets serviced in all the n restaurants exactly once between periods 1 and n and then again the same process is repeated between periods (n+1) and 2n and so on.

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

Searching for artificial equilibrium points to place satellites "above and below" L3 in the Sun-Earth system

NASA Astrophysics Data System (ADS)

de Almeida, A. K., Jr.; Prado, A. F. B. A.; Sanchez, D. M.; Yokoyama, T.

2017-10-01

Regarding practical applications of L3 of the Sun-Earth system, there are few studies with the goal of placing a spacecraft at this point, or in orbit around it. One of the main problems in placing a spacecraft near this equilibrium point is the fact that it is located behind the Sun with respect to the Earth. The Sun would be blocking direct communication between the spacecraft and the Earth. The present research gives several options to solve this problem by using a solar sail to place one or two spacecraft above and/or below the Ecliptic plane. This sail could also be used for the mission itself, to collect energy or particles. By using an adequate size, location and attitude of the solar sail, the equilibrium point can be moved from its original location to allow communications between the spacecraft and the Earth. A preliminary study of a solar sail that uses this strategy is shown here.

Equilibrium configurations of the conducting liquid surface in a nonuniform electric field

NASA Astrophysics Data System (ADS)

Zubarev, N. M.; Zubareva, O. V.

2011-01-01

Possible equilibrium configurations of the free surface of a conducting liquid deformed by a nonuniform external electric field are investigated. The liquid rests on an electrode that has the shape of a dihedral angle formed by two intersecting equipotential half-planes (conducting wedge). It is assumed that the problem has plane symmetry: the surface is invariant under shift along the edge of the dihedral angle. A one-parametric family of exact solutions for the shape of the surface is found in which the opening angle of the region above the wedge serves as a parameter. The solutions are valid when the pressure difference between the inside and outside of the liquid is zero. For an arbitrary pressure difference, approximate solutions to the problem are constructed and it is demonstrated the approximation error is small. It is found that, when the potential difference exceeds a certain threshold value, equilibrium solutions are absent. In this case, the region occupied by the liquid disintegrates, the disintegration scenario depending on the opening angle.

Evolution of a terrestrial magma ocean: Thermodynamics, kinetics, rheology, convection, differentiation

NASA Technical Reports Server (NTRS)

Solomatov, V. S.; Stevenson, D. J.

1992-01-01

The evolution of an initially totally molten magma ocean is constrained on the basis of analysis of various physical problems in the magma ocean. First of all an equilibrium thermodynamics of the magma ocean is developed in the melting temperature range. The equilibrium thermodynamical parameters are found as functions only of temperature and pressure and are used in the subsequent models of kinetics and convection. Kinematic processes determine the crystal size and also determine a non-equilibrium thermodynamics of the system. Rheology controls all dynamical regimes of the magma ocean. The thermal convection models for different rheological laws are developed for both the laminar convection and for turbulent convection in the case of equilibrium thermodynamics of the multiphase system. The evolution is estimated on the basis of all the above analysis.

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

NASA Astrophysics Data System (ADS)

Shi, Yu; Wang, Yue; Xu, Shijie

2018-04-01

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.

SQERTSS: Dynamic rank based throttling of transition probabilities in kinetic Monte Carlo simulations

DOE PAGES

Danielson, Thomas; Sutton, Jonathan E.; Hin, Céline; ...

2017-06-09

Lattice based Kinetic Monte Carlo (KMC) simulations offer a powerful simulation technique for investigating large reaction networks while retaining spatial configuration information, unlike ordinary differential equations. However, large chemical reaction networks can contain reaction processes with rates spanning multiple orders of magnitude. This can lead to the problem of “KMC stiffness” (similar to stiffness in differential equations), where the computational expense has the potential to be overwhelmed by very short time-steps during KMC simulations, with the simulation spending an inordinate amount of KMC steps / cpu-time simulating fast frivolous processes (FFPs) without progressing the system (reaction network). In order tomore » achieve simulation times that are experimentally relevant or desired for predictions, a dynamic throttling algorithm involving separation of the processes into speed-ranks based on event frequencies has been designed and implemented with the intent of decreasing the probability of FFP events, and increasing the probability of slow process events -- allowing rate limiting events to become more likely to be observed in KMC simulations. This Staggered Quasi-Equilibrium Rank-based Throttling for Steady-state (SQERTSS) algorithm designed for use in achieving and simulating steady-state conditions in KMC simulations. Lastly, as shown in this work, the SQERTSS algorithm also works for transient conditions: the correct configuration space and final state will still be achieved if the required assumptions are not violated, with the caveat that the sizes of the time-steps may be distorted during the transient period.« less

SQERTSS: Dynamic rank based throttling of transition probabilities in kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Danielson, Thomas; Sutton, Jonathan E.; Hin, Céline; Savara, Aditya

2017-10-01

Lattice based Kinetic Monte Carlo (KMC) simulations offer a powerful simulation technique for investigating large reaction networks while retaining spatial configuration information, unlike ordinary differential equations. However, large chemical reaction networks can contain reaction processes with rates spanning multiple orders of magnitude. This can lead to the problem of "KMC stiffness" (similar to stiffness in differential equations), where the computational expense has the potential to be overwhelmed by very short time-steps during KMC simulations, with the simulation spending an inordinate amount of KMC steps/CPU time simulating fast frivolous processes (FFPs) without progressing the system (reaction network). In order to achieve simulation times that are experimentally relevant or desired for predictions, a dynamic throttling algorithm involving separation of the processes into speed-ranks based on event frequencies has been designed and implemented with the intent of decreasing the probability of FFP events, and increasing the probability of slow process events-allowing rate limiting events to become more likely to be observed in KMC simulations. This Staggered Quasi-Equilibrium Rank-based Throttling for Steady-state (SQERTSS) algorithm is designed for use in achieving and simulating steady-state conditions in KMC simulations. As shown in this work, the SQERTSS algorithm also works for transient conditions: the correct configuration space and final state will still be achieved if the required assumptions are not violated, with the caveat that the sizes of the time-steps may be distorted during the transient period.

NON-EQUILIBRIUM HELIUM IONIZATION IN AN MHD SIMULATION OF THE SOLAR ATMOSPHERE

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

Golding, Thomas Peter; Carlsson, Mats; Leenaarts, Jorrit, E-mail: thomas.golding@astro.uio.no, E-mail: mats.carlsson@astro.uio.no, E-mail: jorrit.leenaarts@astro.su.se

The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilibrium hydrogen ionization by performing a 2D radiation-magnetohydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyα and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with local thermodynamicmore » equilibrium (LTE) ionization shows that non-equilibrium helium ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behavior with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11–18 kK, compared to models with LTE helium ionization. We conclude that non-equilibrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region. It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed.« less

Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays.

PubMed

Arik, Sabri

2005-05-01

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

Dynamic stability analysis of fractional order leaky integrator echo state neural networks

NASA Astrophysics Data System (ADS)

Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.

2017-06-01

The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.

Oscillator Neural Network Retrieving Sparsely Coded Phase Patterns

NASA Astrophysics Data System (ADS)

Aoyagi, Toshio; Nomura, Masaki

1999-08-01

Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case of sparsely coded patterns, it is biologically important to consider the timings of firings and to study how such consideration influences storage capacities and quality of recalled patterns. For this purpose, we propose a simple extended model of oscillator neural networks to allow for expression of a nonfiring state. Analyzing both equilibrium states and dynamical properties in recalling processes, we find that the system possesses good associative memory.

Nanoscale molecular communication networks: a game-theoretic perspective

NASA Astrophysics Data System (ADS)

Jiang, Chunxiao; Chen, Yan; Ray Liu, K. J.

2015-12-01

Currently, communication between nanomachines is an important topic for the development of novel devices. To implement a nanocommunication system, diffusion-based molecular communication is considered as a promising bio-inspired approach. Various technical issues about molecular communications, including channel capacity, noise and interference, and modulation and coding, have been studied in the literature, while the resource allocation problem among multiple nanomachines has not been well investigated, which is a very important issue since all the nanomachines share the same propagation medium. Considering the limited computation capability of nanomachines and the expensive information exchange cost among them, in this paper, we propose a game-theoretic framework for distributed resource allocation in nanoscale molecular communication systems. We first analyze the inter-symbol and inter-user interference, as well as bit error rate performance, in the molecular communication system. Based on the interference analysis, we formulate the resource allocation problem as a non-cooperative molecule emission control game, where the Nash equilibrium is found and proved to be unique. In order to improve the system efficiency while guaranteeing fairness, we further model the resource allocation problem using a cooperative game based on the Nash bargaining solution, which is proved to be proportionally fair. Simulation results show that the Nash bargaining solution can effectively ensure fairness among multiple nanomachines while achieving comparable social welfare performance with the centralized scheme.

Tensegrity and motor-driven effective interactions in a model cytoskeleton

NASA Astrophysics Data System (ADS)

Wang, Shenshen; Wolynes, Peter G.

2012-04-01

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity, and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.

Game Theory Based Security in Wireless Body Area Network with Stackelberg Security Equilibrium.

PubMed

Somasundaram, M; Sivakumar, R

2015-01-01

Wireless Body Area Network (WBAN) is effectively used in healthcare to increase the value of the patient's life and also the value of healthcare services. The biosensor based approach in medical care system makes it difficult to respond to the patients with minimal response time. The medical care unit does not deploy the accessing of ubiquitous broadband connections full time and hence the level of security will not be high always. The security issue also arises in monitoring the user body function records. Most of the systems on the Wireless Body Area Network are not effective in facing the security deployment issues. To access the patient's information with higher security on WBAN, Game Theory with Stackelberg Security Equilibrium (GTSSE) is proposed in this paper. GTSSE mechanism takes all the players into account. The patients are monitored by placing the power position authority initially. The position authority in GTSSE is the organizer and all the other players react to the organizer decision. Based on our proposed approach, experiment has been conducted on factors such as security ratio based on patient's health information, system flexibility level, energy consumption rate, and information loss rate. Stackelberg Security considerably improves the strength of solution with higher security.

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

Open quantum generalisation of Hopfield neural networks

NASA Astrophysics Data System (ADS)

Rotondo, P.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.; Müller, M.

2018-03-01

We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and quantum coherent effects on the same footing. In particular, we propose an open quantum generalisation of the Hopfield neural network, the simplest toy model of associative memory. We determine its phase diagram and show that quantum fluctuations give rise to a qualitatively new non-equilibrium phase. This novel phase is characterised by limit cycles corresponding to high-dimensional stationary manifolds that may be regarded as a generalisation of storage patterns to the quantum domain.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

PubMed

Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E

2018-07-01

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.

Self-organization in neural networks - Applications in structural optimization

NASA Technical Reports Server (NTRS)

Hajela, Prabhat; Fu, B.; Berke, Laszlo

1993-01-01

The present paper discusses the applicability of ART (Adaptive Resonance Theory) networks, and the Hopfield and Elastic networks, in problems of structural analysis and design. A characteristic of these network architectures is the ability to classify patterns presented as inputs into specific categories. The categories may themselves represent distinct procedural solution strategies. The paper shows how this property can be adapted in the structural analysis and design problem. A second application is the use of Hopfield and Elastic networks in optimization problems. Of particular interest are problems characterized by the presence of discrete and integer design variables. The parallel computing architecture that is typical of neural networks is shown to be effective in such problems. Results of preliminary implementations in structural design problems are also included in the paper.

Equilibrium and Disequilibrium of River Basins: Effects on Stream Captures in Serra do Mar and Serra da Mantiqueira, Brazil

NASA Astrophysics Data System (ADS)

DA Silva, L. M.

2015-12-01

Landscapes are mainly driven by river processes that control the dynamic reorganization of networks. Discovering and identifying whether river basins are in geometric equilibrium or disequilibrium requires an analysis of water divides, channels that shift laterally or expand upstream and river captures. Issues specifically discussed include the variation of drainage area change and erosion rates of the basins. In southeastern Brazil there are two main escarpments with extensive geomorphic surfaces: Serra do Mar and Serra da Mantiqueira Mountains. These landscapes are constituted of Neoproterozoic and early Paleozoic rocks, presenting steep escarpments with low-elevation coastal plains and higher elevation interior plateaus. To identify whether river basins and river profiles are in equilibrium or disequilibrium in Serra do Mar and Serra da Mantiqueira Mountains, we used the proxy (χ), evaluating the effect of drainage area change and erosion rates. We selected basins that drain both sides of these two main escarpments (oceanic and continental sides) and have denudation rates derived from pre-existing cosmogenic isotopes data (Rio de Janeiro, Paraná and Minas Gerais). Despite being an ancient and tectonically stable landscape, part of the coastal plain of Serra do Mar Mountain in Rio de Janeiro and Paraná is in geometric disequilibrium, with water divides moving in the direction of higher χ values. To achieve equilibrium, some basins located in the continental side are retracting and disappearing, losing area to the coastal basins. On the contrary, there are some adjacent sub-basins that are close to equilibrium, without strong contrasts in χ values. The same pattern was observed in Serra da Mantiqueira (Minas Gerais state), with stream captures and river network reorganization in its main rivers. The initial results suggest a strong contrast between erosion rates in the continental and the oceanic portions of the escarpments.

Open Markov Processes and Reaction Networks

NASA Astrophysics Data System (ADS)

Swistock Pollard, Blake Stephen

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

With this thesis, we want to shed some light into the darkness of our understanding of simply defined statistical mechanics systems and the surprisingly complex dynamical behavior they exhibit. We will do so by presenting in turn one equilibrium and then one non-equilibrium system with evolutionary dynamics. In part 1, we will present the seceder-model, a newly developed system that cannot equilibrate. We will then study several properties of the system and obtain an idea of the richness of the dynamics of the seceder model, which is particular impressive given the minimal amount of modeling necessary in its setup. In part 2, we will present extensions to the directed polymer in random media problem on a hypercube and its connection to the Eigen model of evolution. Our main interest will be the influence of time-dependent and time-independent changes in the fitness landscape viewed by an evolving population. This part contains the equilibrium dynamics. The stochastic models and the topic of evolution and non-equilibrium in general will allow us to point out similarities to the various lines of thought in game theory.

On the Uniqueness Conditions and Bifurcation Criteria in Coupled Thermo-Elasto-Plasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2017-02-01

The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This paper is a continuation of some previous works by the author, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermal elastoplastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. The paper contains four Appendices A, B, C and D where the local necessery and sufficient conditions of uniqueness have been derived.

Use of a Mobile Application to Help Students Develop Skills Needed in Solving Force Equilibrium Problems

NASA Astrophysics Data System (ADS)

Yang, Eunice

2016-02-01

This paper discusses the use of a free mobile engineering application (app) called Autodesk® ForceEffect™ to provide students assistance with spatial visualization of forces and more practice in solving/visualizing statics problems compared to the traditional pencil-and-paper method. ForceEffect analyzes static rigid-body systems using free-body diagrams (FBDs) and provides solutions in real time. It is a cost-free software that is available for download on the Internet. The software is supported on the iOS™, Android™, and Google Chrome™ platforms. It is easy to use and the learning curve is approximately two hours using the tutorial provided within the app. The use of ForceEffect has the ability to provide students different problem modalities (textbook, real-world, and design) to help them acquire and improve on skills that are needed to solve force equilibrium problems. Although this paper focuses on the engineering mechanics statics course, the technology discussed is also relevant to the introductory physics course.

Hopfield networks for solving Tower of Hanoi problems

NASA Astrophysics Data System (ADS)

Kaplan, G. B.; Güzeliş, Cüneyt

2001-08-01

In this paper, Hopfield neural networks have been considered in solving the Tower of Hanoi test which is used in the determining of deficit of planning capability of the human prefrontal cortex. The main difference between this paper and the ones in the literature which use neural networks is that the Tower of Hanoi problem has been formulated here as a special shortest-path problem. In the literature, some Hopfield networks are developed for solving the shortest path problem which is a combinatorial optimization problem having a diverse field of application. The approach given in this paper gives the possibility of solving the Tower of Hanoi problem using these Hopfield networks. Also, the paper proposes new Hopfield network models for the shortest path and hence the Tower of Hanoi problems and compares them to the available ones in terms of the memory and time (number of steps) needed in the simulations.

Glucans monomer-exchange dynamics as an open chemical network

NASA Astrophysics Data System (ADS)

Rao, Riccardo; Lacoste, David; Esposito, Massimiliano

2015-12-01

We describe the oligosaccharides-exchange dynamics performed by the so-called D-enzymes on polysaccharides. To mimic physiological conditions, we treat this process as an open chemical network by assuming some of the polymer concentrations fixed (chemostatting). We show that three different long-time behaviors may ensue: equilibrium states, nonequilibrium steady states, and continuous growth states. We dynamically and thermodynamically characterize these states and emphasize the crucial role of conservation laws in identifying the chemostatting conditions inducing them.

Glucans monomer-exchange dynamics as an open chemical network

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

Rao, Riccardo, E-mail: riccardo.rao@uni.lu; Esposito, Massimiliano, E-mail: massimiliano.esposito@uni.lu; Lacoste, David

2015-12-28

We describe the oligosaccharides-exchange dynamics performed by the so-called D-enzymes on polysaccharides. To mimic physiological conditions, we treat this process as an open chemical network by assuming some of the polymer concentrations fixed (chemostatting). We show that three different long-time behaviors may ensue: equilibrium states, nonequilibrium steady states, and continuous growth states. We dynamically and thermodynamically characterize these states and emphasize the crucial role of conservation laws in identifying the chemostatting conditions inducing them.

Dynamic Power Distribution System Management With a Locally Connected Communication Network

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

Dall-Anese, Emiliano; Zhang, Kaiqing; Basar, Tamer

Coordinated optimization and control of distribution-level assets can enable a reliable and optimal integration of massive amount of distributed energy resources (DERs) and facilitate distribution system management (DSM). Accordingly, the objective is to coordinate the power injection at the DERs to maintain certain quantities across the network, e.g., voltage magnitude, line flows, or line losses, to be close to a desired profile. By and large, the performance of the DSM algorithms has been challenged by two factors: i) the possibly non-strongly connected communication network over DERs that hinders the coordination; ii) the dynamics of the real system caused by themore » DERs with heterogeneous capabilities, time-varying operating conditions, and real-time measurement mismatches. In this paper, we investigate the modeling and algorithm design and analysis with the consideration of these two factors. In particular, a game theoretic characterization is first proposed to account for a locally connected communication network over DERs, along with the analysis of the existence and uniqueness of the Nash equilibrium (NE) therein. To achieve the equilibrium in a distributed fashion, a projected-gradient-based asynchronous DSM algorithm is then advocated. The algorithm performance, including the convergence speed and the tracking error, is analytically guaranteed under the dynamic setting. Extensive numerical tests on both synthetic and realistic cases corroborate the analytical results derived.« less

The Right Network for the Right Problem

ERIC Educational Resources Information Center

Gomez, Louis M.; Russell, Jennifer L.; Bryk, Anthony S.; LeMahieu, Paul G.; Mejia, Eva M.

2016-01-01

Educators are realizing that individuals working in isolation can't adequately address the teaching and learning problems that face us today. Collective action networks are needed. Sharing networks use collective energy to support individual action and agency, whereas execution networks typically address complex problems that require sustained…

Inverse dynamic substructuring using the direct hybrid assembly in the frequency domain

NASA Astrophysics Data System (ADS)

D'Ambrogio, Walter; Fregolent, Annalisa

2014-04-01

The paper deals with the identification of the dynamic behaviour of a structural subsystem, starting from the known dynamic behaviour of both the coupled system and the remaining part of the structural system (residual subsystem). This topic is also known as decoupling problem, subsystem subtraction or inverse dynamic substructuring. Whenever it is necessary to combine numerical models (e.g. FEM) and test models (e.g. FRFs), one speaks of experimental dynamic substructuring. Substructure decoupling techniques can be classified as inverse coupling or direct decoupling techniques. In inverse coupling, the equations describing the coupling problem are rearranged to isolate the unknown substructure instead of the coupled structure. On the contrary, direct decoupling consists in adding to the coupled system a fictitious subsystem that is the negative of the residual subsystem. Starting from a reduced version of the 3-field formulation (dynamic equilibrium using FRFs, compatibility and equilibrium of interface forces), a direct hybrid assembly is developed by requiring that both compatibility and equilibrium conditions are satisfied exactly, either at coupling DoFs only, or at additional internal DoFs of the residual subsystem. Equilibrium and compatibility DoFs might not be the same: this generates the so-called non-collocated approach. The technique is applied using experimental data from an assembled system made by a plate and a rigid mass.

Research into Queueing Network Theory.

DTIC Science & Technology

1977-09-01

and Zeigler, B. (1975) "Equilibrium properties of arbitrarily interconnected queueing netowrks ," Tech. Report 75-4, Computer and Communication...Associate. The project was extremely fortunate to secure the services of Dr. Wendel. Dr. Wendel was a project member for one month in the summer of

Insensitive dependence of delay-induced oscillation death on complex networks

NASA Astrophysics Data System (ADS)

Zou, Wei; Zheng, Xing; Zhan, Meng

2011-06-01

Oscillation death (also called amplitude death), a phenomenon of coupling induced stabilization of an unstable equilibrium, is studied for an arbitrary symmetric complex network with delay-coupled oscillators, and the critical conditions for its linear stability are explicitly obtained. All cases including one oscillator, a pair of oscillators, regular oscillator networks, and complex oscillator networks with delay feedback coupling, can be treated in a unified form. For an arbitrary symmetric network, we find that the corresponding smallest eigenvalue of the Laplacian λN (0 >λN ≥ -1) completely determines the death island, and as λN is located within the insensitive parameter region for nearly all complex networks, the death island keeps nearly the largest and does not sensitively depend on the complex network structures. This insensitivity effect has been tested for many typical complex networks including Watts-Strogatz (WS) and Newman-Watts (NW) small world networks, general scale-free (SF) networks, Erdos-Renyi (ER) random networks, geographical networks, and networks with community structures and is expected to be helpful for our understanding of dynamics on complex networks.

Stochastic cycle selection in active flow networks.

PubMed

Woodhouse, Francis G; Forrow, Aden; Fawcett, Joanna B; Dunkel, Jörn

2016-07-19

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models.

Self-Consistent Field Lattice Model for Polymer Networks.

PubMed

Tito, Nicholas B; Storm, Cornelis; Ellenbroek, Wouter G

2017-12-26

A lattice model based on polymer self-consistent field theory is developed to predict the equilibrium statistics of arbitrary polymer networks. For a given network topology, our approach uses moment propagators on a lattice to self-consistently construct the ensemble of polymer conformations and cross-link spatial probability distributions. Remarkably, the calculation can be performed "in the dark", without any prior knowledge on preferred chain conformations or cross-link positions. Numerical results from the model for a test network exhibit close agreement with molecular dynamics simulations, including when the network is strongly sheared. Our model captures nonaffine deformation, mean-field monomer interactions, cross-link fluctuations, and finite extensibility of chains, yielding predictions that differ markedly from classical rubber elasticity theory for polymer networks. By examining polymer networks with different degrees of interconnectivity, we gain insight into cross-link entropy, an important quantity in the macroscopic behavior of gels and self-healing materials as they are deformed.

Stochastic cycle selection in active flow networks

PubMed Central

Woodhouse, Francis G.; Forrow, Aden; Fawcett, Joanna B.; Dunkel, Jörn

2016-01-01

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models. PMID:27382186

Stability of differential susceptibility and infectivity epidemic models

PubMed Central

Bonzi, B.; Fall, A. A.; Iggidr, Abderrahman; Sallet, Gauthier

2011-01-01

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio ≤ 1 and the existence and uniqueness of an endemic equilibrium when > 1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when > 1. Our results encompass and generalize those of [18, 22]. AMS Subject Classification : 34A34,34D23,34D40,92D30 PMID:20148330

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

Recent research in network problems with applications

NASA Technical Reports Server (NTRS)

Thompson, G. L.

1980-01-01

The capabilities of network codes and their extensions are surveyed in regard to specially structured integer programming problems which are solved by using the solutions of a series of ordinary network problems.

Identification and Characterisation of Wetlands For A Correct Basin Management

NASA Astrophysics Data System (ADS)

Quadrado, F.; Gomes, F.

The effects of human activities on water resources have great conse- quences for water users. Some of the problems affecting water resources arise from conflicting uses, including discharge of untreated industrial and domestic wastewater and inadequate agricultural practices on the watersheds. The knowledge of hydrologic and water quality characteristics and behaviour of the system will provide the basis for action to prevent the degradation of water resources. So comprehensive and ratio- nal water management is a necessary condition for social and economic development. The Water Framework Directive defines a good status for all waters all types of waters to be achieved in 15 years. To wetlands the Directive purpose the prevention of their degradation and the protection of those wetlands directly depending on aquatic sys- tems. The sensitiveness of wetlands leads to a difficult management of this resources where it is necessary to know the dynamic of the system and the pressures that can change the ecosystem equilibrium. In spite of the critical role of wetlands, there is a lack of information related with these areas, many times not included in the monitor- ing activity routines. A water quality-monitoring network is an essential instrument of water management. Portugal is now redesigning their freshwater network monitoring in a watershed basis, to provide the necessary data to preserve and control the water quality of the rivers and reservoirs. The combined approach principle to the protec- tion of water that is defended in the Water Framework Directive, was adopted. One of the criterion used to the localisation of sampling stations were characterisation of protected areas. Portugal due to his natural and climate conditions have some impor- tant and unique ecosystems, sometimes being considered as protected areas. Their characteristics must be studied and their equilibrium preserved. Anyhow a little at- tention had been provided to these zones and the actual monitoring network does not take in account the specialities of these areas. Portugal presently has 12 sites desig- nated as Wetlands of International Importance, with a surface area of 66,096 hectares. This work pretend to identify and characterised the wetland areas in Portugal, evaluate their degradation and the requirements of the Water Framework Directive with regard to wetlands. Also the importance of this systems to the watershed management is dis- cussed and the improvements with the implementation of the new monitoring network on controlling and preserving water quality in wetlands areas.

Analog Processor To Solve Optimization Problems

NASA Technical Reports Server (NTRS)

Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.

1993-01-01

Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.

A brief historical introduction to Euler's formula for polyhedra, topology, graph theory and networks

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2010-09-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Microeconomics-based resource allocation in overlay networks by using non-strategic behavior modeling

NASA Astrophysics Data System (ADS)

Analoui, Morteza; Rezvani, Mohammad Hossein

2011-01-01

Behavior modeling has recently been investigated for designing self-organizing mechanisms in the context of communication networks in order to exploit the natural selfishness of the users with the goal of maximizing the overall utility. In strategic behavior modeling, the users of the network are assumed to be game players who seek to maximize their utility with taking into account the decisions that the other players might make. The essential difference between the aforementioned researches and this work is that it incorporates the non-strategic decisions in order to design the mechanism for the overlay network. In this solution concept, the decisions that a peer might make does not affect the actions of the other peers at all. The theory of consumer-firm developed in microeconomics is a model of the non-strategic behavior that we have adopted in our research. Based on it, we have presented distributed algorithms for peers' "joining" and "leaving" operations. We have modeled the overlay network as a competitive economy in which the content provided by an origin server can be viewed as commodity and the origin server and the peers who multicast the content to their downside are considered as the firms. On the other hand, due to the dual role of the peers in the overlay network, they can be considered as the consumers as well. On joining to the overlay economy, each peer is provided with an income and tries to get hold of the service regardless to the behavior of the other peers. We have designed the scalable algorithms in such a way that the existence of equilibrium price (known as Walrasian equilibrium price) is guaranteed.

Mechanical response of transient telechelic networks with many-part stickers

NASA Astrophysics Data System (ADS)

Sing, Michelle K.; Ramírez, Jorge; Olsen, Bradley D.

2017-11-01

A central question in soft matter is understanding how several individual, weak bonds act together to produce collective interactions. Here, gel-forming telechelic polymers with multiple stickers at each chain end are studied through Brownian dynamics simulations to understand how collective interaction of the bonds affects mechanical response of the gels. These polymers are modeled as finitely extensible dumbbells using an explicit tau-leap algorithm and the binding energy of these associations was kept constant regardless of the number of stickers. The addition of multiple bonds to the associating ends of telechelic polymers increases or decreases the network relaxation time depending on the relative kinetics of association but increases both shear stress and extensional viscosity. The relationship between the rate of association and the Rouse time of dangling chains results in two different regimes for the equilibrium stress relaxation of associating physical networks. In case I, a dissociated dangling chain is able to fully relax before re-associating to the network, resulting in two characteristic relaxation times and a non-monotonic terminal relaxation time with increasing number of bonds per polymer endgroup. In case II, the dissociated dangling chain is only able to relax a fraction of the way before it re-attaches to the network, and increasing the number of bonds per endgroup monotonically increases the terminal relaxation time. In flow, increasing the number of stickers increases the steady-state shear and extensional viscosities even though the overall bond kinetics and equilibrium constant remain unchanged. Increased dissipation in the simulations is primarily due to higher average chain extension with increasing bond number. These results indicate that toughness and dissipation in physically associating networks can both be increased by breaking single, strong bonds into smaller components.

Network Design for Reliability and Resilience to Attack

DTIC Science & Technology

2014-03-01

attacker can destroy n arcs in the network SPNI Shortest-Path Network-Interdiction problem TSP Traveling Salesman Problem UB upper bound UKR Ukraine...elimination from the traveling salesman problem (TSP). Literature calls a walk that does not contain a cycle a path [19]. The objective function in...arc lengths as random variables with known probability distributions. The m-median problem seeks to design a network with minimum average travel cost

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

Sensor Authentication in Collaborating Sensor Networks

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

Bielefeldt, Jake Uriah

2014-11-01

In this thesis, we address a new security problem in the realm of collaborating sensor networks. By collaborating sensor networks, we refer to the networks of sensor networks collaborating on a mission, with each sensor network is independently owned and operated by separate entities. Such networks are practical where a number of independent entities can deploy their own sensor networks in multi-national, commercial, and environmental scenarios, and some of these networks will integrate complementary functionalities for a mission. In the scenario, we address an authentication problem wherein the goal is for the Operator O i of Sensor Network S imore » to correctly determine the number of active sensors in Network Si. Such a problem is challenging in collaborating sensor networks where other sensor networks, despite showing an intent to collaborate, may not be completely trustworthy and could compromise the authentication process. We propose two authentication protocols to address this problem. Our protocols rely on Physically Unclonable Functions, which are a hardware based authentication primitive exploiting inherent randomness in circuit fabrication. Our protocols are light-weight, energy efficient, and highly secure against a number of attacks. To the best of our knowledge, ours is the first to addresses a practical security problem in collaborating sensor networks.« less

Robe's restricted problem of 2+2 bodies when the bigger primary is a Roche ellipsoid and the smaller primary is an oblate body

NASA Astrophysics Data System (ADS)

Kaur, Bhavneet; Aggarwal, Rajiv

2014-01-01

In this problem, one of the primaries of mass m 1 is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ 1. The smaller primary of mass m 2 is an oblate body outside the Ellipsoid. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m 2 is describing a circle around m 1. The masses m 3 and m 4 mutually attract each other, do not influence the motions of m 1 and m 2 but are influenced by them. We have extended the Robe's restricted three-body problem to 2+2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar in Ellipsoidal figures of equilibrium, Chap. 8, Dover, New York, 1987). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m 2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m 3 and m 4 and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. In a system where the primaries are considered as Earth-Moon and m 3, m 4 as submarines, the equilibrium solutions of m 3 and m 4 respectively when the displacement is given in the direction of x 1-axis or x 2-axis are unstable.

Equilibrium charge distribution on a finite straight one-dimensional wire

NASA Astrophysics Data System (ADS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed

2017-09-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.

Low temperature geothermal systems in carbonate-evaporitic rocks: Mineral equilibria assumptions and geothermometrical calculations. Insights from the Arnedillo thermal waters (Spain).

PubMed

Blasco, Mónica; Gimeno, María J; Auqué, Luis F

2018-02-15

Geothermometrical calculations in low-medium temperature geothermal systems hosted in carbonate-evaporitic rocks are complicated because 1) some of the classical chemical geothermometers are, usually, inadequate (since they were developed for higher temperature systems with different mineral-water equilibria at depth) and 2) the chemical geothermometers calibrated for these systems (based on the Ca and Mg or SO 4 and F contents) are not free of problems either. The case study of the Arnedillo thermal system, a carbonate-evaporitic system of low temperature, will be used to deal with these problems through the combination of several geothermometrical techniques (chemical and isotopic geothermometers and geochemical modelling). The reservoir temperature of the Arnedillo geothermal system has been established to be in the range of 87±13°C being the waters in equilibrium with respect to calcite, dolomite, anhydrite, quartz, albite, K-feldspar and other aluminosilicates. Anhydrite and quartz equilibria are highly reliable to stablish the reservoir temperature. Additionally, the anhydrite equilibrium explains the coherent results obtained with the δ 18 O anhydrite - water geothermometer. The equilibrium with respect to feldspars and other aluminosilicates is unusual in carbonate-evaporitic systems and it is probably related to the presence of detrital material in the aquifer. The identification of the expected equilibria with calcite and dolomite presents an interesting problem associated to dolomite. Variable order degrees of dolomite can be found in natural systems and this fact affects the associated equilibrium temperature in the geothermometrical modelling and also the results from the Ca-Mg geothermometer. To avoid this uncertainty, the order degree of the dolomite present in the Arnedillo reservoir has been determined and the results indicate 18.4% of ordered dolomite and 81.6% of disordered dolomite. Overall, the results suggest that this multi-technique approach is very useful to solve some of the problems associated to the study of carbonate-evaporitic geothermal systems. Copyright © 2017 Elsevier B.V. All rights reserved.

Influence of the extrinsic curvature on two-dimensional nematic films.

PubMed

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Influence of the extrinsic curvature on two-dimensional nematic films

NASA Astrophysics Data System (ADS)

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

NASA Astrophysics Data System (ADS)

Kmet', Tibor; Kmet'ová, Mária

2009-09-01

A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

A program to compute the soft Robinson-Foulds distance between phylogenetic networks.

PubMed

Lu, Bingxin; Zhang, Louxin; Leong, Hon Wai

2017-03-14

Over the past two decades, phylogenetic networks have been studied to model reticulate evolutionary events. The relationships among phylogenetic networks, phylogenetic trees and clusters serve as the basis for reconstruction and comparison of phylogenetic networks. To understand these relationships, two problems are raised: the tree containment problem, which asks whether a phylogenetic tree is displayed in a phylogenetic network, and the cluster containment problem, which asks whether a cluster is represented at a node in a phylogenetic network. Both the problems are NP-complete. A fast exponential-time algorithm for the cluster containment problem on arbitrary networks is developed and implemented in C. The resulting program is further extended into a computer program for fast computation of the Soft Robinson-Foulds distance between phylogenetic networks. Two computer programs are developed for facilitating reconstruction and validation of phylogenetic network models in evolutionary and comparative genomics. Our simulation tests indicated that they are fast enough for use in practice. Additionally, the distribution of the Soft Robinson-Foulds distance between phylogenetic networks is demonstrated to be unlikely normal by our simulation data.

Optimal signal timing design for urban street networks under user equilibrium based traffic conditions : final report.

DOT National Transportation Integrated Search

2016-09-20

In the ever-growing travel demand, traffic congestion on freeways and expressways : recurs more frequently at a higher number of locations and for longer durations with : added severity. This becomes especially true in large metropolitan areas. Parti...

NSI operations center

NASA Technical Reports Server (NTRS)

Zanley, Nancy L.

1991-01-01

The NASA Science Internet (NSI) Network Operations Staff is responsible for providing reliable communication connectivity for the NASA science community. As the NSI user community expands, so does the demand for greater interoperability with users and resources on other networks (e.g., NSFnet, ESnet), both nationally and internationally. Coupled with the science community's demand for greater access to other resources is the demand for more reliable communication connectivity. Recognizing this, the NASA Science Internet Project Office (NSIPO) expands its Operations activities. By January 1990, Network Operations was equipped with a telephone hotline, and its staff was expanded to six Network Operations Analysts. These six analysts provide 24-hour-a-day, 7-day-a-week coverage to assist site managers with problem determination and resolution. The NSI Operations staff monitors network circuits and their associated routers. In most instances, NSI Operations diagnoses and reports problems before users realize a problem exists. Monitoring of the NSI TCP/IP Network is currently being done with Proteon's Overview monitoring system. The Overview monitoring system displays a map of the NSI network utilizing various colors to indicate the conditions of the components being monitored. Each node or site is polled via the Simple Network Monitoring Protocol (SNMP). If a circuit goes down, Overview alerts the Network Operations staff with an audible alarm and changes the color of the component. When an alert is received, Network Operations personnel immediately verify and diagnose the problem, coordinate repair with other networking service groups, track problems, and document problem and resolution into a trouble ticket data base. NSI Operations offers the NSI science community reliable connectivity by exercising prompt assessment and resolution of network problems.

Building New Bridges between In Vitro and In Vivo in Early Drug Discovery: Where Molecular Modeling Meets Systems Biology.

PubMed

Pearlstein, Robert A; McKay, Daniel J J; Hornak, Viktor; Dickson, Callum; Golosov, Andrei; Harrison, Tyler; Velez-Vega, Camilo; Duca, José

2017-01-01

Cellular drug targets exist within networked function-generating systems whose constituent molecular species undergo dynamic interdependent non-equilibrium state transitions in response to specific perturbations (i.e.. inputs). Cellular phenotypic behaviors are manifested through the integrated behaviors of such networks. However, in vitro data are frequently measured and/or interpreted with empirical equilibrium or steady state models (e.g. Hill, Michaelis-Menten, Briggs-Haldane) relevant to isolated target populations. We propose that cells act as analog computers, "solving" sets of coupled "molecular differential equations" (i.e. represented by populations of interacting species)via "integration" of the dynamic state probability distributions among those populations. Disconnects between biochemical and functional/phenotypic assays (cellular/in vivo) may arise with targetcontaining systems that operate far from equilibrium, and/or when coupled contributions (including target-cognate partner binding and drug pharmacokinetics) are neglected in the analysis of biochemical results. The transformation of drug discovery from a trial-and-error endeavor to one based on reliable design criteria depends on improved understanding of the dynamic mechanisms powering cellular function/dysfunction at the systems level. Here, we address the general mechanisms of molecular and cellular function and pharmacological modulation thereof. We outline a first principles theory on the mechanisms by which free energy is stored and transduced into biological function, and by which biological function is modulated by drug-target binding. We propose that cellular function depends on dynamic counter-balanced molecular systems necessitated by the exponential behavior of molecular state transitions under non-equilibrium conditions, including positive versus negative mass action kinetics and solute-induced perturbations to the hydrogen bonds of solvating water versus kT. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Destabilizing Effects of Impulse in Delayed Bam Neural Networks

NASA Astrophysics Data System (ADS)

Li, Chuandong; Li, Chaojie; Liu, Chao

This paper further studies the global exponential stability of the equilibrium point of the delayed bidirectional associative memory (DBAM) neural networks with impulse effects. Several results characterizing the aggregated effects of impulse and dynamical property of the impulse-free DBAM on the exponential stability of the considered DBAM have been established. It is shown that the impulsive DBAM will preserve the global exponential stability of the impulse-free DBAM even if the impulses have enlarging effects on the states of neurons.

Molecular-level Analysis of Shock-wave Physics and Derivation of the Hugoniot Relations for Soda-lime Glass

DTIC Science & Technology

2011-06-17

based glasses like fused silica and soda - lime glass , the polyhedral central cation is silicon. In this case, each silicon is surrounded by four oxygen...to two network forming cations) oxygen atoms per network polyhedron. The equilibrium values for this parameter in fused silica and soda - lime glass ...Molecular-level analysis of shock-wave physics and derivation of the Hugoniot relations for soda - lime glass M. Grujicic • B. Pandurangan • W. C. Bell

Revisiting a Problem of Two Freezers

ERIC Educational Resources Information Center

Easton, Don

2014-01-01

The January 2013 Physics Challenge for Teachers and Students has some features that are surprising and worth a closer look. The problem concerns a Carnot-cycle refrigeration unit operating inside a tent. It achieves dynamic equilibrium with a freezer ("cold") compartment temperature of T[subscript C] = 13°C, tent temperature of…

The modeling and analysis of the word-of-mouth marketing

NASA Astrophysics Data System (ADS)

Li, Pengdeng; Yang, Xiaofan; Yang, Lu-Xing; Xiong, Qingyu; Wu, Yingbo; Tang, Yuan Yan

2018-03-01

As compared to the traditional advertising, word-of-mouth (WOM) communications have striking advantages such as significantly lower cost and much faster propagation, and this is especially the case with the popularity of online social networks. This paper focuses on the modeling and analysis of the WOM marketing. A dynamic model, known as the SIPNS model, capturing the WOM marketing processes with both positive and negative comments is established. On this basis, a measure of the overall profit of a WOM marketing campaign is proposed. The SIPNS model is shown to admit a unique equilibrium, and the equilibrium is determined. The impact of different factors on the equilibrium of the SIPNS model is illuminated through theoretical analysis. Extensive experimental results suggest that the equilibrium is much likely to be globally attracting. Finally, the influence of different factors on the expected overall profit of a WOM marketing campaign is ascertained both theoretically and experimentally. Thereby, some promotion strategies are recommended. To our knowledge, this is the first time the WOM marketing is treated in this way.

Final Scientific Report: Experimental Investigation of Reconnection in a Line-tied Plasma

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

Forest, Cary

This grant used funding from the NSF/DoE Partnership on Plasma Science to investigate magnetic reconnection phenomena in a line-tied pinch experiment. The experiment was upgraded from a previous device intended to study fusion plasma-related instabilities to a new configuration capable of studying a number of new, previously unstudied configurations. A high spatial and time resolution array of magnetic probes was constructed to measure time evolving structures present as instability and turbulence developed. The most important new equilibrium made possible by this grant was a Zero-Net-Current equilibrium that models the footpoint twisting of solar flux tubes that occurs prior to solarmore » eruptions (flares and coronal mass ejections). This new equilibrium was successfully created in the lab, and it exhibited a host of instabilities. In particular, at low current when the equilibrium was not overly stressed, a saturated internal kink mode oscillation was observed. At high current, 2 D magnetic turbulence developed which we attribute to the lack of a equilibrium brought about by a subcritical transition to turbulence. A second set of experiments involved the turbulent interactions of a collection of flux tubes all being twisted independently, a problem known as the Parker Problem. Current profiles consisting of 2, 3 and 4 guns were used to impose a fine scale drive, and resulted in a new experimental platform in which the injection scale of the magnetic turbulence could be controlled. First experiments in this configuration support the conclusion that an inverse cascade of magnetic energy occurred which self-organized the plasma into a nearly axisymmetric current distribution.« less

Neural networks applications to control and computations

NASA Technical Reports Server (NTRS)

Luxemburg, Leon A.

1994-01-01

Several interrelated problems in the area of neural network computations are described. First an interpolation problem is considered, then a control problem is reduced to a problem of interpolation by a neural network via Lyapunov function approach, and finally a new, faster method of learning as compared with the gradient descent method, was introduced.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

PubMed

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

Against the grain: The physical properties of anisotropic partially molten rocks

NASA Astrophysics Data System (ADS)

Ghanbarzadeh, S.; Hesse, M. A.; Prodanovic, M.

2014-12-01

Partially molten rocks commonly develop textures that appear close to textural equilibrium, where the melt network evolves to minimize the energy of the melt-solid interfaces, while maintaining the dihedral angle θ at solid-solid-melt contact lines. Textural equilibrium provides a powerful model for the melt distribution that controls the petro-physical properties of partially molten rocks, e.g., permeability, elastic moduli, and electrical resistivity. We present the first level-set computations of three-dimensional texturally equilibrated melt networks in rocks with an anisotropic fabric. Our results show that anisotropy induces wetting of smaller grain boundary faces for θ > 0 at realistic porosities ϕ < 3%. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Wetting of the grain boundary faces leads to a dramatic redistribution of the melt from the edges to the faces that introduces strong anisotropy in the petro-physical properties such as permeability, effective electrical conductivity and mechanical properties. Figure, on left, shows that smaller grain boundaries become wetted at relatively low melt fractions of 3% in stretched polyhedral grains with elongation factor 1.5. Right plot represents the ratio of melt electrical conductivity to effective conductivity of medium (known as formation factor) as an example of anisotropy in physical properties. The plot shows that even slight anisotropy in grains induces considerable anisotropy in electrical properties.

Learning in stochastic neural networks for constraint satisfaction problems

NASA Technical Reports Server (NTRS)

Johnston, Mark D.; Adorf, Hans-Martin

1989-01-01

Researchers describe a newly-developed artificial neural network algorithm for solving constraint satisfaction problems (CSPs) which includes a learning component that can significantly improve the performance of the network from run to run. The network, referred to as the Guarded Discrete Stochastic (GDS) network, is based on the discrete Hopfield network but differs from it primarily in that auxiliary networks (guards) are asymmetrically coupled to the main network to enforce certain types of constraints. Although the presence of asymmetric connections implies that the network may not converge, it was found that, for certain classes of problems, the network often quickly converges to find satisfactory solutions when they exist. The network can run efficiently on serial machines and can find solutions to very large problems (e.g., N-queens for N as large as 1024). One advantage of the network architecture is that network connection strengths need not be instantiated when the network is established: they are needed only when a participating neural element transitions from off to on. They have exploited this feature to devise a learning algorithm, based on consistency techniques for discrete CSPs, that updates the network biases and connection strengths and thus improves the network performance.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

PubMed

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

2017-10-01

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra.

PubMed

Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard

2014-06-26

A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

PubMed Central

2014-01-01

Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem. PMID:24965213

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

Stability Analysis of Landslide on the R1 Expressway by Limit Equilibrium and Finite Element Methods

NASA Astrophysics Data System (ADS)

Janták, Viktor

2017-12-01

The most difficult problem by designing the superior infrastructure is tracing the expressways and higways in an environment of Quaternary and Neogene complexes of finegrained cohesive and non-cohesive soils. At the last time the typical examples are stability problems on the R1 Nitra - Tekovské Nemce Expressway. The article is focused on the description of reasons of stability loss in the deep earth cut in the 79,000 km of expressway R1, the course of the landslide, slide correction and especially slope-stability assessment before and after the occurrence of slope failures by limit equilibrium and finite elements methods by comparing the behaviour of the slope in the various model situations.

Punctuated equilibrium as an emergent process and its modified thermodynamic characterization.

PubMed

Wosniack, M E; da Luz, M G E; Schulman, L S

2017-01-07

We address evolutionary dynamics and consider under which conditions the ecosystem interaction network allows punctuated equilibrium (i.e., alternation between hectic and quasi-stable phases). We focus on the links connecting various species and on the strength and sign of those links. For this study we consider the Tangled Nature model, which allows considerable flexibility and plasticity in the analysis of interspecies interactions. We find that it is necessary to have a proper balance of connectivity and interaction intensities so as to establish the kind of mutual cooperation and competition found in nature. It suggests evolutionary punctuated equilibrium as an emergent process, thus displaying features of complex systems. To explicitly demonstrate this fact we consider an extended form of thermodynamics, defining (for the present context) relevant out-of-equilibrium "collective" functions. We then show how to characterize the punctuated equilibrium through entropy-like and free energy-like quantities. Finally, from a close analogy to thermodynamic systems, we propose a protocol similar to simulated annealing. It is based on controlling the species' rate of mutation during the hectic periods, in this way enhancing the exploration of the genome space (similar to the known behavior of bacteria in stressful environments). This allows the system to more rapidly converge to long-duration quasi-stable phases. Copyright © 2016 Elsevier Ltd. All rights reserved.

Preliminary study: Moisture-polymer interaction. Stuby objectives

NASA Technical Reports Server (NTRS)

Wen, L. C.

1985-01-01

The problems associated with mathematically modeling water-module interaction phenomena, including sorption and desorption, diffusion, and permeation are discussed. With reliable analytical models, an extensive materials data base, and solar radiation surface meteorological observations (SOLMET) weather data, predicting module lifetimes in realistic environments can become a practical reality. The status of the present techniques of simulating the various transport mechanisms was reported. The Dent model (a modified Brunauer-Emmet-Teller) approach represented polyvinyl butyral (PVB) sorption data. A 100-layer material model and Fick's diffusion model gave diffusivity values exhibiting adequate agreement with those measured for PVB. Diffusivity of PVB is concentration dependent, decreasing as the water content in PVB increases. The temperature dependence of diffusion in PVB is well modeled by the Arrhenius rate equation. Equilibrium conductivity and leakage current data are well represented by Hearle's model for bulk ionic conductivity. A nodal network analysis using the Systems Improved Numerical Differencing Analyzer (SINDA) Thermal Analyzer gave reasonable correlation with measurable data. It is concluded that realistic lifetime predictions seem to be feasible.

A new neural network model for solving random interval linear programming problems.

PubMed

Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

2017-05-01

This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.