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

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2014-02-01

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

Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

PubMed

Seiffertt, John; Sanyal, Suman; Wunsch, Donald C

2008-08-01

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-06-01

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general method to construct it. We provide new formulae for constructing spectral projection operators and delineate the relations among projection operators, eigenvectors, and left and right generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples. First, we analyze stochastic transition operators in discrete and continuous time. Second, we show that nondiagonalizability can be a robust feature of a stochastic process, induced even by simple counting. As a result, we directly derive distributions of the time-dependent Poisson process and point out that nondiagonalizability is intrinsic to it and the broad class of hidden semi-Markov processes. Third, we show that the Drazin inverse arises naturally in stochastic thermodynamics and that applying the meromorphic functional calculus provides closed-form solutions for the dynamics of key thermodynamic observables. Finally, we draw connections to the Ruelle-Frobenius-Perron and Koopman operators for chaotic dynamical systems and propose how to extract eigenvalues from a time-series.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

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

NASA Astrophysics Data System (ADS)

Penland, C.

2013-12-01

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

Extremal flows in Wasserstein space

NASA Astrophysics Data System (ADS)

Conforti, Giovanni; Pavon, Michele

2018-06-01

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm's and Nelson's stochastic mechanics.

From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index {{alpha} {in} ((1)/(8),(1)/(4))}

NASA Astrophysics Data System (ADS)

Magnen, Jacques; Unterberger, Jérémie

2012-03-01

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise

NASA Astrophysics Data System (ADS)

Hinczewski, Michael; Thirumalai, D.

2014-10-01

Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

NASA Astrophysics Data System (ADS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-04-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevi equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O( N) non-linear α model and it is shown that singular terms appearing in the improved Langevin equation cancel out the σ n(O) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of idependent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalish.

Using Multi-Objective Genetic Programming to Synthesize Stochastic Processes

NASA Astrophysics Data System (ADS)

Ross, Brian; Imada, Janine

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

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

PubMed

Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

2017-10-01

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

Arbitrage with fractional Gaussian processes

NASA Astrophysics Data System (ADS)

Zhang, Xili; Xiao, Weilin

2017-04-01

While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

NASA Astrophysics Data System (ADS)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

Artificial Neural Network Metamodels of Stochastic Computer Simulations

DTIC Science & Technology

1994-08-10

SUBTITLE r 5. FUNDING NUMBERS Artificial Neural Network Metamodels of Stochastic I () Computer Simulations 6. AUTHOR(S) AD- A285 951 Robert Allen...8217!298*1C2 ARTIFICIAL NEURAL NETWORK METAMODELS OF STOCHASTIC COMPUTER SIMULATIONS by Robert Allen Kilmer B.S. in Education Mathematics, Indiana...dedicate this document to the memory of my father, William Ralph Kilmer. mi ABSTRACT Signature ARTIFICIAL NEURAL NETWORK METAMODELS OF STOCHASTIC

Multiscale Dynamics and Information in Data Collection and Assimilation for Environmental Applications

DTIC Science & Technology

2015-07-30

elsewhere such as: prepared in cooperation with; translation of; report supersedes; old edition number, etc. 14. ABSTRACT. A brief (approximately 200...involves the derivative of a stochastic path, which is obtained using Malliavin calculus . 4 DISTRIBUTION A: Distribution approved for public release...predictability, 8th European Nonlinear Oscillations Conference, The Vienna University of Technology, Vienna, Austria, July 06 – 11, 2014. [11] Lingala N

Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.

PubMed

Gursoy, Gamze; Terebus, Anna; Youfang Cao; Jie Liang

2016-08-01

Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.

Optimal control of switching time in switched stochastic systems with multi-switching times and different costs

NASA Astrophysics Data System (ADS)

Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian

2017-08-01

In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.

Chaotic Motions in the Dynamics of Space Tethered Systems. 1. Analysis of the Problem

NASA Astrophysics Data System (ADS)

Pirozhenko, A. V.

The determined-chaos phenomenon in the dynamics of space tethered systems is analyzed. A model problem, the essence of stochastic regimes of motion in the oscillation of masses in the internal degrees of freedom is formulated. A number of calculus approaches to the phenomenon is considered and the supposition is made that it is impossible to define the essence of the phenomenon by the mathematical methods traditional for mechanics.

CYBER DETERRENCE

DTIC Science & Technology

2016-02-11

directed.36 Protected systems operating on secure networks will weigh into the adversaries calculus of risk and cost of their actions versus this... calculus deterring them from attack. Our extended defense with forts and lookouts searching outside the perimeter providing current intelligence of any...Last accessed 30 January 2016). 51 Phil Stewart , U.S. Defense Chief says pre-emptive action possible over cyber threat, Oct 11, 2012, http

From Fractals to Fractional Vector Calculus: Measurement in the Correct Metric

NASA Astrophysics Data System (ADS)

Wheatcraft, S. W.; Meerschaert, M. M.; Mortensen, J.

2005-12-01

Traditional (stationary) stochastic theories have been fairly successful in reproducing transport behavior at relatively homogeneous field sites such as the Borden and Cape Code sites. However, the highly heterogeneous MADE site has produced tracer data that can not be adequately explained with traditional stochastic theories. In recent years, considerable attention has been focused on developing more sophisticated theories that can predict or reproduce the behavior of complex sites such as the MADE site. People began to realize that the model for geologic complexity may in many cases be very different than the model required for stochastic theory. Fractal approaches were useful in conceptualizing scale-invariant heterogeneity by demonstrating that scale dependant transport was just an artifact of our measurement system. Fractal media have dimensions larger than the dimension that measurement is taking place in, thus assuring the scale-dependence of parameters such as dispersivity. What was needed was a rigorous way to develop a theory that was consistent with the fractal dimension of the heterogeneity. The fractional advection-dispersion equation (FADE) was developed with this idea in mind. The second derivative in the dispersion term of the advection-dispersion equation is replaced with a fractional derivative. The order of differentiation, α, is fractional. Values of α in the range: 1 < α < 2 produce super-Fickian dispersion; in essence, the dispersion scaling is controlled by the value of α. When α = 2, the traditional advection-dispersion equation is recovered. The 1-D version of the FADE has been used successfully to back-predict tracer test behavior at several heterogeneous field sites, including the MADE site. It has been hypothesized that the order of differentiation in the FADE is equivalent to (or at least related to) the fractal dimension of the particle tracks (or geologic heterogeneity). With this way of thinking, one can think of the FADE as a governing equation written for the correct dimension, thus eliminating scale-dependent behavior. Before a generalized multi-dimensional form of the FADE can be developed, it has been necessary to develop a generalized fractional vector calculus. The authors have recently developed generalized canonical fractional forms of the gradient, divergence and curl. This fractional vector calculus will be useful in developing fractional forms of many governing equations in physics.

Structural factoring approach for analyzing stochastic networks

NASA Technical Reports Server (NTRS)

Hayhurst, Kelly J.; Shier, Douglas R.

1991-01-01

The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

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

Stability analysis for stochastic BAM nonlinear neural network with delays

NASA Astrophysics Data System (ADS)

Lv, Z. W.; Shu, H. S.; Wei, G. L.

2008-02-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.

Effect of the heterogeneous neuron and information transmission delay on stochastic resonance of neuronal networks

NASA Astrophysics Data System (ADS)

Wang, Qingyun; Zhang, Honghui; Chen, Guanrong

2012-12-01

We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate αh, which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as αh increases, which implies that the heterogeneity can improve stochastic resonance. However, as αh is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.

Bayesian Inference for Source Reconstruction: A Real-World Application

DTIC Science & Technology

2014-09-25

deliberately or acci- dentally . Two examples of operational monitoring sensor networks are the deployment of biological sensor arrays by the Department of...remarkable paper, Cox [16] demonstrated that proba- bility theory, when interpreted as logic, is the only calculus that conforms to a consistent theory...of inference. This demonstration provides the firm logical basis for asserting that probability calculus is the unique quantitative theory of

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

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

Yu, Haitao; Guo, Xinmeng; Wang, Jiang, E-mail: jiangwang@tju.edu.cn

2014-09-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient formore » the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.« less

Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes

NASA Astrophysics Data System (ADS)

Liyanagedera, Chamika M.; Sengupta, Abhronil; Jaiswal, Akhilesh; Roy, Kaushik

2017-12-01

Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway to achieving "brainlike" compact and energy-efficient cognitive intelligence. The computational model attempt to exploit the intrinsic device stochasticity of nanoelectronic synaptic or neural components to perform learning or inference. However, there has been limited analysis on the scaling effect of stochastic spin devices and its impact on the operation of such stochastic networks at the system level. This work attempts to explore the design space and analyze the performance of nanomagnet-based stochastic neuromorphic computing architectures for magnets with different barrier heights. We illustrate how the underlying network architecture must be modified to account for the random telegraphic switching behavior displayed by magnets with low barrier heights as they are scaled into the superparamagnetic regime. We perform a device-to-system-level analysis on a deep neural-network architecture for a digit-recognition problem on the MNIST data set.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

Stochastic associative memory

NASA Astrophysics Data System (ADS)

Baumann, Erwin W.; Williams, David L.

1993-08-01

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

Exponential stability of stochastic complex networks with multi-weights based on graph theory

NASA Astrophysics Data System (ADS)

Zhang, Chunmei; Chen, Tianrui

2018-04-01

In this paper, a novel approach to exponential stability of stochastic complex networks with multi-weights is investigated by means of the graph-theoretical method. New sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights. It is noted that our stability results are closely related with multi-weights and the intensity of stochastic disturbance. Numerical simulations are also presented to substantiate the theoretical results.

Stochastic and deterministic models for agricultural production networks.

PubMed

Bai, P; Banks, H T; Dediu, S; Govan, A Y; Last, M; Lloyd, A L; Nguyen, H K; Olufsen, M S; Rempala, G; Slenning, B D

2007-07-01

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.

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

PubMed

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

2009-11-01

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

Stochastic calculus of protein filament formation under spatial confinement

NASA Astrophysics Data System (ADS)

Michaels, Thomas C. T.; Dear, Alexander J.; Knowles, Tuomas P. J.

2018-05-01

The growth of filamentous aggregates from precursor proteins is a process of central importance to both normal and aberrant biology, for instance as the driver of devastating human disorders such as Alzheimer's and Parkinson's diseases. The conventional theoretical framework for describing this class of phenomena in bulk is based upon the mean-field limit of the law of mass action, which implicitly assumes deterministic dynamics. However, protein filament formation processes under spatial confinement, such as in microdroplets or in the cellular environment, show intrinsic variability due to the molecular noise associated with small-volume effects. To account for this effect, in this paper we introduce a stochastic differential equation approach for investigating protein filament formation processes under spatial confinement. Using this framework, we study the statistical properties of stochastic aggregation curves, as well as the distribution of reaction lag-times. Moreover, we establish the gradual breakdown of the correlation between lag-time and normalized growth rate under spatial confinement. Our results establish the key role of spatial confinement in determining the onset of stochasticity in protein filament formation and offer a formalism for studying protein aggregation kinetics in small volumes in terms of the kinetic parameters describing the aggregation dynamics in bulk.

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

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

Memristor-based neural networks: Synaptic versus neuronal stochasticity

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

The zitterbewegung region

NASA Astrophysics Data System (ADS)

Sidharth, B. G.; Das, Abhishek

2017-07-01

This paper deals with a precise description of the region of zitterbewegung below the Compton scale and the stochastic nature associated with it. We endeavor to delineate this particular region by means of Ito’s calculus and instigate certain features that are in sharp contrast with conventional physics. Interestingly, our work substantiates that the zitterbewegung region represents a pre-space-time region and from therein emerges the notion of our conventional space-time. Interestingly, this unique region engenders the relativistic and quantum mechanical aspects of space-time.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks.

PubMed

Adalsteinsson, David; McMillen, David; Elston, Timothy C

2004-03-08

Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solves the appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Stochastic resonance enhancement of small-world neural networks by hybrid synapses and time delay

NASA Astrophysics Data System (ADS)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang

2017-01-01

The synergistic effect of hybrid electrical-chemical synapses and information transmission delay on the stochastic response behavior in small-world neuronal networks is investigated. Numerical results show that, the stochastic response behavior can be regulated by moderate noise intensity to track the rhythm of subthreshold pacemaker, indicating the occurrence of stochastic resonance (SR) in the considered neural system. Inheriting the characteristics of two types of synapses-electrical and chemical ones, neural networks with hybrid electrical-chemical synapses are of great improvement in neuron communication. Particularly, chemical synapses are conducive to increase the network detectability by lowering the resonance noise intensity, while the information is better transmitted through the networks via electrical coupling. Moreover, time delay is able to enhance or destroy the periodic stochastic response behavior intermittently. In the time-delayed small-world neuronal networks, the introduction of electrical synapses can significantly improve the signal detection capability by widening the range of optimal noise intensity for the subthreshold signal, and the efficiency of SR is largely amplified in the case of pure chemical couplings. In addition, the stochastic response behavior is also profoundly influenced by the network topology. Increasing the rewiring probability in pure chemically coupled networks can always enhance the effect of SR, which is slightly influenced by information transmission delay. On the other hand, the capacity of information communication is robust to the network topology within the time-delayed neuronal systems including electrical couplings.

The Instructional Network: Using Facebook to Enhance Undergraduate Mathematics Instruction

ERIC Educational Resources Information Center

Gregory, Peter; Gregory, Karen; Eddy, Erik

2014-01-01

Facebook is a website with over one billion users worldwide that is synonymous with social-networking. However, in this study, Facebook is used as an "instructional network". Two sections of an undergraduate calculus course were used to study the effects of participating in a Facebook group devoted solely to instruction. One section was…

Stochastic flux analysis of chemical reaction networks

PubMed Central

2013-01-01

Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153

Stochastic flux analysis of chemical reaction networks.

PubMed

Kahramanoğulları, Ozan; Lynch, James F

2013-12-07

Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.

Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

Uncertainty Reduction for Stochastic Processes on Complex Networks

NASA Astrophysics Data System (ADS)

Radicchi, Filippo; Castellano, Claudio

2018-05-01

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

H∞ state estimation of stochastic memristor-based neural networks with time-varying delays.

PubMed

Bao, Haibo; Cao, Jinde; Kurths, Jürgen; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

This paper addresses the problem of H ∞ state estimation for a class of stochastic memristor-based neural networks with time-varying delays. Under the framework of Filippov solution, the stochastic memristor-based neural networks are transformed into systems with interval parameters. The present paper is the first to investigate the H ∞ state estimation problem for continuous-time Itô-type stochastic memristor-based neural networks. By means of Lyapunov functionals and some stochastic technique, sufficient conditions are derived to ensure that the estimation error system is asymptotically stable in the mean square with a prescribed H ∞ performance. An explicit expression of the state estimator gain is given in terms of linear matrix inequalities (LMIs). Compared with other results, our results reduce control gain and control cost effectively. Finally, numerical simulations are provided to demonstrate the efficiency of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks.

PubMed

Samant, Asawari; Ogunnaike, Babatunde A; Vlachos, Dionisios G

2007-05-24

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void. The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm. We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.

Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

NASA Astrophysics Data System (ADS)

Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,

2010-08-01

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

pth moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays.

PubMed

Wang, Fen; Chen, Yuanlong; Liu, Meichun

2018-02-01

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô's differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy-Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Adaptive logical stochastic resonance in time-delayed synthetic genetic networks

NASA Astrophysics Data System (ADS)

Zhang, Lei; Zheng, Wenbin; Song, Aiguo

2018-04-01

In the paper, the concept of logical stochastic resonance is applied to implement logic operation and latch operation in time-delayed synthetic genetic networks derived from a bacteriophage λ. Clear logic operation and latch operation can be obtained when the network is tuned by modulated periodic force and time-delay. In contrast with the previous synthetic genetic networks based on logical stochastic resonance, the proposed system has two advantages. On one hand, adding modulated periodic force to the background noise can increase the length of the optimal noise plateau of obtaining desired logic response and make the system adapt to varying noise intensity. On the other hand, tuning time-delay can extend the optimal noise plateau to larger range. The result provides possible help for designing new genetic regulatory networks paradigm based on logical stochastic resonance.

Stochastic Geometric Network Models for Groups of Functional and Structural Connectomes

PubMed Central

Friedman, Eric J.; Landsberg, Adam S.; Owen, Julia P.; Li, Yi-Ou; Mukherjee, Pratik

2014-01-01

Structural and functional connectomes are emerging as important instruments in the study of normal brain function and in the development of new biomarkers for a variety of brain disorders. In contrast to single-network studies that presently dominate the (non-connectome) network literature, connectome analyses typically examine groups of empirical networks and then compare these against standard (stochastic) network models. Current practice in connectome studies is to employ stochastic network models derived from social science and engineering contexts as the basis for the comparison. However, these are not necessarily best suited for the analysis of connectomes, which often contain groups of very closely related networks, such as occurs with a set of controls or a set of patients with a specific disorder. This paper studies important extensions of standard stochastic models that make them better adapted for analysis of connectomes, and develops new statistical fitting methodologies that account for inter-subject variations. The extensions explicitly incorporate geometric information about a network based on distances and inter/intra hemispherical asymmetries (to supplement ordinary degree-distribution information), and utilize a stochastic choice of networks' density levels (for fixed threshold networks) to better capture the variance in average connectivity among subjects. The new statistical tools introduced here allow one to compare groups of networks by matching both their average characteristics and the variations among them. A notable finding is that connectomes have high “smallworldness” beyond that arising from geometric and degree considerations alone. PMID:25067815

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

PubMed

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

2006-01-01

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

Newton, Laplace, and The Epistemology of Systems Biology

PubMed Central

Bittner, Michael L.; Dougherty, Edward R.

2012-01-01

For science, theoretical or applied, to significantly advance, researchers must use the most appropriate mathematical methods. A century and a half elapsed between Newton’s development of the calculus and Laplace’s development of celestial mechanics. One cannot imagine the latter without the former. Today, more than three-quarters of a century has elapsed since the birth of stochastic systems theory. This article provides a perspective on the utilization of systems theory as the proper vehicle for the development of systems biology and its application to complex regulatory diseases such as cancer. PMID:23170064

The topological particle and Morse theory

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-09-01

Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved space, is used to give an explicit and simple expression for the matrix elements of the evolution operator for the BRST Hamiltonian. These matrix elements lead to a representation of the manifold cohomology in terms of critical points of h along lines developed by Witten (Witten E 1982 J. Diff. Geom. 17 661-92).

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

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

PubMed Central

Chen, Bor-Sen; Ho, Shih-Ju

2014-01-01

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

Stochastic simulation and analysis of biomolecular reaction networks

PubMed Central

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

2009-01-01

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

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

NASA Astrophysics Data System (ADS)

Wang, Ting; Plecháč, Petr

2017-12-01

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

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

2009-06-15

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

Skeleton-supported stochastic networks of organic memristive devices: Adaptations and learning

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

Erokhina, Svetlana; Sorokin, Vladimir; Erokhin, Victor, E-mail: victor.erokhin@fis.unipr.it

Stochastic networks of memristive devices were fabricated using a sponge as a skeleton material. Cyclic voltage-current characteristics, measured on the network, revealed properties, similar to the organic memristive device with deterministic architecture. Application of the external training resulted in the adaptation of the network electrical properties. The system revealed an improved stability with respect to the networks, composed from polymer fibers.

Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects.

PubMed

Huang, Tingwen; Li, Chuandong; Duan, Shukai; Starzyk, Janusz A

2012-06-01

This paper focuses on the hybrid effects of parameter uncertainty, stochastic perturbation, and impulses on global stability of delayed neural networks. By using the Ito formula, Lyapunov function, and Halanay inequality, we established several mean-square stability criteria from which we can estimate the feasible bounds of impulses, provided that parameter uncertainty and stochastic perturbations are well-constrained. Moreover, the present method can also be applied to general differential systems with stochastic perturbation and impulses.

Stochastic approximation methods-Powerful tools for simulation and optimization: A survey of some recent work on multi-agent systems and cyber-physical systems

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

Yin, George; Wang, Le Yi; Zhang, Hongwei

2014-12-10

Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomlymore » switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.« less

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Balasubramaniam, P.

2008-07-01

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

PubMed Central

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R.

2014-01-01

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales. PMID:25099817

Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks.

PubMed

Deng, De-Ming; Chang, Cheng-Hung

2015-05-14

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.

Neuromorphic Optical Signal Processing and Image Understanding for Automated Target Recognition

DTIC Science & Technology

1989-12-01

34 Stochastic Learning Machine " Neuromorphic Target Identification * Cognitive Networks 3. Conclusions ..... ................ .. 12 4. Publications...16 5. References ...... ................... . 17 6. Appendices ....... .................. 18 I. Optoelectronic Neural Networks and...Learning Machines. II. Stochastic Optical Learning Machine. III. Learning Network for Extrapolation AccesFon For and Radar Target Identification

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation

PubMed Central

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO2) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms. PMID:29670508

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation.

PubMed

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO 2 ) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms.

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks

PubMed Central

Li, Yihe; Li, Bofeng; Gao, Yang

2015-01-01

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network. PMID:26633400

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks.

PubMed

Li, Yihe; Li, Bofeng; Gao, Yang

2015-11-30

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network.

Tuning stochastic transition rates in a bistable genetic network.

NASA Astrophysics Data System (ADS)

Chickarmane, Vijay; Peterson, Carsten

2009-03-01

We investigate the stochastic dynamics of a simple genetic network, a toggle switch, in which the system makes transitions between the two alternative states. Our interest is in exploring whether such stochastic transitions, which occur due to the intrinsic noise such as transcriptional and degradation events, can be slowed down/speeded up, without changing the mean expression levels of the two genes, which comprise the toggle network. Such tuning is achieved by linking a signaling network to the toggle switch. The signaling network comprises of a protein, which can exist either in an active (phosphorylated) or inactive (dephosphorylated) form, and where its state is determined by one of the genetic network components. The active form of the protein in turn feeds back on the dynamics of the genetic network. We find that the rate of stochastic transitions from one state to the other, is determined essentially by the speed of phosphorylation, and hence the rate can be modulated by varying the phosphatase levels. We hypothesize that such a network architecture can be implemented as a general mechanism for controlling transition rates and discuss applications in population studies of two differentiated cell lineages, ex: the myeloid/erythroid lineage in hematopoiesis.

Exploring information transmission in gene networks using stochastic simulation and machine learning

NASA Astrophysics Data System (ADS)

Park, Kyemyung; Prüstel, Thorsten; Lu, Yong; Narayanan, Manikandan; Martins, Andrew; Tsang, John

How gene regulatory networks operate robustly despite environmental fluctuations and biochemical noise is a fundamental question in biology. Mathematically the stochastic dynamics of a gene regulatory network can be modeled using chemical master equation (CME), but nonlinearity and other challenges render analytical solutions of CMEs difficult to attain. While approaches of approximation and stochastic simulation have been devised for simple models, obtaining a more global picture of a system's behaviors in high-dimensional parameter space without simplifying the system substantially remains a major challenge. Here we present a new framework for understanding and predicting the behaviors of gene regulatory networks in the context of information transmission among genes. Our approach uses stochastic simulation of the network followed by machine learning of the mapping between model parameters and network phenotypes such as information transmission behavior. We also devised ways to visualize high-dimensional phase spaces in intuitive and informative manners. We applied our approach to several gene regulatory circuit motifs, including both feedback and feedforward loops, to reveal underexplored aspects of their operational behaviors. This work is supported by the Intramural Program of NIAID/NIH.

A Learning Framework for Winner-Take-All Networks with Stochastic Synapses.

PubMed

Mostafa, Hesham; Cauwenberghs, Gert

2018-06-01

Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks operate along similar principles to implement a probabilistic model of the environment through transformations of intrinsic noise processes. The intrinsic neural and synaptic noise processes in biological networks, however, are quite different from the noise processes used in current abstract generative networks. This, together with the discrete nature of spikes and local circuit interactions among the neurons, raises several difficulties when using recent generative modeling frameworks to train biologically motivated models. In this letter, we show that a biologically motivated model based on multilayer winner-take-all circuits and stochastic synapses admits an approximate analytical description. This allows us to use the proposed networks in a variational learning setting where stochastic backpropagation is used to optimize a lower bound on the data log likelihood, thereby learning a generative model of the data. We illustrate the generality of the proposed networks and learning technique by using them in a structured output prediction task and a semisupervised learning task. Our results extend the domain of application of modern stochastic network architectures to networks where synaptic transmission failure is the principal noise mechanism.

Predicate calculus for an architecture of multiple neural networks

NASA Astrophysics Data System (ADS)

Consoli, Robert H.

1990-08-01

Future projects with neural networks will require multiple individual network components. Current efforts along these lines are ad hoc. This paper relates the neural network to a classical device and derives a multi-part architecture from that model. Further it provides a Predicate Calculus variant for describing the location and nature of the trainings and suggests Resolution Refutation as a method for determining the performance of the system as well as the location of needed trainings for specific proofs. 2. THE NEURAL NETWORK AND A CLASSICAL DEVICE Recently investigators have been making reports about architectures of multiple neural networksL234. These efforts are appearing at an early stage in neural network investigations they are characterized by architectures suggested directly by the problem space. Touretzky and Hinton suggest an architecture for processing logical statements1 the design of this architecture arises from the syntax of a restricted class of logical expressions and exhibits syntactic limitations. In similar fashion a multiple neural netword arises out of a control problem2 from the sequence learning problem3 and from the domain of machine learning. 4 But a general theory of multiple neural devices is missing. More general attempts to relate single or multiple neural networks to classical computing devices are not common although an attempt is made to relate single neural devices to a Turing machines and Sun et a!. develop a multiple neural architecture that performs pattern classification.

Approximate dynamic programming for optimal stationary control with control-dependent noise.

PubMed

Jiang, Yu; Jiang, Zhong-Ping

2011-12-01

This brief studies the stochastic optimal control problem via reinforcement learning and approximate/adaptive dynamic programming (ADP). A policy iteration algorithm is derived in the presence of both additive and multiplicative noise using Itô calculus. The expectation of the approximated cost matrix is guaranteed to converge to the solution of some algebraic Riccati equation that gives rise to the optimal cost value. Moreover, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, a numerical example is given to illustrate the efficiency of the proposed ADP methodology.

Theory and calculus of cubical complexes

NASA Technical Reports Server (NTRS)

Perlman, M.

1973-01-01

Combination switching networks with multiple outputs may be represented by Boolean functions. Report has been prepared which describes derivation and use of extraction algorithm that may be adapted to simplification of such simultaneous Boolean functions.

Discovering network behind infectious disease outbreak

NASA Astrophysics Data System (ADS)

Maeno, Yoshiharu

2010-11-01

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network and reveal the transmission parameters which govern the stochastic spreads over the network from a dataset on an infectious disease outbreak in the early growth phase. Populations in a combination of epidemiological compartment models and a meta-population network model are described by stochastic differential equations. Probability density functions are derived from the equations and used for the maximal likelihood estimation of the topology and parameters. The method is tested with computationally synthesized datasets and the WHO dataset on the SARS outbreak.

A Hybrid of the Chemical Master Equation and the Gillespie Algorithm for Efficient Stochastic Simulations of Sub-Networks.

PubMed

Albert, Jaroslav

2016-01-01

Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may require long computing times, while the CME may demand unrealistic memory storage capacity. We propose a method that combines the CME and the GA that allows one to simulate stochastically a part of a reaction network. First, a reaction network is divided into two parts. The first part is simulated via the GA, while the solution of the CME for the second part is fed into the GA in order to update its propensities. The advantage of this method is that it avoids the need to solve the CME or stochastically simulate the entire network, which makes it highly efficient. One of its drawbacks, however, is that most of the information about the second part of the network is lost in the process. Therefore, this method is most useful when only partial information about a reaction network is needed. We tested this method against the GA on two systems of interest in biology--the gene switch and the Griffith model of a genetic oscillator--and have shown it to be highly accurate. Comparing this method to four different stochastic algorithms revealed it to be at least an order of magnitude faster than the fastest among them.

Limitations and tradeoffs in synchronization of large-scale networks with uncertain links

PubMed Central

Diwadkar, Amit; Vaidya, Umesh

2016-01-01

The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scalar nonlinear systems with stochastic linear interactions over large-scale networks. This sufficient condition, expressed in terms of nonlinear dynamics, the Laplacian eigenvalues of the nominal interconnections, and the variance and location of the stochastic uncertainty, allows us to define a synchronization margin. We provide an analytical characterization of important trade-offs between the internal nonlinear dynamics, network topology, and uncertainty in synchronization. For nearest neighbour networks, the existence of an optimal number of neighbours with a maximum synchronization margin is demonstrated. An analytical formula for the optimal gain that produces the maximum synchronization margin allows us to compare the synchronization properties of various complex network topologies. PMID:27067994

Effects of patch quality and network structure on patch occupancy dynamics of a yellow-bellied marmot metapopulation.

PubMed

Ozgul, Arpat; Armitage, Kenneth B; Blumstein, Daniel T; Vanvuren, Dirk H; Oli, Madan K

2006-01-01

1. The presence/absence of a species at a particular site is the simplest form of data that can be collected during ecological field studies. We used 13 years (1990-2002) of survey data to parameterize a stochastic patch occupancy model for a metapopulation of the yellow-bellied marmot in Colorado, and investigated the significance of particular patches and the influence of site quality, network characteristics and regional stochasticity on the metapopulation persistence. 2. Persistence of the yellow-bellied marmot metapopulation was strongly dependent on the high quality colony sites, and persistence probability was highly sensitive to small changes in the quality of these sites. 3. A relatively small number of colony sites was ultimately responsible for the regional persistence. However, lower quality satellite sites also made a significant contribution to long-term metapopulation persistence, especially when regional stochasticity was high. 4. The northern network of the marmot metapopulation was more stable compared to the southern network, and the persistence of the southern network depended heavily on the northern network. 5. Although complex models of metapopulation dynamics may provide a more accurate description of metapopulation dynamics, such models are data-intensive. Our study, one of the very few applications of stochastic patch occupancy models to a mammalian species, suggests that stochastic patch occupancy models can provide important insights into metapopulation dynamics using data that are easy to collect.

Path integrals and large deviations in stochastic hybrid systems.

PubMed

Bressloff, Paul C; Newby, Jay M

2014-04-01

We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

Transient Response of a Second Order System Using State Variables.

ERIC Educational Resources Information Center

LePage, Wilbur R.

This programed booklet is designed for the engineering student who is familiar with the techniques of integral calculus and electrical networks. The booklet teaches how to determine the current and voltages across a resistor, inductor, and capacitor after the switch in a network has been closed. This is a classical problem in engineering, the…

Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

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

Wang, Hong; Aziz, H M Abdul; Young, Stan

Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections.more » In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.« less

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

PubMed Central

2009-01-01

Background The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is orchestrated. One of the reasons for the complexity of this pathway is the extensive network of inter-connected components involved in the signaling. In the aim of identifying critical mechanisms controlling signal transduction we have performed extensive analysis of an executable model of the EGFR pathway using the stochastic pi-calculus as a modeling language. Results Our analysis, done through simulation of various perturbations, suggests that the EGFR pathway contains regions of functional redundancy in the upstream parts; in the event of low EGF stimulus or partial system failure, this redundancy helps to maintain functional robustness. Downstream parts, like the parts controlling Ras and ERK, have fewer redundancies, and more than 50% inhibition of specific reactions in those parts greatly attenuates signal response. In addition, we suggest an abstract model that captures the main control mechanisms in the pathway. Simulation of this abstract model suggests that without redundancies in the upstream modules, signal transduction through the entire pathway could be attenuated. In terms of specific control mechanisms, we have identified positive feedback loops whose role is to prolong the active state of key components (e.g., MEK-PP, Ras-GTP), and negative feedback loops that help promote signal adaptation and stabilization. Conclusions The insights gained from simulating this executable model facilitate the formulation of specific hypotheses regarding the control mechanisms of the EGFR signaling, and further substantiate the benefit to construct abstract executable models of large complex biological networks. PMID:20028552

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

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

FERN - a Java framework for stochastic simulation and evaluation of reaction networks.

PubMed

Erhard, Florian; Friedel, Caroline C; Zimmer, Ralf

2008-08-29

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new systems biology applications. Finally, complex scenarios requiring intervention during the simulation progress can be modelled easily with FERN.

Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

NASA Astrophysics Data System (ADS)

Yu, Haitao; Wang, Jiang; Liu, Chen; Deng, Bin; Wei, Xile

2011-12-01

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.

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.

Stochastic Routing and Scheduling Policies for Energy Harvesting Communication Networks

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

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

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

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

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

Ensemble methods for stochastic networks with special reference to the biological clock of Neurospora crassa.

PubMed

Caranica, C; Al-Omari, A; Deng, Z; Griffith, J; Nilsen, R; Mao, L; Arnold, J; Schüttler, H-B

2018-01-01

A major challenge in systems biology is to infer the parameters of regulatory networks that operate in a noisy environment, such as in a single cell. In a stochastic regime it is hard to distinguish noise from the real signal and to infer the noise contribution to the dynamical behavior. When the genetic network displays oscillatory dynamics, it is even harder to infer the parameters that produce the oscillations. To address this issue we introduce a new estimation method built on a combination of stochastic simulations, mass action kinetics and ensemble network simulations in which we match the average periodogram and phase of the model to that of the data. The method is relatively fast (compared to Metropolis-Hastings Monte Carlo Methods), easy to parallelize, applicable to large oscillatory networks and large (~2000 cells) single cell expression data sets, and it quantifies the noise impact on the observed dynamics. Standard errors of estimated rate coefficients are typically two orders of magnitude smaller than the mean from single cell experiments with on the order of ~1000 cells. We also provide a method to assess the goodness of fit of the stochastic network using the Hilbert phase of single cells. An analysis of phase departures from the null model with no communication between cells is consistent with a hypothesis of Stochastic Resonance describing single cell oscillators. Stochastic Resonance provides a physical mechanism whereby intracellular noise plays a positive role in establishing oscillatory behavior, but may require model parameters, such as rate coefficients, that differ substantially from those extracted at the macroscopic level from measurements on populations of millions of communicating, synchronized cells.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks. PMID:21423355

Impact of deterministic and stochastic updates on network reciprocity in the prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Tanimoto, Jun

2014-08-01

In 2 × 2 prisoner's dilemma games, network reciprocity is one mechanism for adding social viscosity, which leads to cooperative equilibrium. This study introduced an intriguing framework for the strategy update rule that allows any combination of a purely deterministic method, imitation max (IM), and a purely probabilistic one, pairwise Fermi (Fermi-PW). A series of simulations covering the whole range from IM to Fermi-PW reveals that, as a general tendency, the larger fractions of stochastic updating reduce network reciprocity, so long as the underlying lattice contains no noise in the degree of distribution. However, a small amount of stochastic flavor added to an otherwise perfectly deterministic update rule was actually found to enhance network reciprocity. This occurs because a subtle stochastic effect in the update rule improves the evolutionary trail in games having more stag-hunt-type dilemmas, although the same stochastic effect degenerates evolutionary trails in games having more chicken-type dilemmas. We explain these effects by dividing evolutionary trails into the enduring and expanding periods defined by Shigaki et al. [Phys. Rev. E 86, 031141 (2012), 10.1103/PhysRevE.86.031141].

Robust stability for stochastic bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

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.

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

PubMed

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

2014-01-01

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

Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainties, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. This includes spectral decomposition calculations for one representative example in full detail.

Stochastic multiresonance in coupled excitable FHN neurons

NASA Astrophysics Data System (ADS)

Li, Huiyan; Sun, Xiaojuan; Xiao, Jinghua

2018-04-01

In this paper, effects of noise on Watts-Strogatz small-world neuronal networks, which are stimulated by a subthreshold signal, have been investigated. With the numerical simulations, it is surprisingly found that there exist several optimal noise intensities at which the subthreshold signal can be detected efficiently. This indicates the occurrence of stochastic multiresonance in the studied neuronal networks. Moreover, it is revealed that the occurrence of stochastic multiresonance has close relationship with the period of subthreshold signal Te and the noise-induced mean period of the neuronal networks T0. In detail, we find that noise could induce the neuronal networks to generate stochastic resonance for M times if Te is not very large and falls into the interval ( M × T 0 , ( M + 1 ) × T 0 ) with M being a positive integer. In real neuronal system, subthreshold signal detection is very meaningful. Thus, the obtained results in this paper could give some important implications on detecting subthreshold signal and propagating neuronal information in neuronal systems.

Algorithms for optimization of branching gravity-driven water networks

NASA Astrophysics Data System (ADS)

Dardani, Ian; Jones, Gerard F.

2018-05-01

The design of a water network involves the selection of pipe diameters that satisfy pressure and flow requirements while considering cost. A variety of design approaches can be used to optimize for hydraulic performance or reduce costs. To help designers select an appropriate approach in the context of gravity-driven water networks (GDWNs), this work assesses three cost-minimization algorithms on six moderate-scale GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution which is mapped onto a discrete-diameter set. The backtracking algorithm finds the global optimum for all but the largest of cases tested, for which its long runtime makes it an infeasible option. The calculus-based algorithm's discrete-diameter solution produced slightly higher-cost results but was more scalable to larger network cases. Furthermore, the new calculus-based algorithm's continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. The genetic algorithm produced solutions even closer to the global optimum with consistently short run times, although slightly higher solution costs were seen for the larger network cases tested. The results of this study highlight the advantages and weaknesses of each GDWN design method including closeness to the global optimum, the ability to prune the solution space of infeasible and suboptimal candidates without missing the global optimum, and algorithm run time. We also extend an existing closed-form model of Jones (2011) to include minor losses and a more comprehensive two-part cost model, which realistically applies to pipe sizes that span a broad range typical of GDWNs of interest in this work, and for smooth and commercial steel roughness values.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2017-02-01

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons

PubMed Central

Pecevski, Dejan; Buesing, Lars; Maass, Wolfgang

2011-01-01

An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons. PMID:22219717

Markov State Models of gene regulatory networks.

PubMed

Chu, Brian K; Tse, Margaret J; Sato, Royce R; Read, Elizabeth L

2017-02-06

Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking. The method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models. Application of transition path theory to the constructed Markov State Model decomposes global dynamics into a set of dominant transition paths and associated relative probabilities for stochastic state-switching. In this proof-of-concept study, we found that the Markov State Model provides a general framework for analyzing and visualizing stochastic multistability and state-transitions in gene networks. Our results suggest that this framework-adopted from the field of atomistic Molecular Dynamics-can be a useful tool for quantitative Systems Biology at the network scale.

Delay-distribution-dependent H∞ state estimation for delayed neural networks with (x,v)-dependent noises and fading channels.

PubMed

Sheng, Li; Wang, Zidong; Tian, Engang; Alsaadi, Fuad E

2016-12-01

This paper deals with the H ∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H ∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stochastic architecture for Hopfield neural nets

NASA Technical Reports Server (NTRS)

Pavel, Sandy

1992-01-01

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

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Robust synthetic biology design: stochastic game theory approach.

PubMed

Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching

2009-07-15

Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi-Sugeno (T-S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf.

Stochastic unilateral free vibration of an in-plane cable network

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Barbiellini, Bernardo; Caracoglia, Luca

2015-03-01

Cross-ties are often used on cable-stayed bridges for mitigating wind-induced stay vibration since they can be easily installed on existing systems. The system obtained by connecting two (or more) stays with a transverse restrainer is designated as an "in-plane cable-network". Failures in the restrainers of an existing network have been observed. In a previous study [1] a model was proposed to explain the failures in the cross-ties as being related to a loss in the initial pre-tensioning force imparted to the connector. This effect leads to the "unilateral" free vibration of the network. Deterministic free vibrations of a three-cable network were investigated by using the "equivalent linearization method". Since the value of the initial vibration amplitude is often not well known due to the complex aeroelastic vibration regimes, which can be experienced by the stays, the stochastic nature of the problem must be considered. This issue is investigated in the present paper. Free-vibration dynamics of the cable network, driven by an initial stochastic disturbance associated with uncertain vibration amplitudes, is examined. The corresponding random eigen-value problem for the vibration frequencies is solved through an implementation of Stochastic Approximation, (SA) based on the Robbins-Monro Theorem. Monte-Carlo methods are also used for validating the SA results.

A Diagrammatic Language for Biochemical Networks

NASA Astrophysics Data System (ADS)

Maimon, Ron

2002-03-01

I present a diagrammatic language for representing the structure of biochemical networks. The language is designed to represent modular structure in a computational fasion, with composition of reactions replacing functional composition. This notation is used to represent arbitrarily large networks efficiently. The notation finds its most natural use in representing biological interaction networks, but it is a general computing language appropriate to any naturally occuring computation. Unlike lambda-calculus, or text-derived languages, it does not impose a tree-structure on the diagrams, and so is more effective at representing biological fucntion than competing notations.

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

PubMed

Giebel, S; Rainer, M

2010-01-01

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

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks.

PubMed

Meng, X Flora; Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M

2017-05-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. © 2017 The Author(s).

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

PubMed Central

Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M.

2017-01-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. PMID:28566513

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation.

PubMed

Erban, Radek; Kevrekidis, Ioannis G; Adalsteinsson, David; Elston, Timothy C

2006-02-28

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering

NASA Astrophysics Data System (ADS)

Hernandez-Hernandez, Gonzalo; Myers, Jesse; Alvarez-Lacalle, Enrique; Shiferaw, Yohannes

2017-03-01

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological function.

Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

PubMed Central

Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang

2011-01-01

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons. PMID:22096452

HRSSA - Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

NASA Astrophysics Data System (ADS)

Marchetti, Luca; Priami, Corrado; Thanh, Vo Hong

2016-07-01

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

Fault detection and diagnosis for non-Gaussian stochastic distribution systems with time delays via RBF neural networks.

PubMed

Yi, Qu; Zhan-ming, Li; Er-chao, Li

2012-11-01

A new fault detection and diagnosis (FDD) problem via the output probability density functions (PDFs) for non-gausian stochastic distribution systems (SDSs) is investigated. The PDFs can be approximated by radial basis functions (RBFs) neural networks. Different from conventional FDD problems, the measured information for FDD is the output stochastic distributions and the stochastic variables involved are not confined to Gaussian ones. A (RBFs) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings of the RBFs neural network. In this work, a nonlinear adaptive observer-based fault detection and diagnosis algorithm is presented by introducing the tuning parameter so that the residual is as sensitive as possible to the fault. Stability and Convergency analysis is performed in fault detection and fault diagnosis analysis for the error dynamic system. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and satisfactory results have been obtained. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

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

PubMed Central

Chen, Bor-Sen; Lin, Ying-Po

2011-01-01

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

Solving Constraint Satisfaction Problems with Networks of Spiking Neurons

PubMed Central

Jonke, Zeno; Habenschuss, Stefan; Maass, Wolfgang

2016-01-01

Network of neurons in the brain apply—unlike processors in our current generation of computer hardware—an event-based processing strategy, where short pulses (spikes) are emitted sparsely by neurons to signal the occurrence of an event at a particular point in time. Such spike-based computations promise to be substantially more power-efficient than traditional clocked processing schemes. However, it turns out to be surprisingly difficult to design networks of spiking neurons that can solve difficult computational problems on the level of single spikes, rather than rates of spikes. We present here a new method for designing networks of spiking neurons via an energy function. Furthermore, we show how the energy function of a network of stochastically firing neurons can be shaped in a transparent manner by composing the networks of simple stereotypical network motifs. We show that this design approach enables networks of spiking neurons to produce approximate solutions to difficult (NP-hard) constraint satisfaction problems from the domains of planning/optimization and verification/logical inference. The resulting networks employ noise as a computational resource. Nevertheless, the timing of spikes plays an essential role in their computations. Furthermore, networks of spiking neurons carry out for the Traveling Salesman Problem a more efficient stochastic search for good solutions compared with stochastic artificial neural networks (Boltzmann machines) and Gibbs sampling. PMID:27065785

New exponential stability criteria for stochastic BAM neural networks with impulses

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Samidurai, R.; Anthoni, S. M.

2010-10-01

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.

HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

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

Marchetti, Luca, E-mail: marchetti@cosbi.eu; Priami, Corrado, E-mail: priami@cosbi.eu; University of Trento, Department of Mathematics

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance andmore » accuracy of HRSSA against other state of the art algorithms.« less

A strand graph semantics for DNA-based computation

PubMed Central

Petersen, Rasmus L.; Lakin, Matthew R.; Phillips, Andrew

2015-01-01

DNA nanotechnology is a promising approach for engineering computation at the nanoscale, with potential applications in biofabrication and intelligent nanomedicine. DNA strand displacement is a general strategy for implementing a broad range of nanoscale computations, including any computation that can be expressed as a chemical reaction network. Modelling and analysis of DNA strand displacement systems is an important part of the design process, prior to experimental realisation. As experimental techniques improve, it is important for modelling languages to keep pace with the complexity of structures that can be realised experimentally. In this paper we present a process calculus for modelling DNA strand displacement computations involving rich secondary structures, including DNA branches and loops. We prove that our calculus is also sufficiently expressive to model previous work on non-branching structures, and propose a mapping from our calculus to a canonical strand graph representation, in which vertices represent DNA strands, ordered sites represent domains, and edges between sites represent bonds between domains. We define interactions between strands by means of strand graph rewriting, and prove the correspondence between the process calculus and strand graph behaviours. Finally, we propose a mapping from strand graphs to an efficient implementation, which we use to perform modelling and simulation of DNA strand displacement systems with rich secondary structure. PMID:27293306

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay.

PubMed

Wei, Yanling; Park, Ju H; Karimi, Hamid Reza; Tian, Yu-Chu; Jung, Hoyoul; Yanling Wei; Park, Ju H; Karimi, Hamid Reza; Yu-Chu Tian; Hoyoul Jung; Tian, Yu-Chu; Wei, Yanling; Jung, Hoyoul; Karimi, Hamid Reza; Park, Ju H

2018-06-01

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

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

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

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

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

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

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

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

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

Mlynarczyk, Paul J.; Pullen, Robert H.; Abel, Steven M., E-mail: abel@utk.edu

2016-01-07

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations.more » Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.« less

Emergent Oscillations in Networks of Stochastic Spiking Neurons

PubMed Central

van Drongelen, Wim; Cowan, Jack D.

2011-01-01

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework. PMID:21573105

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

NASA Astrophysics Data System (ADS)

Bedi, Amrit Singh; Rajawat, Ketan

2018-05-01

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

A Novel Biobjective Risk-Based Model for Stochastic Air Traffic Network Flow Optimization Problem.

PubMed

Cai, Kaiquan; Jia, Yaoguang; Zhu, Yanbo; Xiao, Mingming

2015-01-01

Network-wide air traffic flow management (ATFM) is an effective way to alleviate demand-capacity imbalances globally and thereafter reduce airspace congestion and flight delays. The conventional ATFM models assume the capacities of airports or airspace sectors are all predetermined. However, the capacity uncertainties due to the dynamics of convective weather may make the deterministic ATFM measures impractical. This paper investigates the stochastic air traffic network flow optimization (SATNFO) problem, which is formulated as a weighted biobjective 0-1 integer programming model. In order to evaluate the effect of capacity uncertainties on ATFM, the operational risk is modeled via probabilistic risk assessment and introduced as an extra objective in SATNFO problem. Computation experiments using real-world air traffic network data associated with simulated weather data show that presented model has far less constraints compared to stochastic model with nonanticipative constraints, which means our proposed model reduces the computation complexity.

Resilient filtering for time-varying stochastic coupling networks under the event-triggering scheduling

NASA Astrophysics Data System (ADS)

Wang, Fan; Liang, Jinling; Dobaie, Abdullah M.

2018-07-01

The resilient filtering problem is considered for a class of time-varying networks with stochastic coupling strengths. An event-triggered strategy is adopted to save the network resources by scheduling the signal transmission from the sensors to the filters based on certain prescribed rules. Moreover, the filter parameters to be designed are subject to gain perturbations. The primary aim of the addressed problem is to determine a resilient filter that ensures an acceptable filtering performance for the considered network with event-triggering scheduling. To handle such an issue, an upper bound on the estimation error variance is established for each node according to the stochastic analysis. Subsequently, the resilient filter is designed by locally minimizing the derived upper bound at each iteration. Moreover, rigorous analysis shows the monotonicity of the minimal upper bound regarding the triggering threshold. Finally, a simulation example is presented to show effectiveness of the established filter scheme.

Dynamic Infinite Mixed-Membership Stochastic Blockmodel.

PubMed

Fan, Xuhui; Cao, Longbing; Xu, Richard Yi Da

2015-09-01

Directional and pairwise measurements are often used to model interactions in a social network setting. The mixed-membership stochastic blockmodel (MMSB) was a seminal work in this area, and its ability has been extended. However, models such as MMSB face particular challenges in modeling dynamic networks, for example, with the unknown number of communities. Accordingly, this paper proposes a dynamic infinite mixed-membership stochastic blockmodel, a generalized framework that extends the existing work to potentially infinite communities inside a network in dynamic settings (i.e., networks are observed over time). Additional model parameters are introduced to reflect the degree of persistence among one's memberships at consecutive time stamps. Under this framework, two specific models, namely mixture time variant and mixture time invariant models, are proposed to depict two different time correlation structures. Two effective posterior sampling strategies and their results are presented, respectively, using synthetic and real-world data.

Stochastic fluctuations and the detectability limit of network communities.

PubMed

Floretta, Lucio; Liechti, Jonas; Flammini, Alessandro; De Los Rios, Paolo

2013-12-01

We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and every instance of the benchmark, we come to the conclusion that the native, putative partition of the network is completely lost even before the in-degree/out-degree ratio becomes equal to that of a structureless Erdös-Rényi network. We develop a simple iterative scheme, analytically well described by an infinite branching process, to provide an estimate of the true detectability limit. Using various algorithms based on modularity optimization, we show that all of them behave (semiquantitatively) in the same way, with the same functional form of the detectability threshold as a function of the network parameters. Because the same behavior has also been found by further modularity-optimization methods and for methods based on different heuristics implementations, we conclude that indeed a correct definition of the detectability limit must take into account the stochastic fluctuations of the network construction.

Stochastic Simulation of Biomolecular Networks in Dynamic Environments

PubMed Central

Voliotis, Margaritis; Thomas, Philipp; Grima, Ramon; Bowsher, Clive G.

2016-01-01

Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits. PMID:27248512

Degree Distribution of Position-Dependent Ball-Passing Networks in Football Games

NASA Astrophysics Data System (ADS)

Narizuka, Takuma; Yamamoto, Ken; Yamazaki, Yoshihiro

2015-08-01

We propose a simple stochastic model describing the position-dependent ball-passing network in football (soccer) games. In this network, a player in a certain area in a divided field is a node, and a pass between two nodes corresponds to an edge. Our stochastic process model is characterized by the consecutive choice of a node depending on its intrinsic fitness. We derive an explicit expression for the degree distribution and find that the derived distribution reproduces that for actual data reasonably well.

Accelerating deep neural network training with inconsistent stochastic gradient descent.

PubMed

Wang, Linnan; Yang, Yi; Min, Renqiang; Chakradhar, Srimat

2017-09-01

Stochastic Gradient Descent (SGD) updates Convolutional Neural Network (CNN) with a noisy gradient computed from a random batch, and each batch evenly updates the network once in an epoch. This model applies the same training effort to each batch, but it overlooks the fact that the gradient variance, induced by Sampling Bias and Intrinsic Image Difference, renders different training dynamics on batches. In this paper, we develop a new training strategy for SGD, referred to as Inconsistent Stochastic Gradient Descent (ISGD) to address this problem. The core concept of ISGD is the inconsistent training, which dynamically adjusts the training effort w.r.t the loss. ISGD models the training as a stochastic process that gradually reduces down the mean of batch's loss, and it utilizes a dynamic upper control limit to identify a large loss batch on the fly. ISGD stays on the identified batch to accelerate the training with additional gradient updates, and it also has a constraint to penalize drastic parameter changes. ISGD is straightforward, computationally efficient and without requiring auxiliary memories. A series of empirical evaluations on real world datasets and networks demonstrate the promising performance of inconsistent training. Copyright © 2017 Elsevier Ltd. All rights reserved.

Quantum stochastic walks on networks for decision-making.

PubMed

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-31

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

NASA Astrophysics Data System (ADS)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

PubMed Central

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-01-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making. PMID:27030372

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines.

PubMed

Neftci, Emre O; Pedroni, Bruno U; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

PubMed Central

Neftci, Emre O.; Pedroni, Bruno U.; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware. PMID:27445650

Spreading paths in partially observed social networks

NASA Astrophysics Data System (ADS)

Onnela, Jukka-Pekka; Christakis, Nicholas A.

2012-03-01

Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.

Spreading paths in partially observed social networks.

PubMed

Onnela, Jukka-Pekka; Christakis, Nicholas A

2012-03-01

Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.

Stochastic Nature in Cellular Processes

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

Modeling of contact tracing in social networks

NASA Astrophysics Data System (ADS)

Tsimring, Lev S.; Huerta, Ramón

2003-07-01

Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks which incorporates an additional (traced) state. We describe a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also discuss the role of contact tracing in epidemics control in small-world and scale-free networks. Effectiveness of contact tracing grows as the rewiring probability is reduced.

PRODIGEN: visualizing the probability landscape of stochastic gene regulatory networks in state and time space.

PubMed

Ma, Chihua; Luciani, Timothy; Terebus, Anna; Liang, Jie; Marai, G Elisabeta

2017-02-15

Visualizing the complex probability landscape of stochastic gene regulatory networks can further biologists' understanding of phenotypic behavior associated with specific genes. We present PRODIGEN (PRObability DIstribution of GEne Networks), a web-based visual analysis tool for the systematic exploration of probability distributions over simulation time and state space in such networks. PRODIGEN was designed in collaboration with bioinformaticians who research stochastic gene networks. The analysis tool combines in a novel way existing, expanded, and new visual encodings to capture the time-varying characteristics of probability distributions: spaghetti plots over one dimensional projection, heatmaps of distributions over 2D projections, enhanced with overlaid time curves to display temporal changes, and novel individual glyphs of state information corresponding to particular peaks. We demonstrate the effectiveness of the tool through two case studies on the computed probabilistic landscape of a gene regulatory network and of a toggle-switch network. Domain expert feedback indicates that our visual approach can help biologists: 1) visualize probabilities of stable states, 2) explore the temporal probability distributions, and 3) discover small peaks in the probability landscape that have potential relation to specific diseases.

A Markov model for the temporal dynamics of balanced random networks of finite size

PubMed Central

Lagzi, Fereshteh; Rotter, Stefan

2014-01-01

The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between neuronal populations also opens new doors to analyze the joint dynamics of multiple interacting networks. PMID:25520644

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

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

Taranenko, Y.; Barnes, C.

1996-12-31

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

Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection.

PubMed

Chai, Bian-fang; Yu, Jian; Jia, Cai-Yan; Yang, Tian-bao; Jiang, Ya-wen

2013-07-01

Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.

Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection

NASA Astrophysics Data System (ADS)

Chai, Bian-fang; Yu, Jian; Jia, Cai-yan; Yang, Tian-bao; Jiang, Ya-wen

2013-07-01

Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.

EARLINET Single Calculus Chain - overview on methodology and strategy

NASA Astrophysics Data System (ADS)

D'Amico, G.; Amodeo, A.; Baars, H.; Binietoglou, I.; Freudenthaler, V.; Mattis, I.; Wandinger, U.; Pappalardo, G.

2015-11-01

In this paper we describe the EARLINET Single Calculus Chain (SCC), a tool for the automatic analysis of lidar measurements. The development of this tool started in the framework of EARLINET-ASOS (European Aerosol Research Lidar Network - Advanced Sustainable Observation System); it was extended within ACTRIS (Aerosol, Clouds and Trace gases Research InfraStructure Network), and it is continuing within ACTRIS-2. The main idea was to develop a data processing chain that allows all EARLINET stations to retrieve, in a fully automatic way, the aerosol backscatter and extinction profiles starting from the raw lidar data of the lidar systems they operate. The calculus subsystem of the SCC is composed of two modules: a pre-processor module which handles the raw lidar data and corrects them for instrumental effects and an optical processing module for the retrieval of aerosol optical products from the pre-processed data. All input parameters needed to perform the lidar analysis are stored in a database to keep track of all changes which may occur for any EARLINET lidar system over the time. The two calculus modules are coordinated and synchronized by an additional module (daemon) which makes the whole analysis process fully automatic. The end user can interact with the SCC via a user-friendly web interface. All SCC modules are developed using open-source and freely available software packages. The final products retrieved by the SCC fulfill all requirements of the EARLINET quality assurance programs on both instrumental and algorithm levels. Moreover, the manpower needed to provide aerosol optical products is greatly reduced and thus the near-real-time availability of lidar data is improved. The high-quality of the SCC products is proven by the good agreement between the SCC analysis, and the corresponding independent manual retrievals. Finally, the ability of the SCC to provide high-quality aerosol optical products is demonstrated for an EARLINET intense observation period.

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

PubMed Central

Longtin, André

2017-01-01

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

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Anti-synchronization control of BAM memristive neural networks with multiple proportional delays and stochastic perturbations

NASA Astrophysics Data System (ADS)

Wang, Weiping; Yuan, Manman; Luo, Xiong; Liu, Linlin; Zhang, Yao

2018-01-01

Proportional delay is a class of unbounded time-varying delay. A class of bidirectional associative memory (BAM) memristive neural networks with multiple proportional delays is concerned in this paper. First, we propose the model of BAM memristive neural networks with multiple proportional delays and stochastic perturbations. Furthermore, by choosing suitable nonlinear variable transformations, the BAM memristive neural networks with multiple proportional delays can be transformed into the BAM memristive neural networks with constant delays. Based on the drive-response system concept, differential inclusions theory and Lyapunov stability theory, some anti-synchronization criteria are obtained. Finally, the effectiveness of proposed criteria are demonstrated through numerical examples.

Selected-node stochastic simulation algorithm

NASA Astrophysics Data System (ADS)

Duso, Lorenzo; Zechner, Christoph

2018-04-01

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

Stochastic Averaging for Constrained Optimization With Application to Online Resource Allocation

NASA Astrophysics Data System (ADS)

Chen, Tianyi; Mokhtari, Aryan; Wang, Xin; Ribeiro, Alejandro; Giannakis, Georgios B.

2017-06-01

Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.

Learning in Stochastic Bit Stream Neural Networks.

PubMed

van Daalen, Max; Shawe-Taylor, John; Zhao, Jieyu

1996-08-01

This paper presents learning techniques for a novel feedforward stochastic neural network. The model uses stochastic weights and the "bit stream" data representation. It has a clean analysable functionality and is very attractive with its great potential to be implemented in hardware using standard digital VLSI technology. The design allows simulation at three different levels and learning techniques are described for each level. The lowest level corresponds to on-chip learning. Simulation results on three benchmark MONK's problems and handwritten digit recognition with a clean set of 500 16 x 16 pixel digits demonstrate that the new model is powerful enough for the real world applications. Copyright 1996 Elsevier Science Ltd

Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks

PubMed Central

Lähdesmäki, Harri; Hautaniemi, Sampsa; Shmulevich, Ilya; Yli-Harja, Olli

2006-01-01

A significant amount of attention has recently been focused on modeling of gene regulatory networks. Two frequently used large-scale modeling frameworks are Bayesian networks (BNs) and Boolean networks, the latter one being a special case of its recent stochastic extension, probabilistic Boolean networks (PBNs). PBN is a promising model class that generalizes the standard rule-based interactions of Boolean networks into the stochastic setting. Dynamic Bayesian networks (DBNs) is a general and versatile model class that is able to represent complex temporal stochastic processes and has also been proposed as a model for gene regulatory systems. In this paper, we concentrate on these two model classes and demonstrate that PBNs and a certain subclass of DBNs can represent the same joint probability distribution over their common variables. The major benefit of introducing the relationships between the models is that it opens up the possibility of applying the standard tools of DBNs to PBNs and vice versa. Hence, the standard learning tools of DBNs can be applied in the context of PBNs, and the inference methods give a natural way of handling the missing values in PBNs which are often present in gene expression measurements. Conversely, the tools for controlling the stationary behavior of the networks, tools for projecting networks onto sub-networks, and efficient learning schemes can be used for DBNs. In other words, the introduced relationships between the models extend the collection of analysis tools for both model classes. PMID:17415411

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

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

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

Quantum stochastic thermodynamic on harmonic networks

DOE PAGES

Deffner, Sebastian

2016-01-04

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Quantum stochastic thermodynamic on harmonic networks

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

Deffner, Sebastian

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Tensor calculus: unlearning vector calculus

NASA Astrophysics Data System (ADS)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-02-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

Selfish routing equilibrium in stochastic traffic network: A probability-dominant description.

PubMed

Zhang, Wenyi; He, Zhengbing; Guan, Wei; Ma, Rui

2017-01-01

This paper suggests a probability-dominant user equilibrium (PdUE) model to describe the selfish routing equilibrium in a stochastic traffic network. At PdUE, travel demands are only assigned to the most dominant routes in the same origin-destination pair. A probability-dominant rerouting dynamic model is proposed to explain the behavioral mechanism of PdUE. To facilitate applications, the logit formula of PdUE is developed, of which a well-designed route set is not indispensable and the equivalent varitional inequality formation is simple. Two routing strategies, i.e., the probability-dominant strategy (PDS) and the dominant probability strategy (DPS), are discussed through a hypothetical experiment. It is found that, whether out of insurance or striving for perfection, PDS is a better choice than DPS. For more general cases, the conducted numerical tests lead to the same conclusion. These imply that PdUE (rather than the conventional stochastic user equilibrium) is a desirable selfish routing equilibrium for a stochastic network, given that the probability distributions of travel time are available to travelers.

Selfish routing equilibrium in stochastic traffic network: A probability-dominant description

PubMed Central

Zhang, Wenyi; Guan, Wei; Ma, Rui

2017-01-01

This paper suggests a probability-dominant user equilibrium (PdUE) model to describe the selfish routing equilibrium in a stochastic traffic network. At PdUE, travel demands are only assigned to the most dominant routes in the same origin-destination pair. A probability-dominant rerouting dynamic model is proposed to explain the behavioral mechanism of PdUE. To facilitate applications, the logit formula of PdUE is developed, of which a well-designed route set is not indispensable and the equivalent varitional inequality formation is simple. Two routing strategies, i.e., the probability-dominant strategy (PDS) and the dominant probability strategy (DPS), are discussed through a hypothetical experiment. It is found that, whether out of insurance or striving for perfection, PDS is a better choice than DPS. For more general cases, the conducted numerical tests lead to the same conclusion. These imply that PdUE (rather than the conventional stochastic user equilibrium) is a desirable selfish routing equilibrium for a stochastic network, given that the probability distributions of travel time are available to travelers. PMID:28829834

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control.

PubMed

Zhang, Wanli; Yang, Shiju; Li, Chuandong; Zhang, Wei; Yang, Xinsong

2018-08-01

This paper focuses on stochastic exponential synchronization of delayed memristive neural networks (MNNs) by the aid of systems with interval parameters which are established by using the concept of Filippov solution. New intermittent controller and adaptive controller with logarithmic quantization are structured to deal with the difficulties induced by time-varying delays, interval parameters as well as stochastic perturbations, simultaneously. Moreover, not only control cost can be reduced but also communication channels and bandwidth are saved by using these controllers. Based on novel Lyapunov functions and new analytical methods, several synchronization criteria are established to realize the exponential synchronization of MNNs with stochastic perturbations via intermittent control and adaptive control with or without logarithmic quantization. Finally, numerical simulations are offered to substantiate our theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks.

PubMed

Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki

2008-06-01

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

H∞ state estimation for discrete-time memristive recurrent neural networks with stochastic time-delays

NASA Astrophysics Data System (ADS)

Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2016-07-01

This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

PubMed

Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S

2018-06-21

The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

Harmonic stochastic resonance-enhanced signal detecting in NW small-world neural network

NASA Astrophysics Data System (ADS)

Wang, Dao-Guang; Liang, Xiao-Ming; Wang, Jing; Yang, Cheng-Fang; Liu, Kai; Lü, Hua-Ping

2010-11-01

The harmonic stochastic resonance-enhanced signal detecting in Newman-Watts small-world neural network is studied using the Hodgkin-Huxley dynamical equation with noise. If the connection probability p, coupling strength gsyn and noise intensity D matches well, higher order resonance will be found and an optimal signal-to-noise ratio will be obtained. Then, the reasons are given to explain the mechanism of this appearance.

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

PubMed

Verdonck, Stijn; Tuerlinckx, Francis

2014-07-01

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

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

PubMed

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

2016-06-01

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

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik

2014-03-01

The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Hybrid stochastic simplifications for multiscale gene networks.

PubMed

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-09-07

Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.

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

PubMed

Jenkins, Dafyd J; Stekel, Dov J

2010-02-01

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

Modeling student success in engineering education

NASA Astrophysics Data System (ADS)

Jin, Qu

In order for the United States to maintain its global competitiveness, the long-term success of our engineering students in specific courses, programs, and colleges is now, more than ever, an extremely high priority. Numerous studies have focused on factors that impact student success, namely academic performance, retention, and/or graduation. However, there are only a limited number of works that have systematically developed models to investigate important factors and to predict student success in engineering. Therefore, this research presents three separate but highly connected investigations to address this gap. The first investigation involves explaining and predicting engineering students' success in Calculus I courses using statistical models. The participants were more than 4000 first-year engineering students (cohort years 2004 - 2008) who enrolled in Calculus I courses during the first semester in a large Midwestern university. Predictions from statistical models were proposed to be used to place engineering students into calculus courses. The success rates were improved by 12% in Calculus IA using predictions from models developed over traditional placement method. The results showed that these statistical models provided a more accurate calculus placement method than traditional placement methods and help improve success rates in those courses. In the second investigation, multi-outcome and single-outcome neural network models were designed to understand and to predict first-year retention and first-year GPA of engineering students. The participants were more than 3000 first year engineering students (cohort years 2004 - 2005) enrolled in a large Midwestern university. The independent variables include both high school academic performance factors and affective factors measured prior to entry. The prediction performances of the multi-outcome and single-outcome models were comparable. The ability to predict cumulative GPA at the end of an engineering student's first year of college was about a half of a grade point for both models. The predictors of retention and cumulative GPA while being similar differ in that high school academic metrics play a more important role in predicting cumulative GPA with the affective measures playing a more important role in predicting retention. In the last investigation, multi-outcome neural network models were used to understand and to predict engineering students' retention, GPA, and graduation from entry to departure. The participants were more than 4000 engineering students (cohort years 2004 - 2006) enrolled in a large Midwestern university. Different patterns of important predictors were identified for GPA, retention, and graduation. Overall, this research explores the feasibility of using modeling to enhance a student's educational experience in engineering. Student success modeling was used to identify the most important cognitive and affective predictors for a student's first calculus course retention, GPA, and graduation. The results suggest that the statistical modeling methods have great potential to assist decision making and help ensure student success in engineering education.

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Activity-dependent stochastic resonance in recurrent neuronal networks

NASA Astrophysics Data System (ADS)

Volman, Vladislav

2009-03-01

An important source of noise for neuronal networks is that of the stochastic nature of synaptic transmission. In particular, there can occur spontaneous asynchronous release of neurotransmitter at a rate that is strongly dependent on the presynaptic Ca2+ concentration and hence strongly dependent on the rate of spike induced Ca2+. Here it is shown that this noise can lead to a new form of stochastic resonance for local circuits consisting of roughly 100 neurons - a ``microcolumn''- coupled via noisy plastic synapses. Furthermore, due to the plastic coupling and activity-dependent noise component, the detection of weak stimuli will also depend on the structure of the latter. In addition, the circuit can exhibit short-term memory, by which we mean that spiking will continue to occur for a transient period following removal of the stimulus. These results can be directly tested in experiments on cultured networks.

Stochasticity in the signalling network of a model microbe

NASA Astrophysics Data System (ADS)

Bischofs, Ilka; Foley, Jonathan; Battenberg, Eric; Fontaine-Bodin, Lisa; Price, Gavin; Wolf, Denise; Arkin, Adam

2007-03-01

The soil dwelling bacterium Bacillus subtilis is an excellent model organism for studying stochastic stress response induction in an isoclonal population. Subjected to the same stressor cells undergo different cell fates, including sporulation, competence, degradative enzyme synthesis and motility. For example, under conditions of nutrient deprivation and high cell density only a portion of the cell population forms an endospore. Here we use a combined experimental and theoretical approach to study stochastic sporulation induction in Bacillus subtilis. Using several fluorescent reporter strains we apply time lapse fluorescent microscopy in combination with quantitative image analysis to study cell fate progression on a single cell basis and elucidate key noise generators in the underlying cellular network.

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Stochastic models for regulatory networks of the genetic toggle switch.

PubMed

Tian, Tianhai; Burrage, Kevin

2006-05-30

Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic models for regulatory networks of the genetic toggle switch

PubMed Central

Tian, Tianhai; Burrage, Kevin

2006-01-01

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks. PMID:16714385

Integrated seismic stochastic inversion and multi-attributes to delineate reservoir distribution: Case study MZ fields, Central Sumatra Basin

NASA Astrophysics Data System (ADS)

Haris, A.; Novriyani, M.; Suparno, S.; Hidayat, R.; Riyanto, A.

2017-07-01

This study presents the integration of seismic stochastic inversion and multi-attributes for delineating the reservoir distribution in term of lithology and porosity in the formation within depth interval between the Top Sihapas and Top Pematang. The method that has been used is a stochastic inversion, which is integrated with multi-attribute seismic by applying neural network Probabilistic Neural Network (PNN). Stochastic methods are used to predict the probability mapping sandstone as the result of impedance varied with 50 realizations that will produce a good probability. Analysis of Stochastic Seismic Tnversion provides more interpretive because it directly gives the value of the property. Our experiment shows that AT of stochastic inversion provides more diverse uncertainty so that the probability value will be close to the actual values. The produced AT is then used for an input of a multi-attribute analysis, which is used to predict the gamma ray, density and porosity logs. To obtain the number of attributes that are used, stepwise regression algorithm is applied. The results are attributes which are used in the process of PNN. This PNN method is chosen because it has the best correlation of others neural network method. Finally, we interpret the product of the multi-attribute analysis are in the form of pseudo-gamma ray volume, density volume and volume of pseudo-porosity to delineate the reservoir distribution. Our interpretation shows that the structural trap is identified in the southeastern part of study area, which is along the anticline.

SATA II - Stochastic Algebraic Topology and Applications

DTIC Science & Technology

2017-01-30

AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications ...has recently been submitted to AFOSR. 15. SUBJECT TERMS Network Theory, Sensor Technology, Mathematical Modeling, EOARD 16. SECURITY CLASSIFICATION OF

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Stochastic Models of Emerging Infectious Disease Transmission on Adaptive Random Networks

PubMed Central

Pipatsart, Navavat; Triampo, Wannapong

2017-01-01

We presented adaptive random network models to describe human behavioral change during epidemics and performed stochastic simulations of SIR (susceptible-infectious-recovered) epidemic models on adaptive random networks. The interplay between infectious disease dynamics and network adaptation dynamics was investigated in regard to the disease transmission and the cumulative number of infection cases. We found that the cumulative case was reduced and associated with an increasing network adaptation probability but was increased with an increasing disease transmission probability. It was found that the topological changes of the adaptive random networks were able to reduce the cumulative number of infections and also to delay the epidemic peak. Our results also suggest the existence of a critical value for the ratio of disease transmission and adaptation probabilities below which the epidemic cannot occur. PMID:29075314

Collective stochastic coherence in recurrent neuronal networks

NASA Astrophysics Data System (ADS)

Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi

2016-09-01

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.

Reconstruction of stochastic temporal networks through diffusive arrival times

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xiang

2017-06-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications.

Reconstruction of stochastic temporal networks through diffusive arrival times

PubMed Central

Li, Xun; Li, Xiang

2017-01-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks

PubMed Central

Vestergaard, Christian L.; Génois, Mathieu

2015-01-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling. PMID:26517860

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

PubMed

Vestergaard, Christian L; Génois, Mathieu

2015-10-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

Learning Orthographic Structure With Sequential Generative Neural Networks.

PubMed

Testolin, Alberto; Stoianov, Ivilin; Sperduti, Alessandro; Zorzi, Marco

2016-04-01

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine (RBM), a stochastic recurrent neural network that extracts high-order structure from sensory data through unsupervised generative learning and can encode contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high-quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non-connectionist probabilistic models (n-grams and hidden Markov models). We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain. Copyright © 2015 Cognitive Science Society, Inc.

Game-theoretic cooperativity in networks of self-interested units

NASA Astrophysics Data System (ADS)

Barto, Andrew G.

1986-08-01

The behavior of theoretical neural networks is often described in terms of competition and cooperation. I present an approach to network learning that is related to game and team problems in which competition and cooperation have more technical meanings. I briefly describe the application of stochastic learning automata to game and team problems and then present an adaptive element that is a synthesis of aspects of stochastic learning automata and typical neuron-like adaptive elements. These elements act as self-interested agents that work toward improving their performance with respect to their individual preference orderings. Networks of these elements can solve a variety of team decision problems, some of which take the form of layered networks in which the ``hidden units'' become appropriate functional components as they attempt to improve their own payoffs.

Hybrid stochastic simplifications for multiscale gene networks

PubMed Central

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-01-01

Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach. PMID:19735554

A scalable moment-closure approximation for large-scale biochemical reaction networks

PubMed Central

Kazeroonian, Atefeh; Theis, Fabian J.; Hasenauer, Jan

2017-01-01

Abstract Motivation: Stochastic molecular processes are a leading cause of cell-to-cell variability. Their dynamics are often described by continuous-time discrete-state Markov chains and simulated using stochastic simulation algorithms. As these stochastic simulations are computationally demanding, ordinary differential equation models for the dynamics of the statistical moments have been developed. The number of state variables of these approximating models, however, grows at least quadratically with the number of biochemical species. This limits their application to small- and medium-sized processes. Results: In this article, we present a scalable moment-closure approximation (sMA) for the simulation of statistical moments of large-scale stochastic processes. The sMA exploits the structure of the biochemical reaction network to reduce the covariance matrix. We prove that sMA yields approximating models whose number of state variables depends predominantly on local properties, i.e. the average node degree of the reaction network, instead of the overall network size. The resulting complexity reduction is assessed by studying a range of medium- and large-scale biochemical reaction networks. To evaluate the approximation accuracy and the improvement in computational efficiency, we study models for JAK2/STAT5 signalling and NFκB signalling. Our method is applicable to generic biochemical reaction networks and we provide an implementation, including an SBML interface, which renders the sMA easily accessible. Availability and implementation: The sMA is implemented in the open-source MATLAB toolbox CERENA and is available from https://github.com/CERENADevelopers/CERENA. Contact: jan.hasenauer@helmholtz-muenchen.de or atefeh.kazeroonian@tum.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881983

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

Laomettachit, Teeraphan; Chen, Katherine C; Baumann, William T; Tyson, John J

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

PubMed Central

Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

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

Gupta, Chinmaya; López, José Manuel; Azencott, Robert

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemicalmore » Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.« less

Stochastic Computations in Cortical Microcircuit Models

PubMed Central

Maass, Wolfgang

2013-01-01

Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving. PMID:24244126

Clustering network layers with the strata multilayer stochastic block model.

PubMed

Stanley, Natalie; Shai, Saray; Taylor, Dane; Mucha, Peter J

2016-01-01

Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the "strata multilayer stochastic block model" (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called "strata", which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project.

Clustering network layers with the strata multilayer stochastic block model

PubMed Central

Stanley, Natalie; Shai, Saray; Taylor, Dane; Mucha, Peter J.

2016-01-01

Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the “strata multilayer stochastic block model” (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called “strata”, which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project. PMID:28435844

A stochastic multi-agent optimization model for energy infrastructure planning under uncertainty and competition.

DOT National Transportation Integrated Search

2017-07-04

This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...

Real-time estimation of incident delay in dynamic and stochastic networks

DOT National Transportation Integrated Search

1997-01-01

The ability to predict the link travel times is a necessary requirement for most intelligent transportation systems (ITS) applications such as route guidance systems. In an urban traffic environment, these travel times are dynamic and stochastic and ...

The impact of taking a college pre-calculus course on students' college calculus performance

NASA Astrophysics Data System (ADS)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Relevance of phenotypic noise to adaptation and evolution.

PubMed

Kaneko, K; Furusawa, C

2008-09-01

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

Stochastic Modeling of Sediment Connectivity for Reconstructing Sand Fluxes and Origins in the Unmonitored Se Kong, Se San, and Sre Pok Tributaries of the Mekong River

NASA Astrophysics Data System (ADS)

Schmitt, R. J. P.; Bizzi, S.; Castelletti, A. F.; Kondolf, G. M.

2018-01-01

Sediment supply to rivers, subsequent fluvial transport, and the resulting sediment connectivity on network scales are often sparsely monitored and subject to major uncertainty. We propose to approach that uncertainty by adopting a stochastic method for modeling network sediment connectivity, which we present for the Se Kong, Se San, and Sre Pok (3S) tributaries of the Mekong. We quantify how unknown properties of sand sources translate into uncertainty regarding network connectivity by running the CASCADE (CAtchment Sediment Connectivity And DElivery) modeling framework in a Monte Carlo approach for 7,500 random realizations. Only a small ensemble of realizations reproduces downstream observations of sand transport. This ensemble presents an inverse stochastic approximation of the magnitude and variability of transport capacity, sediment flux, and grain size distribution of the sediment transported in the network (i.e., upscaling point observations to the entire network). The approximated magnitude of sand delivered from each tributary to the Mekong is controlled by reaches of low transport capacity ("bottlenecks"). These bottlenecks limit the ability to predict transport in the upper parts of the catchment through inverse stochastic approximation, a limitation that could be addressed by targeted monitoring upstream of identified bottlenecks. Nonetheless, bottlenecks also allow a clear partitioning of natural sand deliveries from the 3S to the Mekong, with the Se Kong delivering less (1.9 Mt/yr) and coarser (median grain size: 0.4 mm) sand than the Se San (5.3 Mt/yr, 0.22 mm) and Sre Pok (11 Mt/yr, 0.19 mm).

Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.

PubMed

Zhang, Jian J; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W J; Hasenberg, Tom; Kang, Hyun Wook

2015-01-01

Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391  mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.

A simple model of bipartite cooperation for ecological and organizational networks.

PubMed

Saavedra, Serguei; Reed-Tsochas, Felix; Uzzi, Brian

2009-01-22

In theoretical ecology, simple stochastic models that satisfy two basic conditions about the distribution of niche values and feeding ranges have proved successful in reproducing the overall structural properties of real food webs, using species richness and connectance as the only input parameters. Recently, more detailed models have incorporated higher levels of constraint in order to reproduce the actual links observed in real food webs. Here, building on previous stochastic models of consumer-resource interactions between species, we propose a highly parsimonious model that can reproduce the overall bipartite structure of cooperative partner-partner interactions, as exemplified by plant-animal mutualistic networks. Our stochastic model of bipartite cooperation uses simple specialization and interaction rules, and only requires three empirical input parameters. We test the bipartite cooperation model on ten large pollination data sets that have been compiled in the literature, and find that it successfully replicates the degree distribution, nestedness and modularity of the empirical networks. These properties are regarded as key to understanding cooperation in mutualistic networks. We also apply our model to an extensive data set of two classes of company engaged in joint production in the garment industry. Using the same metrics, we find that the network of manufacturer-contractor interactions exhibits similar structural patterns to plant-animal pollination networks. This surprising correspondence between ecological and organizational networks suggests that the simple rules of cooperation that generate bipartite networks may be generic, and could prove relevant in many different domains, ranging from biological systems to human society.

Estimating the epidemic threshold on networks by deterministic connections

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

Li, Kezan, E-mail: lkzzr@sohu.com; Zhu, Guanghu; Fu, Xinchu

2014-12-15

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect thanmore » those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.« less

Stochastic Network Interdiction

DTIC Science & Technology

1998-04-01

UB(6, g) are monotonic in the sense that if 69 is a refinement of 6: wI~6! < wI~69! and w# ~6, g! > w# ~69, g!. See Hausch and Ziemba (1983) for...of Vulnerability—The Integrity Family. Networks 24, 207–213. HAUSCH, D. B., AND W. T. ZIEMBA . 1983. Bounds on the Value of Information in Uncertain...Decision Problems II. Stochastics 10, 181–217. HUANG, C. C., W. T. ZIEMBA , AND A. BEN-TAL. 1977. Bounds on the Expectation of a Convex Function of a

Stochastical modeling for Viral Disease: Statistical Mechanics and Network Theory

NASA Astrophysics Data System (ADS)

Zhou, Hao; Deem, Michael

2007-04-01

Theoretical methods of statistical mechanics are developed and applied to study the immunological response against viral disease, such as dengue. We use this theory to show how the immune response to four different dengue serotypes may be sculpted. It is the ability of avian influenza, to change and to mix, that has given rise to the fear of a new human flu pandemic. Here we propose to utilize a scale free network based stochastic model to investigate the mitigation strategies and analyze the risk.

Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

PubMed

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

Splitting nodes and linking channels: A method for assembling biocircuits from stochastic elementary units

NASA Astrophysics Data System (ADS)

Ferwerda, Cameron; Lipan, Ovidiu

2016-11-01

Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system; and (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signaling pathways and quantifying naturally existing regulatory networks.

Network reliability maximization for stochastic-flow network subject to correlated failures using genetic algorithm and tabu\\xA0search

NASA Astrophysics Data System (ADS)

Yeh, Cheng-Ta; Lin, Yi-Kuei; Yang, Jo-Yun

2018-07-01

Network reliability is an important performance index for many real-life systems, such as electric power systems, computer systems and transportation systems. These systems can be modelled as stochastic-flow networks (SFNs) composed of arcs and nodes. Most system supervisors respect the network reliability maximization by finding the optimal multi-state resource assignment, which is one resource to each arc. However, a disaster may cause correlated failures for the assigned resources, affecting the network reliability. This article focuses on determining the optimal resource assignment with maximal network reliability for SFNs. To solve the problem, this study proposes a hybrid algorithm integrating the genetic algorithm and tabu search to determine the optimal assignment, called the hybrid GA-TS algorithm (HGTA), and integrates minimal paths, recursive sum of disjoint products and the correlated binomial distribution to calculate network reliability. Several practical numerical experiments are adopted to demonstrate that HGTA has better computational quality than several popular soft computing algorithms.

Adaptive hybrid simulations for multiscale stochastic reaction networks

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

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

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.

Light Propagation in Turbulent Media

NASA Astrophysics Data System (ADS)

Perez, Dario G.

2003-07-01

First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter H) a good candidate to simulate the turbulent refractive index. Moreover, we obtained its fractal dimension which matches the estimated by Constantin for passive scalar, and thus the parameter H determines the state of the turbulence. Next, using a path integral velocity representation, with the Markovian model, to calculate the effects of the turbulence over a system of grids. Finally, with the tools of Stochastic Calculus for fractional Brownian motions we studied the ray-equation coming from the Geometric Optics in the turbulent case. Our analysis covers those cases where average temperature gradients are relevant.

Event-Based $H_\\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

PubMed

Sheng, Li; Wang, Zidong; Zou, Lei; Alsaadi, Fuad E

2017-10-01

In this paper, the event-based finite-horizon H ∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H ∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

A non-local model of fractional heat conduction in rigid bodies

NASA Astrophysics Data System (ADS)

Borino, G.; di Paola, M.; Zingales, M.

2011-03-01

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.

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

PubMed

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

2017-10-01

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

A Hybrid Stochastic-Neuro-Fuzzy Model-Based System for In-Flight Gas Turbine Engine Diagnostics

DTIC Science & Technology

2001-04-05

Margin (ADM) and (ii) Fault Detection Margin (FDM). Key Words: ANFIS, Engine Health Monitoring , Gas Path Analysis, and Stochastic Analysis Adaptive Network...The paper illustrates the application of a hybrid Stochastic- Fuzzy -Inference Model-Based System (StoFIS) to fault diagnostics and prognostics for both...operational history monitored on-line by the engine health management (EHM) system. To capture the complex functional relationships between different

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

PubMed Central

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

2015-01-01

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

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

PubMed Central

2012-01-01

Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology. PMID:22583770

Pandemic Diseases and the Aviation Network SARS, a case study

NASA Astrophysics Data System (ADS)

Hufnagel, Lars; Brockmann, Dirk; Geisel, Theo

2005-03-01

We investigate the mechanisms of the worldwide spread of infectious diseases in a modern world in which humans travel on all scales. We introduce a probabilistic model which accounts for the worldwide spread of infectious diseases on the global aviation network. The analysis indicates that a forecast of the geographical spread of an epidemic is indeed possible, provided that local dynamical parameters of the disease such as the basic reproduction number are known. The model consists of local stochastic infection dynamics and stochastic transport of individuals on the worldwide aviation network which takes into account over 95% of the entire the national and international civil aviation traffic. Our simulations of the SARS outbreak are in surprisingly good agreement with published case reports. Despite the fact that the system is stochastic with a high number of degrees of freedom the outcome of a single simulation exhibits only a small magnitude of variability. We show that this is due to the strong heterogeneity of the network ranging from a few two over 25,000 passengers between nodes of the network. Thus, we propose that our model can be employed to predict the worldwide spread of future pandemic diseases and to identify endangered regions in advance. Based on the connectivity of the aviation network we evaluate the performance of different control strategies and show that a quick and focused reaction is essential to inhibit the global spread of infectious diseases.

Factors Associated with Success in College Calculus II

ERIC Educational Resources Information Center

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Magnetic Tunnel Junction Based Long-Term Short-Term Stochastic Synapse for a Spiking Neural Network with On-Chip STDP Learning

NASA Astrophysics Data System (ADS)

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-01

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-09-01

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

Magnetic Tunnel Junction Based Long-Term Short-Term Stochastic Synapse for a Spiking Neural Network with On-Chip STDP Learning.

PubMed

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-13

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.

Random noise effects in pulse-mode digital multilayer neural networks.

PubMed

Kim, Y C; Shanblatt, M A

1995-01-01

A pulse-mode digital multilayer neural network (DMNN) based on stochastic computing techniques is implemented with simple logic gates as basic computing elements. The pulse-mode signal representation and the use of simple logic gates for neural operations lead to a massively parallel yet compact and flexible network architecture, well suited for VLSI implementation. Algebraic neural operations are replaced by stochastic processes using pseudorandom pulse sequences. The distributions of the results from the stochastic processes are approximated using the hypergeometric distribution. Synaptic weights and neuron states are represented as probabilities and estimated as average pulse occurrence rates in corresponding pulse sequences. A statistical model of the noise (error) is developed to estimate the relative accuracy associated with stochastic computing in terms of mean and variance. Computational differences are then explained by comparison to deterministic neural computations. DMNN feedforward architectures are modeled in VHDL using character recognition problems as testbeds. Computational accuracy is analyzed, and the results of the statistical model are compared with the actual simulation results. Experiments show that the calculations performed in the DMNN are more accurate than those anticipated when Bernoulli sequences are assumed, as is common in the literature. Furthermore, the statistical model successfully predicts the accuracy of the operations performed in the DMNN.

Stochastic simulation of enzyme-catalyzed reactions with disparate timescales.

PubMed

Barik, Debashis; Paul, Mark R; Baumann, William T; Cao, Yang; Tyson, John J

2008-10-01

Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of protein interactions (e.g., complex formation may occur in fractions of a second, whereas catalytic conversions may take minutes). Exact stochastic simulation may be very inefficient under these circumstances, and methods for speeding up the simulation without sacrificing accuracy have been widely studied. We show that the "total quasi-steady-state approximation" for enzyme-catalyzed reactions provides a useful framework for efficient and accurate stochastic simulations. The method is applied to three examples: a simple enzyme-catalyzed reaction where enzyme and substrate have comparable abundances, a Goldbeter-Koshland switch, where a kinase and phosphatase regulate the phosphorylation state of a common substrate, and coupled Goldbeter-Koshland switches that exhibit bistability. Simulations based on the total quasi-steady-state approximation accurately capture the steady-state probability distributions of all components of these reaction networks. In many respects, the approximation also faithfully reproduces time-dependent aspects of the fluctuations. The method is accurate even under conditions of poor timescale separation.

Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks.

PubMed

Arunkumar, A; Sakthivel, R; Mathiyalagan, K; Park, Ju H

2014-07-01

This paper focuses the issue of robust stochastic stability for a class of uncertain fuzzy Markovian jumping discrete-time neural networks (FMJDNNs) with various activation functions and mixed time delay. By employing the Lyapunov technique and linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions are established for the robust stochastic stability of uncertain FMJDNNs. More precisely, the parameter uncertainties are assumed to be time varying, unknown and norm bounded. The obtained stability conditions are established in terms of LMIs, which can be easily checked by using the efficient MATLAB-LMI toolbox. Finally, numerical examples with simulation result are provided to illustrate the effectiveness and less conservativeness of the obtained results. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Deep neural network for traffic sign recognition systems: An analysis of spatial transformers and stochastic optimisation methods.

PubMed

Arcos-García, Álvaro; Álvarez-García, Juan A; Soria-Morillo, Luis M

2018-03-01

This paper presents a Deep Learning approach for traffic sign recognition systems. Several classification experiments are conducted over publicly available traffic sign datasets from Germany and Belgium using a Deep Neural Network which comprises Convolutional layers and Spatial Transformer Networks. Such trials are built to measure the impact of diverse factors with the end goal of designing a Convolutional Neural Network that can improve the state-of-the-art of traffic sign classification task. First, different adaptive and non-adaptive stochastic gradient descent optimisation algorithms such as SGD, SGD-Nesterov, RMSprop and Adam are evaluated. Subsequently, multiple combinations of Spatial Transformer Networks placed at distinct positions within the main neural network are analysed. The recognition rate of the proposed Convolutional Neural Network reports an accuracy of 99.71% in the German Traffic Sign Recognition Benchmark, outperforming previous state-of-the-art methods and also being more efficient in terms of memory requirements. Copyright © 2018 Elsevier Ltd. All rights reserved.

Performance improvement of optical CDMA networks with stochastic artificial bee colony optimization technique

NASA Astrophysics Data System (ADS)

Panda, Satyasen

2018-05-01

This paper proposes a modified artificial bee colony optimization (ABC) algorithm based on levy flight swarm intelligence referred as artificial bee colony levy flight stochastic walk (ABC-LFSW) optimization for optical code division multiple access (OCDMA) network. The ABC-LFSW algorithm is used to solve asset assignment problem based on signal to noise ratio (SNR) optimization in OCDM networks with quality of service constraints. The proposed optimization using ABC-LFSW algorithm provides methods for minimizing various noises and interferences, regulating the transmitted power and optimizing the network design for improving the power efficiency of the optical code path (OCP) from source node to destination node. In this regard, an optical system model is proposed for improving the network performance with optimized input parameters. The detailed discussion and simulation results based on transmitted power allocation and power efficiency of OCPs are included. The experimental results prove the superiority of the proposed network in terms of power efficiency and spectral efficiency in comparison to networks without any power allocation approach.

Financial Time Series Prediction Using Elman Recurrent Random Neural Networks

PubMed Central

Wang, Jie; Wang, Jun; Fang, Wen; Niu, Hongli

2016-01-01

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed an architecture which combined Elman recurrent neural networks with stochastic time effective function. By analyzing the proposed model with the linear regression, complexity invariant distance (CID), and multiscale CID (MCID) analysis methods and taking the model compared with different models such as the backpropagation neural network (BPNN), the stochastic time effective neural network (STNN), and the Elman recurrent neural network (ERNN), the empirical results show that the proposed neural network displays the best performance among these neural networks in financial time series forecasting. Further, the empirical research is performed in testing the predictive effects of SSE, TWSE, KOSPI, and Nikkei225 with the established model, and the corresponding statistical comparisons of the above market indices are also exhibited. The experimental results show that this approach gives good performance in predicting the values from the stock market indices. PMID:27293423

Financial Time Series Prediction Using Elman Recurrent Random Neural Networks.

PubMed

Wang, Jie; Wang, Jun; Fang, Wen; Niu, Hongli

2016-01-01

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed an architecture which combined Elman recurrent neural networks with stochastic time effective function. By analyzing the proposed model with the linear regression, complexity invariant distance (CID), and multiscale CID (MCID) analysis methods and taking the model compared with different models such as the backpropagation neural network (BPNN), the stochastic time effective neural network (STNN), and the Elman recurrent neural network (ERNN), the empirical results show that the proposed neural network displays the best performance among these neural networks in financial time series forecasting. Further, the empirical research is performed in testing the predictive effects of SSE, TWSE, KOSPI, and Nikkei225 with the established model, and the corresponding statistical comparisons of the above market indices are also exhibited. The experimental results show that this approach gives good performance in predicting the values from the stock market indices.

Bus-based park-and-ride system: a stochastic model on multimodal network with congestion pricing schemes

NASA Astrophysics Data System (ADS)

Liu, Zhiyuan; Meng, Qiang

2014-05-01

This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users' route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users' generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit (bus) flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.

Impact of Calculus Reform in a Liberal Arts Calculus Course.

ERIC Educational Resources Information Center

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

MmWave Vehicle-to-Infrastructure Communication :Analysis of Urban Microcellular Networks

DOT National Transportation Integrated Search

2017-05-01

Vehicle-to-infrastructure (V2I) communication may provide high data rates to vehicles via millimeterwave (mmWave) microcellular networks. This report uses stochastic geometry to analyze the coverage of urban mmWave microcellular networks. Prior work ...

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Irregular synchronous activity in stochastically-coupled networks of integrate-and-fire neurons.

PubMed

Lin, J K; Pawelzik, K; Ernst, U; Sejnowski, T J

1998-08-01

We investigate the spatial and temporal aspects of firing patterns in a network of integrate-and-fire neurons arranged in a one-dimensional ring topology. The coupling is stochastic and shaped like a Mexican hat with local excitation and lateral inhibition. With perfect precision in the couplings, the attractors of activity in the network occur at every position in the ring. Inhomogeneities in the coupling break the translational invariance of localized attractors and lead to synchronization within highly active as well as weakly active clusters. The interspike interval variability is high, consistent with recent observations of spike time distributions in visual cortex. The robustness of our results is demonstrated with more realistic simulations on a network of McGregor neurons which model conductance changes and after-hyperpolarization potassium currents.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

NASA Astrophysics Data System (ADS)

Costa, Ariadne; Brochini, Ludmila; Kinouchi, Osame

2017-08-01

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

The development of computer networks: First results from a microeconomic model

NASA Astrophysics Data System (ADS)

Maier, Gunther; Kaufmann, Alexander

Computer networks like the Internet are gaining importance in social and economic life. The accelerating pace of the adoption of network technologies for business purposes is a rather recent phenomenon. Many applications are still in the early, sometimes even experimental, phase. Nevertheless, it seems to be certain that networks will change the socioeconomic structures we know today. This is the background for our special interest in the development of networks, in the role of spatial factors influencing the formation of networks, and consequences of networks on spatial structures, and in the role of externalities. This paper discusses a simple economic model - based on a microeconomic calculus - that incorporates the main factors that generate the growth of computer networks. The paper provides analytic results about the generation of computer networks. The paper discusses (1) under what conditions economic factors will initiate the process of network formation, (2) the relationship between individual and social evaluation, and (3) the efficiency of a network that is generated based on economic mechanisms.

Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations

NASA Astrophysics Data System (ADS)

Zhang, Wanli; Li, Chuandong; Huang, Tingwen; Huang, Junjian

2018-02-01

This paper investigates the fixed-time synchronization of complex networks (CNs) with nonidentical nodes and stochastic noise perturbations. By designing new controllers, constructing Lyapunov functions and using the properties of Weiner process, different synchronization criteria are derived according to whether the node systems in the CNs or the goal system satisfies the corresponding conditions. Moreover, the role of the designed controllers is analyzed in great detail by constructing a suitable comparison system and a new method is presented to estimate the settling time by utilizing the comparison system. Results of this paper can be applied to both directed and undirected weighted networks. Numerical simulations are offered to verify the effectiveness of our new results.

Stochastic Switching Induced Adaptation in a Starved Escherichia coli Population

PubMed Central

Ito, Yoichiro; Ying, Bei-Wen; Yomo, Tetsuya

2011-01-01

Population adaptation can be determined by stochastic switching in living cells. To examine how stochastic switching contributes to the fate decision for a population under severe stress, we constructed an Escherichia coli strain crucially dependent on the expression of a rewired gene. The gene essential for tryptophan biosynthesis, trpC, was removed from the native regulatory unit, the Trp operon, and placed under the extraneous control of the lactose utilisation network. Bistability of the network provided the cells two discrete phenotypes: the induced and suppressed level of trpC. The two phenotypes permitted the cells to grow or not, respectively, under conditions of tryptophan depletion. We found that stochastic switching between the two states allowed the initially suppressed cells to form a new population with induced trpC in response to tryptophan starvation. However, the frequency of the transition from suppressed to induced state dropped off dramatically in the starved population, in comparison to that in the nourished population. This reduced switching rate was compensated by increasing the initial population size, which probably provided the cell population more chances to wait for the rarely appearing fit cells from the unfit cells. Taken together, adaptation of a starved bacterial population because of stochasticity in the gene rewired from the ancient regulon was experimentally confirmed, and the nutritional status and the population size played a great role in stochastic adaptation. PMID:21931628

The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

ERIC Educational Resources Information Center

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Research Note: The consequences of different methods for handling missing network data in Stochastic Actor Based Models

PubMed Central

Hipp, John R.; Wang, Cheng; Butts, Carter T.; Jose, Rupa; Lakon, Cynthia M.

2015-01-01

Although stochastic actor based models (e.g., as implemented in the SIENA software program) are growing in popularity as a technique for estimating longitudinal network data, a relatively understudied issue is the consequence of missing network data for longitudinal analysis. We explore this issue in our research note by utilizing data from four schools in an existing dataset (the AddHealth dataset) over three time points, assessing the substantive consequences of using four different strategies for addressing missing network data. The results indicate that whereas some measures in such models are estimated relatively robustly regardless of the strategy chosen for addressing missing network data, some of the substantive conclusions will differ based on the missing data strategy chosen. These results have important implications for this burgeoning applied research area, implying that researchers should more carefully consider how they address missing data when estimating such models. PMID:25745276

Research Note: The consequences of different methods for handling missing network data in Stochastic Actor Based Models.

PubMed

Hipp, John R; Wang, Cheng; Butts, Carter T; Jose, Rupa; Lakon, Cynthia M

2015-05-01

Although stochastic actor based models (e.g., as implemented in the SIENA software program) are growing in popularity as a technique for estimating longitudinal network data, a relatively understudied issue is the consequence of missing network data for longitudinal analysis. We explore this issue in our research note by utilizing data from four schools in an existing dataset (the AddHealth dataset) over three time points, assessing the substantive consequences of using four different strategies for addressing missing network data. The results indicate that whereas some measures in such models are estimated relatively robustly regardless of the strategy chosen for addressing missing network data, some of the substantive conclusions will differ based on the missing data strategy chosen. These results have important implications for this burgeoning applied research area, implying that researchers should more carefully consider how they address missing data when estimating such models.

Extreme fluctuations in stochastic network coordination with time delays

NASA Astrophysics Data System (ADS)

Hunt, D.; Molnár, F.; Szymanski, B. K.; Korniss, G.

2015-12-01

We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.

Fluctuation relations between hierarchical kinetically equivalent networks with Arrhenius-type transitions and their roles in systems and structural biology.

PubMed

Deng, De-Ming; Lu, Yi-Ta; Chang, Cheng-Hung

2017-06-01

The legality of using simple kinetic schemes to determine the stochastic properties of a complex system depends on whether the fluctuations generated from hierarchical equivalent schemes are consistent with one another. To analyze this consistency, we perform lumping processes on the stochastic differential equations and the generalized fluctuation-dissipation theorem and apply them to networks with the frequently encountered Arrhenius-type transition rates. The explicit Langevin force derived from those networks enables us to calculate the state fluctuations caused by the intrinsic and extrinsic noises on the free energy surface and deduce their relations between kinetically equivalent networks. In addition to its applicability to wide classes of network related systems, such as those in structural and systems biology, the result sheds light on the fluctuation relations for general physical variables in Keizer's canonical theory.

Disassortativity of random critical branching trees

NASA Astrophysics Data System (ADS)

Kim, J. S.; Kahng, B.; Kim, D.

2009-06-01

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

ERIC Educational Resources Information Center

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

NASA Astrophysics Data System (ADS)

Seif, Dariush; Ghoniem, Nasr M.

2014-12-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô's calculus, rate equations for the first five moments of the size distribution in helium-vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium-vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the implementation of a path-integral approach may proceed if the distribution is known experimentally to significantly stray from a Gaussian description.

Application of stochastic processes in random growth and evolutionary dynamics

NASA Astrophysics Data System (ADS)

Oikonomou, Panagiotis

We study the effect of power-law distributed randomness on the dynamical behavior of processes such as stochastic growth patterns and evolution. First, we examine the geometrical properties of random shapes produced by a generalized stochastic Loewner Evolution driven by a superposition of a Brownian motion and a stable Levy process. The situation is defined by the usual stochastic Loewner Evolution parameter, kappa, as well as alpha which defines the power-law tail of the stable Levy distribution. We show that the properties of these patterns change qualitatively and singularly at critical values of kappa and alpha. It is reasonable to call such changes "phase transitions". These transitions occur as kappa passes through four and as alpha passes through one. Numerical simulations are used to explore the global scaling behavior of these patterns in each "phase". We show both analytically and numerically that the growth continues indefinitely in the vertical direction for alpha greater than 1, goes as logarithmically with time for alpha equals to 1, and saturates for alpha smaller than 1. The probability density has two different scales corresponding to directions along and perpendicular to the boundary. Scaling functions for the probability density are given for various limiting cases. Second, we study the effect of the architecture of biological networks on their evolutionary dynamics. In recent years, studies of the architecture of large networks have unveiled a common topology, called scale-free, in which a majority of the elements are poorly connected except for a small fraction of highly connected components. We ask how networks with distinct topologies can evolve towards a pre-established target phenotype through a process of random mutations and selection. We use networks of Boolean components as a framework to model a large class of phenotypes. Within this approach, we find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. While homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps, scale-free networks evolve rapidly and continuously towards the target phenotype. Moreover, we show that scale-free networks always evolve faster than homogeneous random networks; remarkably, this property does not depend on the precise value of the topological parameter. By contrast, homogeneous random networks require a specific tuning of their topological parameter in order to optimize their fitness. This model suggests that the evolutionary paths of biological networks, punctuated or continuous, may solely be determined by the network topology.

Revisiting node-based SIR models in complex networks with degree correlations

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alofi, Abdulaziz; AL-Mazrooei, Abdullah; Elaiw, Ahmed

2015-11-01

In this paper, we consider two growing networks which will lead to the degree-degree correlations between two nearest neighbors in the network. When the network grows to some certain size, we introduce an SIR-like disease such as pandemic influenza H1N1/09 to the population. Due to its rapid spread, the population size changes slowly, and thus the disease spreads on correlated networks with approximately fixed size. To predict the disease evolution on correlated networks, we first review two node-based SIR models incorporating degree correlations and an edge-based SIR model without considering degree correlation, and then compare the predictions of these models with stochastic SIR simulations, respectively. We find that the edge-based model, even without considering degree correlations, agrees much better than the node-based models incorporating degree correlations with stochastic SIR simulations in many respects. Moreover, simulation results show that for networks with positive correlation, the edge-based model provides a better upper bound of the cumulative incidence than the node-based SIR models, whereas for networks with negative correlation, it provides a lower bound of the cumulative incidence.

Detection and localization of change points in temporal networks with the aid of stochastic block models

NASA Astrophysics Data System (ADS)

De Ridder, Simon; Vandermarliere, Benjamin; Ryckebusch, Jan

2016-11-01

A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset (2015 Proc. 29th AAAI Conf. on Artificial Intelligence). We build on this methodology and extend it to also include the versatile stochastic block models (SBMs) as a parametric family for reconstructing the empirical networks. We use five different techniques for change point detection on prototypical temporal networks, including empirical and synthetic ones. We find that none of the considered methods can consistently outperform the others when it comes to detecting and locating the expected change points in empirical temporal networks. With respect to the precision and the recall of the results of the change points, we find that the method based on a degree-corrected SBM has better recall properties than other dedicated methods, especially for sparse networks and smaller sliding time window widths.

Novel approaches to pin cluster synchronization on complex dynamical networks in Lur'e forms

NASA Astrophysics Data System (ADS)

Tang, Ze; Park, Ju H.; Feng, Jianwen

2018-04-01

This paper investigates the cluster synchronization of complex dynamical networks consisted of identical or nonidentical Lur'e systems. Due to the special topology structure of the complex networks and the existence of stochastic perturbations, a kind of randomly occurring pinning controller is designed which not only synchronizes all Lur'e systems in the same cluster but also decreases the negative influence among different clusters. Firstly, based on an extended integral inequality, the convex combination theorem and S-procedure, the conditions for cluster synchronization of identical Lur'e networks are derived in a convex domain. Secondly, randomly occurring adaptive pinning controllers with two independent Bernoulli stochastic variables are designed and then sufficient conditions are obtained for the cluster synchronization on complex networks consisted of nonidentical Lur'e systems. In addition, suitable control gains for successful cluster synchronization of nonidentical Lur'e networks are acquired by designing some adaptive updating laws. Finally, we present two numerical examples to demonstrate the validity of the control scheme and the theoretical analysis.

Cascades on a stochastic pulse-coupled network

NASA Astrophysics Data System (ADS)

Wray, C. M.; Bishop, S. R.

2014-09-01

While much recent research has focused on understanding isolated cascades of networks, less attention has been given to dynamical processes on networks exhibiting repeated cascades of opposing influence. An example of this is the dynamic behaviour of financial markets where cascades of buying and selling can occur, even over short timescales. To model these phenomena, a stochastic pulse-coupled oscillator network with upper and lower thresholds is described and analysed. Numerical confirmation of asynchronous and synchronous regimes of the system is presented, along with analytical identification of the fixed point state vector of the asynchronous mean field system. A lower bound for the finite system mean field critical value of network coupling probability is found that separates the asynchronous and synchronous regimes. For the low-dimensional mean field system, a closed-form equation is found for cascade size, in terms of the network coupling probability. Finally, a description of how this model can be applied to interacting agents in a financial market is provided.

Neutral Community Dynamics and the Evolution of Species Interactions.

PubMed

Coelho, Marco Túlio P; Rangel, Thiago F

2018-04-01

A contemporary goal in ecology is to determine the ecological and evolutionary processes that generate recurring structural patterns in mutualistic networks. One of the great challenges is testing the capacity of neutral processes to replicate observed patterns in ecological networks, since the original formulation of the neutral theory lacks trophic interactions. Here, we develop a stochastic-simulation neutral model adding trophic interactions to the neutral theory of biodiversity. Without invoking ecological differences among individuals of different species, and assuming that ecological interactions emerge randomly, we demonstrate that a spatially explicit multitrophic neutral model is able to capture the recurrent structural patterns of mutualistic networks (i.e., degree distribution, connectance, nestedness, and phylogenetic signal of species interactions). Nonrandom species distribution, caused by probabilistic events of migration and speciation, create nonrandom network patterns. These findings have broad implications for the interpretation of niche-based processes as drivers of ecological networks, as well as for the integration of network structures with demographic stochasticity.

Cascades on a stochastic pulse-coupled network

PubMed Central

Wray, C. M.; Bishop, S. R.

2014-01-01

While much recent research has focused on understanding isolated cascades of networks, less attention has been given to dynamical processes on networks exhibiting repeated cascades of opposing influence. An example of this is the dynamic behaviour of financial markets where cascades of buying and selling can occur, even over short timescales. To model these phenomena, a stochastic pulse-coupled oscillator network with upper and lower thresholds is described and analysed. Numerical confirmation of asynchronous and synchronous regimes of the system is presented, along with analytical identification of the fixed point state vector of the asynchronous mean field system. A lower bound for the finite system mean field critical value of network coupling probability is found that separates the asynchronous and synchronous regimes. For the low-dimensional mean field system, a closed-form equation is found for cascade size, in terms of the network coupling probability. Finally, a description of how this model can be applied to interacting agents in a financial market is provided. PMID:25213626

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

PubMed

Xu, Dongpo; Xia, Yili; Mandic, Danilo P

2016-02-01

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.

Stochastic Dynamical Model of a Growing Citation Network Based on a Self-Exciting Point Process

NASA Astrophysics Data System (ADS)

Golosovsky, Michael; Solomon, Sorin

2012-08-01

We put under experimental scrutiny the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose a citation network of physics papers and traced the citation history of 40 195 papers published in one year. Contrary to common belief, we find that the citation dynamics of the individual papers follows the superlinear preferential attachment, with the exponent α=1.25-1.3. Moreover, we show that the citation process cannot be described as a memoryless Markov chain since there is a substantial correlation between the present and recent citation rates of a paper. Based on our findings we construct a stochastic growth model of the citation network, perform numerical simulations based on this model and achieve an excellent agreement with the measured citation distributions.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Heat exchanger expert system logic

NASA Technical Reports Server (NTRS)

Cormier, R.

1988-01-01

The reduction is described of the operation and fault diagnostics of a Deep Space Network heat exchanger to a rule base by the application of propositional calculus to a set of logic statements. The value of this approach lies in the ease of converting the logic and subsequently implementing it on a computer as an expert system. The rule base was written in Process Intelligent Control software.

Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Emelyanova, Natalya; Demin, Sergey; Gafarov, Fail; Hänggi, Peter; Yulmetyeva, Dinara

2003-05-01

For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long-time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long-range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non-Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks with a view to time discreteness and effects of statistical memory.

Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics.

PubMed

Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang

2014-06-01

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

Perception Accuracy of Affiliative Relationships in Elementary School Children and Young Adolescents

PubMed Central

Daniel, João R.; Silva, Rita R.; Santos, António J.; Cardoso, Jordana; Coelho, Leandra; Freitas, Miguel; Ribeiro, Olívia

2017-01-01

There has been a rapid growth of studies focused on selection and socialization processes of peer groups, mostly due to the development of stochastic actor-based models to analyze longitudinal social network data. One of the core assumptions of these models is that individuals have an accurate knowledge of the dyadic relationships within their network (i.e., who is and is not connected to whom). Recent cross-sectional findings suggest that elementary school children are very inaccurate in perceiving their classmates’ dyadic relationships. These findings question the validity of stochastic actor-based models to study the developmental dynamics of children and carry implications for future research as well as for the interpretation of past findings. The goal of the present study was thus to further explore the adequacy of the accuracy assumption, analysing data from three longitudinal samples of different age groups (elementary school children and adolescents). Our results support the validity of stochastic actor-based models to study the network of adolescents and suggest that the violation of the accuracy assumption for elementary school children is not as severe as previously thought. PMID:29163310

Autapse-induced multiple stochastic resonances in a modular neuronal network

NASA Astrophysics Data System (ADS)

Yang, XiaoLi; Yu, YanHu; Sun, ZhongKui

2017-08-01

This study investigates the nontrivial effects of autapse on stochastic resonance in a modular neuronal network subjected to bounded noise. The resonance effect of autapse is detected by imposing a self-feedback loop with autaptic strength and autaptic time delay to each constituent neuron. Numerical simulations have demonstrated that bounded noise with the proper level of amplitude can induce stochastic resonance; moreover, the noise induced resonance dynamics can be significantly shaped by the autapse. In detail, for a specific range of autaptic strength, multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted. These appropriately adjusted delays are detected to nearly approach integer multiples of the period of the external weak signal when the autaptic strength is very near zero; otherwise, they do not match the period of the external weak signal when the autaptic strength is slightly greater than zero. Surprisingly, in both cases, the differences between arbitrary two adjacent adjusted autaptic delays are always approximately equal to the period of the weak signal. The phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of the external weak signal and the intramodule probability of subnetwork. These findings could have important implications for weak signal detection and information propagation in realistic neural systems.

Incorporating Wind Power Forecast Uncertainties Into Stochastic Unit Commitment Using Neural Network-Based Prediction Intervals.

PubMed

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2015-09-01

Penetration of renewable energy resources, such as wind and solar power, into power systems significantly increases the uncertainties on system operation, stability, and reliability in smart grids. In this paper, the nonparametric neural network-based prediction intervals (PIs) are implemented for forecast uncertainty quantification. Instead of a single level PI, wind power forecast uncertainties are represented in a list of PIs. These PIs are then decomposed into quantiles of wind power. A new scenario generation method is proposed to handle wind power forecast uncertainties. For each hour, an empirical cumulative distribution function (ECDF) is fitted to these quantile points. The Monte Carlo simulation method is used to generate scenarios from the ECDF. Then the wind power scenarios are incorporated into a stochastic security-constrained unit commitment (SCUC) model. The heuristic genetic algorithm is utilized to solve the stochastic SCUC problem. Five deterministic and four stochastic case studies incorporated with interval forecasts of wind power are implemented. The results of these cases are presented and discussed together. Generation costs, and the scheduled and real-time economic dispatch reserves of different unit commitment strategies are compared. The experimental results show that the stochastic model is more robust than deterministic ones and, thus, decreases the risk in system operations of smart grids.

What physicists should learn about finance (if they want to)

NASA Astrophysics Data System (ADS)

Schmidt, Anatoly

2006-03-01

There has been growing interest among physicists to Econophysics, i.e. analysis and modeling of financial and economic processes using the concepts of theoretical Physics. There has been also perception that the financial industry is a viable alternative for those physicists who are not able or are not willing to pursue career in their major field. However in our times, the Wall Street expects from applicants for quantitative positions not only the knowledge of the stochastic calculus and the methods of time series analysis but also of such concepts as option pricing, portfolio management, and risk measurement. Here I describe a synthetic course based on my book ``Quantitative Finance for Physicists'' (Elsevier, 2004) that outlines both worlds: Econophysics and Mathematical Finance. This course may be offered as elective for senior undergraduate or graduate Physics majors.

Fractional calculus applied to the analysis of spectral electrical conductivity of clay-water system.

PubMed

Korosak, Dean; Cvikl, Bruno; Kramer, Janja; Jecl, Renata; Prapotnik, Anita

2007-06-16

The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. The frequency dependence of the conductivity is shown to follow the power-law with the exponent n=0.67 before reaching the frequency-independent part. When scaled with the value of the frequency-independent part of the spectrum the conductivity spectra for samples at different water content values are shown to fit to a single master curve. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. The fractional Langevin equation is then used to describe the stochastic dynamics of the single ion. The results indicate that the experimentally observed dielectric properties originate in anomalous ion transport in clay-water system characterized with time-dependent diffusion coefficient.

Towards an Analytic Foundation for Network Architecture

DTIC Science & Technology

2010-12-31

SUPPLEMENTARY NOTES N/A 14. ABSTRACT In this project, we develop the analytic tools of stochastic optimization for wireless network design and apply them...and Mung Chiang, “ DaVinci : Dynamically Adaptive Virtual Networks for a Customized Internet,” in Proc. ACM SIGCOMM CoNext Conference, December 2008

Coexistence of Stochastic Oscillations and Self-Organized Criticality in a Neuronal Network: Sandpile Model Application.

PubMed

Saeedi, Alireza; Jannesari, Mostafa; Gharibzadeh, Shahriar; Bakouie, Fatemeh

2018-04-01

Self-organized criticality (SOC) and stochastic oscillations (SOs) are two theoretically contradictory phenomena that are suggested to coexist in the brain. Recently it has been shown that an accumulation-release process like sandpile dynamics can generate SOC and SOs simultaneously. We considered the effect of the network structure on this coexistence and showed that the sandpile dynamics on a small-world network can produce two power law regimes along with two groups of SOs-two peaks in the power spectrum of the generated signal simultaneously. We also showed that external stimuli in the sandpile dynamics do not affect the coexistence of SOC and SOs but increase the frequency of SOs, which is consistent with our knowledge of the brain.

Qualitative modeling of normal blood coagulation and its pathological states using stochastic activity networks.

PubMed

Mounts, W M; Liebman, M N

1997-07-01

We have developed a method for representing biological pathways and simulating their behavior based on the use of stochastic activity networks (SANs). SANs, an extension of the original Petri net, have been used traditionally to model flow systems including data-communications networks and manufacturing processes. We apply the methodology to the blood coagulation cascade, a biological flow system, and present the representation method as well as results of simulation studies based on published experimental data. In addition to describing the dynamic model, we also present the results of its utilization to perform simulations of clinical states including hemophilia's A and B as well as sensitivity analysis of individual factors and their impact on thrombin production.

Nonparametric weighted stochastic block models

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2018-01-01

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.

Patients with dental calculus have increased saliva and gingival crevicular fluid fetuin-A levels but no association with fetuin-A polymorphisms.

PubMed

Doğan, Gülnihal Emrem; Demir, Turgut; Laloğlu, Esra; Sağlam, Ebru; Aksoy, Hülya; Yildirim, Abdulkadir; Akçay, Fatih

2016-12-22

Fetuin-A is a potent inhibitor of calcium-phosphate precipitation and of the calcification process, therefore it can also be related with dental calculus. Thus, we aimed to investigate a possible relationship between fetuin-A gene polymorphism and the presence of dental calculus. A possible relationship between serum, saliva and gingival crevicular fluid (GCF) levels of fetuin-A was also investigated. Fetuin-A c.742C > T and c.766C > G polymorphisms were investigated in 103 patients with or without dental calculus. Additionally, serum, saliva and GCF fetuin-A levels of patients were compared according to dental calculus presence. A significant difference was not observed in the distribution of the fetuin-A c.742C > T and c.766C > G polymorphisms between patients with or without dental calculus. Saliva and GCF fetuin-A concentrations of patients with dental calculus were statistically higher than those without dental calculus (P=0.001, P=0.036 respectively). According to our results, fetuin-A c.742C > T and c.766C > G polymorphisms were not associated with presence of dental calculus. However, higher GCF and saliva fetuin-A levels were detected in patients with dental calculus than in patients without dental calculus, which may result from an adaptive mechanism to inhibit mineral precipitation and eventually calculus formation.

Variance decomposition in stochastic simulators.

PubMed

Le Maître, O P; Knio, O M; Moraes, A

2015-06-28

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Variance decomposition in stochastic simulators

NASA Astrophysics Data System (ADS)

Le Maître, O. P.; Knio, O. M.; Moraes, A.

2015-06-01

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

A Simple Acronym for Doing Calculus: CAL

ERIC Educational Resources Information Center

Hathaway, Richard J.

2008-01-01

An acronym is presented that provides students a potentially useful, unifying view of the major topics covered in an elementary calculus sequence. The acronym (CAL) is based on viewing the calculus procedure for solving a calculus problem P* in three steps: (1) recognizing that the problem cannot be solved using simple (non-calculus) techniques;…

Giant calculus: review and report of a case.

PubMed

Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S

2013-01-01

Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.

Calculus: The Dynamics of Change. MAA Notes Number 39.

ERIC Educational Resources Information Center

Roberts, A. Wayne, Ed.

This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches…

Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.

PubMed

Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye

2015-07-02

Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.

Development of spiral wave in a regular network of excitatory neurons due to stochastic poisoning of ion channels

NASA Astrophysics Data System (ADS)

Wu, Xinyi; Ma, Jun; Li, Fan; Jia, Ya

2013-12-01

Some experimental evidences show that spiral wave could be observed in the cortex of brain, and the propagation of this spiral wave plays an important role in signal communication as a pacemaker. The profile of spiral wave generated in a numerical way is often perfect while the observed profile in experiments is not perfect and smooth. In this paper, formation and development of spiral wave in a regular network of Morris-Lecar neurons, which neurons are placed on nodes uniformly in a two-dimensional array and each node is coupled with nearest-neighbor type, are investigated by considering the effect of stochastic ion channels poisoning and channel noise. The formation and selection of spiral wave could be detected as follows. (1) External forcing currents with diversity are imposed on neurons in the network of excitatory neurons with nearest-neighbor connection, a target-like wave emerges and its potential mechanism is discussed; (2) artificial defects and local poisoned area are selected in the network to induce new wave to interact with the target wave; (3) spiral wave can be induced to occupy the network when the target wave is blocked by the artificial defects or poisoned area with regular border lines; (4) the stochastic poisoning effect is introduced by randomly modifying the border lines (areas) of specific regions in the network. It is found that spiral wave can be also developed to occupy the network under appropriate poisoning ratio. The process of growth for the poisoned area of ion channels poisoning is measured, the effect of channels noise is also investigated. It is confirmed that perfect spiral wave emerges in the network under gradient poisoning even if the channel noise is considered.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Perspective: Stochastic magnetic devices for cognitive computing

NASA Astrophysics Data System (ADS)

Roy, Kaushik; Sengupta, Abhronil; Shim, Yong

2018-06-01

Stochastic switching of nanomagnets can potentially enable probabilistic cognitive hardware consisting of noisy neural and synaptic components. Furthermore, computational paradigms inspired from the Ising computing model require stochasticity for achieving near-optimality in solutions to various types of combinatorial optimization problems such as the Graph Coloring Problem or the Travelling Salesman Problem. Achieving optimal solutions in such problems are computationally exhaustive and requires natural annealing to arrive at the near-optimal solutions. Stochastic switching of devices also finds use in applications involving Deep Belief Networks and Bayesian Inference. In this article, we provide a multi-disciplinary perspective across the stack of devices, circuits, and algorithms to illustrate how the stochastic switching dynamics of spintronic devices in the presence of thermal noise can provide a direct mapping to the computational units of such probabilistic intelligent systems.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

A dynamical framework for integrated corridor management.

DOT National Transportation Integrated Search

2016-01-11

We develop analysis and control synthesis tools for dynamic traffic flow over networks. Our analysis : relies on exploiting monotonicity properties of the dynamics, and on adapting relevant tools from : stochastic queuing networks. We develop proport...

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

NASA Astrophysics Data System (ADS)

Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.

2013-02-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Reliability of recordings of subgingival calculus detected using an ultrasonic device.

PubMed

Corraini, Priscila; López, Rodrigo

2015-04-01

To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥  4 mm and with furcation involvement  ≥  degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.

Dynamical influence processes on networks: general theory and applications to social contagion.

PubMed

Harris, Kameron Decker; Danforth, Christopher M; Dodds, Peter Sheridan

2013-08-01

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. By allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean-field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from steady state to chaotic depending on the response functions, network connectivity, and update synchronicity. As a specific example, we model the competing tendencies of imitation and nonconformity by incorporating an off-threshold into standard threshold models of social contagion. In this way, we attempt to capture important aspects of fashions and societal trends. We compare our theory to extensive simulations of this "limited imitation contagion" model on Poisson random graphs, finding agreement between the mean-field theory and stochastic simulations.

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

NASA Astrophysics Data System (ADS)

Forman, Yakir; Cameron, Maria

2017-07-01

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for N+1, and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters.

Stochastic ecological network occupancy (SENO) models: a new tool for modeling ecological networks across spatial scales

USGS Publications Warehouse

Lafferty, Kevin D.; Dunne, Jennifer A.

2010-01-01

Stochastic ecological network occupancy (SENO) models predict the probability that species will occur in a sample of an ecological network. In this review, we introduce SENO models as a means to fill a gap in the theoretical toolkit of ecologists. As input, SENO models use a topological interaction network and rates of colonization and extinction (including consumer effects) for each species. A SENO model then simulates the ecological network over time, resulting in a series of sub-networks that can be used to identify commonly encountered community modules. The proportion of time a species is present in a patch gives its expected probability of occurrence, whose sum across species gives expected species richness. To illustrate their utility, we provide simple examples of how SENO models can be used to investigate how topological complexity, species interactions, species traits, and spatial scale affect communities in space and time. They can categorize species as biodiversity facilitators, contributors, or inhibitors, making this approach promising for ecosystem-based management of invasive, threatened, or exploited species.

Utilizing semantic networks to database and retrieve generalized stochastic colored Petri nets

NASA Technical Reports Server (NTRS)

Farah, Jeffrey J.; Kelley, Robert B.

1992-01-01

Previous work has introduced the Planning Coordinator (PCOORD), a coordinator functioning within the hierarchy of the Intelligent Machine Mode. Within the structure of the Planning Coordinator resides the Primitive Structure Database (PSDB) functioning to provide the primitive structures utilized by the Planning Coordinator in the establishing of error recovery or on-line path plans. This report further explores the Primitive Structure Database and establishes the potential of utilizing semantic networks as a means of efficiently storing and retrieving the Generalized Stochastic Colored Petri Nets from which the error recovery plans are derived.

Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation.

PubMed

Sturrock, Marc; Hellander, Andreas; Matzavinos, Anastasios; Chaplain, Mark A J

2013-03-06

Individual mouse embryonic stem cells have been found to exhibit highly variable differentiation responses under the same environmental conditions. The noisy cyclic expression of Hes1 and its downstream genes are known to be responsible for this, but the mechanism underlying this variability in expression is not well understood. In this paper, we show that the observed experimental data and diverse differentiation responses can be explained by a spatial stochastic model of the Hes1 gene regulatory network. We also propose experiments to control the precise differentiation response using drug treatment.

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks.

PubMed

Rathinam, Muruhan; Sheppard, Patrick W; Khammash, Mustafa

2010-01-21

Parametric sensitivity of biochemical networks is an indispensable tool for studying system robustness properties, estimating network parameters, and identifying targets for drug therapy. For discrete stochastic representations of biochemical networks where Monte Carlo methods are commonly used, sensitivity analysis can be particularly challenging, as accurate finite difference computations of sensitivity require a large number of simulations for both nominal and perturbed values of the parameters. In this paper we introduce the common random number (CRN) method in conjunction with Gillespie's stochastic simulation algorithm, which exploits positive correlations obtained by using CRNs for nominal and perturbed parameters. We also propose a new method called the common reaction path (CRP) method, which uses CRNs together with the random time change representation of discrete state Markov processes due to Kurtz to estimate the sensitivity via a finite difference approximation applied to coupled reaction paths that emerge naturally in this representation. While both methods reduce the variance of the estimator significantly compared to independent random number finite difference implementations, numerical evidence suggests that the CRP method achieves a greater variance reduction. We also provide some theoretical basis for the superior performance of CRP. The improved accuracy of these methods allows for much more efficient sensitivity estimation. In two example systems reported in this work, speedup factors greater than 300 and 10,000 are demonstrated.

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

NASA Astrophysics Data System (ADS)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

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

Using Dynamic Software to Address Common College Calculus Stumbling Blocks

ERIC Educational Resources Information Center

Seneres, Alice W.; Kerrigan, John A.

2014-01-01

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Leveraging Prior Calculus Study with Embedded Review

ERIC Educational Resources Information Center

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

The Effects of Two Semesters of Secondary School Calculus on Students' First and Second Quarter Calculus Grades at the University of Utah

ERIC Educational Resources Information Center

Robinson, William Baker

1970-01-01

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

Deterministic ripple-spreading model for complex networks.

PubMed

Hu, Xiao-Bing; Wang, Ming; Leeson, Mark S; Hines, Evor L; Di Paolo, Ezequiel

2011-04-01

This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.

Stochastic Geomorphology: A Framework for Creating General Principles on Erosion and Sedimentation in River Basins (Invited)

NASA Astrophysics Data System (ADS)

Benda, L. E.

2009-12-01

Stochastic geomorphology refers to the interaction of the stochastic field of sediment supply with hierarchically branching river networks where erosion, sediment flux and sediment storage are described by their probability densities. There are a number of general principles (hypotheses) that stem from this conceptual and numerical framework that may inform the science of erosion and sedimentation in river basins. Rainstorms and other perturbations, characterized by probability distributions of event frequency and magnitude, stochastically drive sediment influx to channel networks. The frequency-magnitude distribution of sediment supply that is typically skewed reflects strong interactions among climate, topography, vegetation, and geotechnical controls that vary between regions; the distribution varies systematically with basin area and the spatial pattern of erosion sources. Probability densities of sediment flux and storage evolve from more to less skewed forms downstream in river networks due to the convolution of the population of sediment sources in a watershed that should vary with climate, network patterns, topography, spatial scale, and degree of erosion asynchrony. The sediment flux and storage distributions are also transformed downstream due to diffusion, storage, interference, and attrition. In stochastic systems, the characteristically pulsed sediment supply and transport can create translational or stationary-diffusive valley and channel depositional landforms, the geometries of which are governed by sediment flux-network interactions. Episodic releases of sediment to the network can also drive a system memory reflected in a Hurst Effect in sediment yields and thus in sedimentological records. Similarly, discreet events of punctuated erosion on hillslopes can lead to altered surface and subsurface properties of a population of erosion source areas that can echo through time and affect subsequent erosion and sediment flux rates. Spatial patterns of probability densities have implications for the frequency and magnitude of sediment transport and storage and thus for the formation of alluvial and colluvial landforms throughout watersheds. For instance, the combination and interference of probability densities of sediment flux at confluences creates patterns of riverine heterogeneity, including standing waves of sediment with associated age distributions of deposits that can vary from younger to older depending on network geometry and position. Although the watershed world of probability densities is rarified and typically confined to research endeavors, it has real world implications for the day-to-day work on hillslopes and in fluvial systems, including measuring erosion, sediment transport, mapping channel morphology and aquatic habitats, interpreting deposit stratigraphy, conducting channel restoration, and applying environmental regulations. A question for the geomorphology community is whether the stochastic framework is useful for advancing our understanding of erosion and sedimentation and whether it should stimulate research to further develop, refine and test these and other principles. For example, a changing climate should lead to shifts in probability densities of erosion, sediment flux, storage, and associated habitats and thus provide a useful index of climate change in earth science forecast models.

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks

PubMed Central

Arampatzis, Georgios; Katsoulakis, Markos A.; Pantazis, Yannis

2015-01-01

Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in “sloppy” systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters. PMID:26161544

A VLSI recurrent network of integrate-and-fire neurons connected by plastic synapses with long-term memory.

PubMed

Chicca, E; Badoni, D; Dante, V; D'Andreagiovanni, M; Salina, G; Carota, L; Fusi, S; Del Giudice, P

2003-01-01

Electronic neuromorphic devices with on-chip, on-line learning should be able to modify quickly the synaptic couplings to acquire information about new patterns to be stored (synaptic plasticity) and, at the same time, preserve this information on very long time scales (synaptic stability). Here, we illustrate the electronic implementation of a simple solution to this stability-plasticity problem, recently proposed and studied in various contexts. It is based on the observation that reducing the analog depth of the synapses to the extreme (bistable synapses) does not necessarily disrupt the performance of the device as an associative memory, provided that 1) the number of neurons is large enough; 2) the transitions between stable synaptic states are stochastic; and 3) learning is slow. The drastic reduction of the analog depth of the synaptic variable also makes this solution appealing from the point of view of electronic implementation and offers a simple methodological alternative to the technological solution based on floating gates. We describe the full custom analog very large-scale integration (VLSI) realization of a small network of integrate-and-fire neurons connected by bistable deterministic plastic synapses which can implement the idea of stochastic learning. In the absence of stimuli, the memory is preserved indefinitely. During the stimulation the synapse undergoes quick temporary changes through the activities of the pre- and postsynaptic neurons; those changes stochastically result in a long-term modification of the synaptic efficacy. The intentionally disordered pattern of connectivity allows the system to generate a randomness suited to drive the stochastic selection mechanism. We check by a suitable stimulation protocol that the stochastic synaptic plasticity produces the expected pattern of potentiation and depression in the electronic network.

Stochastic inference with spiking neurons in the high-conductance state

NASA Astrophysics Data System (ADS)

Petrovici, Mihai A.; Bill, Johannes; Bytschok, Ilja; Schemmel, Johannes; Meier, Karlheinz

2016-10-01

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

PubMed

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

2018-04-01

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

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Adiabatic coarse-graining and simulations of stochastic biochemical networks

PubMed Central

Sinitsyn, N. A.; Hengartner, Nicolas; Nemenman, Ilya

2009-01-01

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach is similar to the Born–Oppenheimer approximation in quantum mechanics and follows from the stochastic path integral representation of the cumulant generating function of reaction events. In applications with a small number of chemical reactions, it produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, interpretable representation and can be used for high-accuracy, low-complexity coarse-grained numerical simulations. As an example, we derive the coarse-grained description for a chain of biochemical reactions and show that the coarse-grained and the microscopic simulations agree, but the former is 3 orders of magnitude faster. PMID:19525397

[Fluorescence control of dental calculus removal].

PubMed

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

A scaling law for random walks on networks

PubMed Central

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-01-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

Network-based stochastic semisupervised learning.

PubMed

Silva, Thiago Christiano; Zhao, Liang

2012-03-01

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Stochastic competitive learning in complex networks.

PubMed

Silva, Thiago Christiano; Zhao, Liang

2012-03-01

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning..

A scaling law for random walks on networks

NASA Astrophysics Data System (ADS)

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A scaling law for random walks on networks.

PubMed

Perkins, Theodore J; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-14

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

The Development of Newtonian Calculus in Britain, 1700-1800

NASA Astrophysics Data System (ADS)

Guicciardini, Niccoló

2003-11-01

Introduction; Overture: Newton's published work on the calculus of fluxions; Part I. The Early Period: 1. The diffusion of the calculus (1700-1730); 2. Developments in the calculus of fluxions (1714-1733); 3. The controversy on the foundations of the calculus (1734-1742); Part II. The Middle Period: 4. The textbooks on fluxions (1736-1758); 5. Some applications of the calculus (1740-1743); 6. The analytic art (1755-1785); Part III. The Reform: 7. Scotland (1785-1809); 8. The Military Schools (1773-1819); 9. Cambridge and Dublin (1790-1820); 10. Tables; Endnotes; Bibliography; Index.

Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics.

PubMed

Ocone, Andrea; Millar, Andrew J; Sanguinetti, Guido

2013-04-01

Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. http://homepages.inf.ed.ac.uk/gsanguin/software.html. Supplementary data are available at Bioinformatics online.

Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks

PubMed Central

Hallen, Mark; Li, Bochong; Tanouchi, Yu; Tan, Cheemeng; West, Mike; You, Lingchong

2011-01-01

Cellular processes are “noisy”. In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry. PMID:22022252

Thermodynamic efficiency of learning a rule in neural networks

NASA Astrophysics Data System (ADS)

Goldt, Sebastian; Seifert, Udo

2017-11-01

Biological systems have to build models from their sensory input data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a binary classification rule for these inputs from examples provided by a teacher. We analyse the ability of the network to apply the rule to new inputs, that is to generalise from past experience. Using stochastic thermodynamics, we show that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning. This allows us to introduce a thermodynamic efficiency of learning. We analytically compute the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit. In particular, we analyse three popular learning algorithms, namely Hebbian, Perceptron and AdaTron learning. Our work extends the methods of stochastic thermodynamics to a new type of learning problem and might form a suitable basis for investigating the thermodynamics of decision-making.

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

NASA Astrophysics Data System (ADS)

Barthel, Thomas; De Bacco, Caterina; Franz, Silvio

2018-01-01

We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages—conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

NASA Astrophysics Data System (ADS)

Han, Fei; Cheng, Lin

2017-04-01

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.

Markov stochasticity coordinates

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

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

The impacts of gingivitis and calculus on Thai children's quality of life.

PubMed

Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios

2012-09-01

To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

NASA Astrophysics Data System (ADS)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Stochastic blockmodeling of the modules and core of the Caenorhabditis elegans connectome.

PubMed

Pavlovic, Dragana M; Vértes, Petra E; Bullmore, Edward T; Schafer, William R; Nichols, Thomas E

2014-01-01

Recently, there has been much interest in the community structure or mesoscale organization of complex networks. This structure is characterised either as a set of sparsely inter-connected modules or as a highly connected core with a sparsely connected periphery. However, it is often difficult to disambiguate these two types of mesoscale structure or, indeed, to summarise the full network in terms of the relationships between its mesoscale constituents. Here, we estimate a community structure with a stochastic blockmodel approach, the Erdős-Rényi Mixture Model, and compare it to the much more widely used deterministic methods, such as the Louvain and Spectral algorithms. We used the Caenorhabditis elegans (C. elegans) nervous system (connectome) as a model system in which biological knowledge about each node or neuron can be used to validate the functional relevance of the communities obtained. The deterministic algorithms derived communities with 4-5 modules, defined by sparse inter-connectivity between all modules. In contrast, the stochastic Erdős-Rényi Mixture Model estimated a community with 9 blocks or groups which comprised a similar set of modules but also included a clearly defined core, made of 2 small groups. We show that the "core-in-modules" decomposition of the worm brain network, estimated by the Erdős-Rényi Mixture Model, is more compatible with prior biological knowledge about the C. elegans nervous system than the purely modular decomposition defined deterministically. We also show that the blockmodel can be used both to generate stochastic realisations (simulations) of the biological connectome, and to compress network into a small number of super-nodes and their connectivity. We expect that the Erdős-Rényi Mixture Model may be useful for investigating the complex community structures in other (nervous) systems.

Compartmental and Spatial Rule-Based Modeling with Virtual Cell.

PubMed

Blinov, Michael L; Schaff, James C; Vasilescu, Dan; Moraru, Ion I; Bloom, Judy E; Loew, Leslie M

2017-10-03

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

ERIC Educational Resources Information Center

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States

ERIC Educational Resources Information Center

Judson, Thomas W.; Nishimori, Toshiyuki

2005-01-01

In this study we investigated above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26…

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes

PubMed Central

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; SM, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome. PMID:27632566

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes.

PubMed

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; Sm, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome.

Signaling in large-scale neural networks.

PubMed

Berg, Rune W; Hounsgaard, Jørn

2009-02-01

We examine the recent finding that neurons in spinal motor circuits enter a high conductance state during functional network activity. The underlying concomitant increase in random inhibitory and excitatory synaptic activity leads to stochastic signal processing. The possible advantages of this metabolically costly organization are analyzed by comparing with synaptically less intense networks driven by the intrinsic response properties of the network neurons.

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

[Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

PubMed

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P < 0.01). GABA content of zolpidem group and Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P < 0.05). GABA content of Calculus Bovis group was higher than combination group (P < 0.05). GABA content of zolpidem group was not significantly different from combination group. Gly content of Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P < 0.05). Contents of two inhibitive neurotransmitters in rat striatum corpora were all significantly increased in Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics.

PubMed

Arampatzis, Georgios; Katsoulakis, Markos A; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

NASA Astrophysics Data System (ADS)

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-01

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

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

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systemsmore » with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.« less

A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks

PubMed Central

Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed

2015-01-01

We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056

Some basic results on the sets of sequences with geometric calculus

NASA Astrophysics Data System (ADS)

Türkmen, Cengiz; Başar, Feyzi

2012-08-01

As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G).

Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks

NASA Astrophysics Data System (ADS)

Smith, Eric; Krishnamurthy, Supriya

2017-12-01

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1 /n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical meaning of deficiency not only for first-moment conditions but for all orders in fluctuations.

Restricted diversity of dental calculus methanogens over five centuries, France.

PubMed

Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel

2016-05-11

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Electrical conductivity modeling and experimental study of densely packed SWCNT networks.

PubMed

Jack, D A; Yeh, C-S; Liang, Z; Li, S; Park, J G; Fielding, J C

2010-05-14

Single-walled carbon nanotube (SWCNT) networks have become a subject of interest due to their ability to support structural, thermal and electrical loadings, but to date their application has been hindered due, in large part, to the inability to model macroscopic responses in an industrial product with any reasonable confidence. This paper seeks to address the relationship between macroscale electrical conductivity and the nanostructure of a dense network composed of SWCNTs and presents a uniquely formulated physics-based computational model for electrical conductivity predictions. The proposed model incorporates physics-based stochastic parameters for the individual nanotubes to construct the nanostructure such as: an experimentally obtained orientation distribution function, experimentally derived length and diameter distributions, and assumed distributions of chirality and registry of individual CNTs. Case studies are presented to investigate the relationship between macroscale conductivity and nanostructured variations in the bulk stochastic length, diameter and orientation distributions. Simulation results correspond nicely with those available in the literature for case studies of conductivity versus length and conductivity versus diameter. In addition, predictions for the increasing anisotropy of the bulk conductivity as a function of the tube orientation distribution are in reasonable agreement with our experimental results. Examples are presented to demonstrate the importance of incorporating various stochastic characteristics in bulk conductivity predictions. Finally, a design consideration for industrial applications is discussed based on localized network power emission considerations and may lend insight to the design engineer to better predict network failure under high current loading applications.

Maximizing information exchange between complex networks

NASA Astrophysics Data System (ADS)

West, Bruce J.; Geneston, Elvis L.; Grigolini, Paolo

2008-10-01

Science is not merely the smooth progressive interaction of hypothesis, experiment and theory, although it sometimes has that form. More realistically the scientific study of any given complex phenomenon generates a number of explanations, from a variety of perspectives, that eventually requires synthesis to achieve a deep level of insight and understanding. One such synthesis has created the field of out-of-equilibrium statistical physics as applied to the understanding of complex dynamic networks. Over the past forty years the concept of complexity has undergone a metamorphosis. Complexity was originally seen as a consequence of memory in individual particle trajectories, in full agreement with a Hamiltonian picture of microscopic dynamics and, in principle, macroscopic dynamics could be derived from the microscopic Hamiltonian picture. The main difficulty in deriving macroscopic dynamics from microscopic dynamics is the need to take into account the actions of a very large number of components. The existence of events such as abrupt jumps, considered by the conventional continuous time random walk approach to describing complexity was never perceived as conflicting with the Hamiltonian view. Herein we review many of the reasons why this traditional Hamiltonian view of complexity is unsatisfactory. We show that as a result of technological advances, which make the observation of single elementary events possible, the definition of complexity has shifted from the conventional memory concept towards the action of non-Poisson renewal events. We show that the observation of crucial processes, such as the intermittent fluorescence of blinking quantum dots as well as the brain’s response to music, as monitored by a set of electrodes attached to the scalp, has forced investigators to go beyond the traditional concept of complexity and to establish closer contact with the nascent field of complex networks. Complex networks form one of the most challenging areas of modern research overarching all of the traditional scientific disciplines. The transportation networks of planes, highways and railroads; the economic networks of global finance and stock markets; the social networks of terrorism, governments, businesses and churches; the physical networks of telephones, the Internet, earthquakes and global warming and the biological networks of gene regulation, the human body, clusters of neurons and food webs, share a number of apparently universal properties as the networks become increasingly complex. Ubiquitous aspects of such complex networks are the appearance of non-stationary and non-ergodic statistical processes and inverse power-law statistical distributions. Herein we review the traditional dynamical and phase-space methods for modeling such networks as their complexity increases and focus on the limitations of these procedures in explaining complex networks. Of course we will not be able to review the entire nascent field of network science, so we limit ourselves to a review of how certain complexity barriers have been surmounted using newly applied theoretical concepts such as aging, renewal, non-ergodic statistics and the fractional calculus. One emphasis of this review is information transport between complex networks, which requires a fundamental change in perception that we express as a transition from the familiar stochastic resonance to the new concept of complexity matching.

Stochastic Estimation and Control of Queues Within a Computer Network

DTIC Science & Technology

2009-03-01

3]. And NS-2 is a network simulator developed at UC Berkely and is a well known, free, powerful network simulator tool. As will be more discussed...HA011118931033.aspx 7. James Trulove , “Broadband Networking”, CRC Press, 2nd edition, 2000 8. Jonathan Pengelly “MONTE CARLO METHODS” University of Otago

Adaptive Dynamics, Control, and Extinction in Networked Populations

DTIC Science & Technology

2015-07-09

network geometries. From the pre-history of paths that go extinct, a density function is created from the prehistory of these paths, and a clear local...density plots of Fig. 3b. Using the IAMM to compute the most probable path and comparing it to the prehistory of extinction events on stochastic networks

Sparse cliques trump scale-free networks in coordination and competition

PubMed Central

Gianetto, David A.; Heydari, Babak

2016-01-01

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner’s Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner’s Dilemma game. PMID:26899456

Sparse cliques trump scale-free networks in coordination and competition

NASA Astrophysics Data System (ADS)

Gianetto, David A.; Heydari, Babak

2016-02-01

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner’s Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner’s Dilemma game.

Real-Time Optimization in Complex Stochastic Environment

DTIC Science & Technology

2015-06-24

simpler ones, thus addressing scalability and the limited resources of networked wireless devices. This, however, comes at the expense of increased...Maximization of Wireless Sensor Networks with Non-ideal Batteries”, IEEE Trans. on Control of Network Systems, Vol. 1, 1, pp. 86-98, 2014. [27...C.G., “Optimal Energy-Efficient Downlink Transmission Scheduling for Real-Time Wireless Networks ”, subm. to IEEE Trans. on Control of Network Systems

Convex functions and some inequalities in terms of the Non-Newtonian Calculus

NASA Astrophysics Data System (ADS)

Unluyol, Erdal; Salas, Seren; Iscan, Imdat

2017-04-01

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, and thus establish a new calculus, called Non-Newtonian Calculus. So, in this paper, it is investigated to the convex functions and some inequalities in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.

In vitro and clinical evaluation of optical coherence tomography for the detection of subgingival calculus and root cementum.

PubMed

Tsubokawa, Masaki; Aoki, Akira; Kakizaki, Sho; Taniguchi, Yoichi; Ejiri, Kenichiro; Mizutani, Koji; Koshy, Geena; Akizuki, Tatsuya; Oda, Shigeru; Sumi, Yasunori; Izumi, Yuichi

2018-05-24

This study evaluated the effectiveness of swept-source optical coherence tomography (ss-OCT) for detecting calculus and root cementum during periodontal therapy. Optical coherence tomography (OCT) images were taken before and after removal of subgingival calculus from extracted teeth and compared with non-decalcified histological sections. Porcine gingival sheets of various thicknesses were applied to the root surfaces of extracted teeth with calculus and OCT images were taken. OCT images were also taken before and after scaling and root planing (SRP) in human patients. In vitro, calculus was clearly detected as a white-gray amorphous structure on the root surface, which disappeared after removal. Cementum was identified as a thin, dark-gray layer. The calculus could not be clearly observed when soft tissues were present on the root surface. Clinically, supragingival calculus and cementum could be detected clearly with OCT, and subgingival calculus in the buccal cervical area of the anterior and premolar teeth was identified, which disappeared after SRP. Digital processing of the original OCT images was useful for clarifying the calculus. In conclusion, ss-OCT showed potential as a periodontal diagnostic tool for detecting cementum and subgingival calculus, although the practical applications of subgingival imaging remain limited.

Supragingival calculus in children with gastrostomy feeding: significant reduction with a caregiver-applied tartar-control dentifrice.

PubMed

Brown, Laurie M; Casamassimo, Paul S; Griffen, Ann; Tatakis, Dimitris

2006-01-01

This study assessed the anti-calculus benefit of Crest Dual Action Whitening Toothpaste in gastrostomy (GT) children compared to a control anti-caries dentifrice. A double-blind randomized crossover design was used to compare the two dentifrices. A convenience sample of 24 GT subjects, 3-12 years old, was given a consensus baseline Volpe-Manhold Index calculus score by 2 trained examiners, followed by a dental prophylaxis to remove all calculus. Each child was randomly assigned to either study or control dentifrice groups. Caregivers brushed subjects' teeth twice daily with the unlabelled dentifrice for at least 45 seconds. Calculus was scored at 8 weeks (+/- 1 week) by the same investigators. Subjects then had a prophylaxis and received the alternative dentifrice. Subjects returned 8 weeks (+/- 1 week) later for final calculus scoring. The study dentifrice significantly reduced supragingival calculus from baseline by 58% compared to control dentifrice (p<0.005 need exact p-value unless it is <.001; maybe it's reported in the paper). Calculus levels decreased by 68% over the study duration, irrespective of dentifrice. ANOVA found no significant differences in calculus scores based on gender, race, history of reflux, aspiration pneumonia, or oral intake of food. Calculus was significantly related to history of aspiration pneumonia (p<0.05 need exact p-value here). Crest Dual Action Whitening Toothpaste was effective and better than anti-caries control dentifrice in reducing calculus in GT children.

Stochastic oscillations in models of epidemics on a network of cities

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.; McKane, A. J.

2011-11-01

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction fjk of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

New picosecond laser emitting blue light for use in periodontology

NASA Astrophysics Data System (ADS)

Hennig, Thomas; Nieswand, Elmar; Rechmann, Peter

2001-04-01

Aim of the study was to investigate the impact of a new picosecond laser emitting blue light on tooth surfaces in order to remove calculus. The radiation may be comfortably transmitted via 25 micrometers diameter fiber optics. The resulting fluence at the tooth was found to be to low for ablation of calculus via nonlinear effects. Higher absorption of the 446 nm radiation by calculus compared to heathy tissues can provide preferential heating and evaporation of the calculus. The surface of thick calculus is irregular rough thus comprising a large interface to the surrounding cooling medium contra acting the preferential heating. In summary the study indicates the possibility flat layers of calculus by thermal effects. Carbonization in healthy tissues is the major problem concerning removal of subgingival calculus with thermal effects.

Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation

PubMed Central

Sturrock, Marc; Hellander, Andreas; Matzavinos, Anastasios; Chaplain, Mark A. J.

2013-01-01

Individual mouse embryonic stem cells have been found to exhibit highly variable differentiation responses under the same environmental conditions. The noisy cyclic expression of Hes1 and its downstream genes are known to be responsible for this, but the mechanism underlying this variability in expression is not well understood. In this paper, we show that the observed experimental data and diverse differentiation responses can be explained by a spatial stochastic model of the Hes1 gene regulatory network. We also propose experiments to control the precise differentiation response using drug treatment. PMID:23325756

Stochastic methods for analysis of power flow in electric networks

NASA Astrophysics Data System (ADS)

1982-09-01

The modeling and effects of probabilistic behavior on steady state power system operation were analyzed. A solution to the steady state network flow equations which adhere both to Kirchoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques was obtained. The development of sound techniques for producing meaningful data to serve as input is examined. Electric demand modeling, equipment failure analysis, and algorithm development are investigated. Two major development areas are described: a decomposition of stochastic processes which gives stationarity, ergodicity, and even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.

Variable-free exploration of stochastic models: a gene regulatory network example.

PubMed

Erban, Radek; Frewen, Thomas A; Wang, Xiao; Elston, Timothy C; Coifman, Ronald; Nadler, Boaz; Kevrekidis, Ioannis G

2007-04-21

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2014-01-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013

[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].

PubMed

Chong, Hong-Heng; An, Geng

2009-02-15

To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.

Dental Calculus Arrest of Dental Caries.

PubMed

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

PubMed Central

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

Variance decomposition in stochastic simulators

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

Le Maître, O. P., E-mail: olm@limsi.fr; Knio, O. M., E-mail: knio@duke.edu; Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance.more » Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.« less

Calculating second derivatives of population growth rates for ecology and evolution

PubMed Central

Shyu, Esther; Caswell, Hal

2014-01-01

1. Second derivatives of the population growth rate measure the curvature of its response to demographic, physiological or environmental parameters. The second derivatives quantify the response of sensitivity results to perturbations, provide a classification of types of selection and provide one way to calculate sensitivities of the stochastic growth rate. 2. Using matrix calculus, we derive the second derivatives of three population growth rate measures: the discrete-time growth rate λ, the continuous-time growth rate r = log λ and the net reproductive rate R0, which measures per-generation growth. 3. We present a suite of formulae for the second derivatives of each growth rate and show how to compute these derivatives with respect to projection matrix entries and to lower-level parameters affecting those matrix entries. 4. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb Calathea ovandensis. PMID:25793101

Time-Series Analysis of Intermittent Velocity Fluctuations in Turbulent Boundary Layers

NASA Astrophysics Data System (ADS)

Zayernouri, Mohsen; Samiee, Mehdi; Meerschaert, Mark M.; Klewicki, Joseph

2017-11-01

Classical turbulence theory is modified under the inhomogeneities produced by the presence of a wall. In this regard, we propose a new time series model for the streamwise velocity fluctuations in the inertial sub-layer of turbulent boundary layers. The new model employs tempered fractional calculus and seamlessly extends the classical 5/3 spectral model of Kolmogorov in the inertial subrange to the whole spectrum from large to small scales. Moreover, the proposed time-series model allows the quantification of data uncertainties in the underlying stochastic cascade of turbulent kinetic energy. The model is tested using well-resolved streamwise velocity measurements up to friction Reynolds numbers of about 20,000. The physics of the energy cascade are briefly described within the context of the determined model parameters. This work was supported by the AFOSR Young Investigator Program (YIP) award (FA9550-17-1-0150) and partially by MURI/ARO (W911NF-15-1-0562).

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Tempered fractional calculus

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

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

Random Evolutionary Dynamics Driven by Fitness and House-of-Cards Mutations: Sampling Formulae

NASA Astrophysics Data System (ADS)

Huillet, Thierry E.

2017-07-01

We first revisit the multi-allelic mutation-fitness balance problem, especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a Shahshahani potential. We then consider multi-allelic Wright-Fisher stochastic models whose deviation to neutrality is from the Shahshahani mutation/selection potential. We next focus on the weak selection, weak mutation cases and, making use of a Gamma calculus, we compute the normalizing partition functions of the invariant probability densities appearing in their Wright-Fisher diffusive approximations. Using these results, generalized Ewens sampling formulae (ESF) from the equilibrium distributions are derived. We start treating the ESF in the mixed mutation/selection potential case and then we restrict ourselves to the ESF in the simpler house-of-cards mutations only situation. We also address some issues concerning sampling problems from infinitely-many alleles weak limits.

Feedback control for unsteady flow and its application to the stochastic Burgers equation

NASA Technical Reports Server (NTRS)

Choi, Haecheon; Temam, Roger; Moin, Parviz; Kim, John

1993-01-01

The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.

A new method for identification of natural, artificial and in vitro cultured Calculus bovis using high-performance liquid chromatography-mass spectrometry

PubMed Central

Liu, Yonggang; Tan, Peng; Liu, Shanshan; Shi, Hang; Feng, Xin; Ma, Qun

2015-01-01

Objective: Calculus bovis have been widely used in Chinese herbology for the treatment of hyperpyrexia, convulsions, and epilepsy. Nowadays, due to the limited source and high market price, the substitutes, artificial and in vitro cultured Calculus bovis, are getting more and more commonly used. The adulteration phenomenon is serious. Therefore, it is crucial to establish a fast and simple method in discriminating the natural, artificial and in vitro cultured Calculus bovis. Bile acids, one of the main active constituents, are taken as an important indicator for evaluating the quality of Calculus bovis and the substitutes. Several techniques have been built to analyze bile acids in Calculus bovis. Whereas, as bile acids are with poor ultraviolet absorbance and high structural similarity, effective technology for identification and quality control is still lacking. Methods: In this study, high-performance liquid chromatography (HPLC) coupled with tandem mass spectrometry (LC/MS/MS) was applied in the analysis of bile acids, which effectively identified natural, artificial and in vitro cultured Calculus bovis and provide a new method for their quality control. Results: Natural, artificial and in vitro cultured Calculus bovis were differentiated by bile acids analysis. A new compound with protonated molecule at m/z 405 was found, which we called 3α, 12α-dihydroxy-7-oxo-5α-cholanic acid. This compound was discovered in in vitro cultured Calculus bovis, but almost not detected in natural and artificial Calculus bovis. A total of 13 constituents was identified. Among them, three bio-markers, including glycocholic acid, glycodeoxycholic acid and taurocholic acid (TCA) were detected in both natural and artificial Calculus bovis, but the density of TCA was different in two kinds of Calculus bovis. In addition, the characteristics of bile acids were illustrated. Conclusions: The HPLC coupled with tandem MS (LC/MS/MS) method was feasible, easy, rapid and accurate in identifying natural, artificial and in vitro cultured Calculus bovis. PMID:25829769

Maxima and Minima Without Calculus.

ERIC Educational Resources Information Center

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Pulsed laser ablation of dental calculus in the near ultraviolet.

PubMed

Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter

2014-02-01

Pulsed lasers emitting wavelengths near 400 nm can selectively ablate dental calculus without damaging underlying and surrounding sound dental hard tissue. Our results indicate that calculus ablation at this wavelength relies on the absorption of porphyrins endogenous to oral bacteria commonly found in calculus. Sub- and supragingival calculus on extracted human teeth, irradiated with 400-nm, 60-ns laser pulses at ≤8  J/cm2, exhibits a photobleached surface layer. Blue-light microscopy indicates this layer highly scatters 400-nm photons, whereas fluorescence spectroscopy indicates that bacterial porphyrins are permanently photobleached. A modified blow-off model for ablation is proposed that is based upon these observations and also reproduces our calculus ablation rates measured from laser profilometry. Tissue scattering and a stratified layering of absorbers within the calculus medium explain the gradual decrease in ablation rate from successive pulses. Depending on the calculus thickness, ablation stalling may occur at <5  J/cm2 but has not been observed above this fluence.

A generalized nonlocal vector calculus

NASA Astrophysics Data System (ADS)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Stochastic simulation of karst conduit networks

NASA Astrophysics Data System (ADS)

Pardo-Igúzquiza, Eulogio; Dowd, Peter A.; Xu, Chaoshui; Durán-Valsero, Juan José

2012-01-01

Karst aquifers have very high spatial heterogeneity. Essentially, they comprise a system of pipes (i.e., the network of conduits) superimposed on rock porosity and on a network of stratigraphic surfaces and fractures. This heterogeneity strongly influences the hydraulic behavior of the karst and it must be reproduced in any realistic numerical model of the karst system that is used as input to flow and transport modeling. However, the directly observed karst conduits are only a small part of the complete karst conduit system and knowledge of the complete conduit geometry and topology remains spatially limited and uncertain. Thus, there is a special interest in the stochastic simulation of networks of conduits that can be combined with fracture and rock porosity models to provide a realistic numerical model of the karst system. Furthermore, the simulated model may be of interest per se and other uses could be envisaged. The purpose of this paper is to present an efficient method for conditional and non-conditional stochastic simulation of karst conduit networks. The method comprises two stages: generation of conduit geometry and generation of topology. The approach adopted is a combination of a resampling method for generating conduit geometries from templates and a modified diffusion-limited aggregation method for generating the network topology. The authors show that the 3D karst conduit networks generated by the proposed method are statistically similar to observed karst conduit networks or to a hypothesized network model. The statistical similarity is in the sense of reproducing the tortuosity index of conduits, the fractal dimension of the network, the direction rose of directions, the Z-histogram and Ripley's K-function of the bifurcation points (which differs from a random allocation of those bifurcation points). The proposed method (1) is very flexible, (2) incorporates any experimental data (conditioning information) and (3) can easily be modified when implemented in a hydraulic inverse modeling procedure. Several synthetic examples are given to illustrate the methodology and real conduit network data are used to generate simulated networks that mimic real geometries and topology.

The effects of noise on binocular rivalry waves: a stochastic neural field model

NASA Astrophysics Data System (ADS)

Webber, Matthew A.; Bressloff, Paul C.

2013-03-01

We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave.

Detection, removal and prevention of calculus: Literature Review

PubMed Central

Kamath, Deepa G.; Umesh Nayak, Sangeeta

2013-01-01

Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus. PMID:24526823

Developing the Fundamental Theorem of Calculus. Applications of Calculus to Work, Area, and Distance Problems. [and] Atmospheric Pressure in Relation to Height and Temperature. Applications of Calculus to Atmospheric Pressure. [and] The Gradient and Some of Its Applications. Applications of Multivariate Calculus to Physics. [and] Kepler's Laws and the Inverse Square Law. Applications of Calculus to Physics. UMAP Units 323, 426, 431, 473.

ERIC Educational Resources Information Center

Lindstrom, Peter A.; And Others

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

The clinical anticalculus efficacy of a tartar control whitening dentifrice for the prevention of supragingival calculus in a three-month study.

PubMed

Sowinski, J; Petrone, D M; Battista, G; Petrone, M E; Crawford, R; Patel, S; DeVizio, W; Chaknis, P; Volpe, A R; Proskin, H M

1999-01-01

The objective of this double-blind clinical study was to compare the effect of a new dentifrice (Colgate Tartar Control Plus Whitening Fluoride Toothpaste) for the prevention of supragingival calculus, with that of a commercially available calculus-inhibiting dentifrice (Crest Tartar Control Toothpaste). The study involved adult male and female subjects who had pre-qualified for participation by developing sufficient supragingival calculus (greater than 7.0 on the Volpe-Manhold Calculus Index) during an eight-week screening period. Subjects received a full oral prophylaxis, and were stratified into two treatment groups balanced for age, sex and qualifying calculus score. Subjects were instructed to brush their teeth twice daily (morning and evening) for one minute with their assigned dentifrice using a soft-bristled toothbrush. Examinations for dental calculus were performed after twelve weeks' use of the study dentifrices, using the Volpe-Manhold Calculus Index, Fifty-eight (58) subjects complied with the protocol and completed the entire study. The Colgate Tartar Control Plus Whitening group exhibited a statistically significant (p < 0.001) 34.6% reduction in mean calculus score compared to the Crest Tartar Control group.

Stochastic switching in biology: from genotype to phenotype

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-03-01

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

Regenerating time series from ordinal networks.

PubMed

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

Regenerating time series from ordinal networks

NASA Astrophysics Data System (ADS)

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

A stochastic model of input effectiveness during irregular gamma rhythms.

PubMed

Dumont, Grégory; Northoff, Georg; Longtin, André

2016-02-01

Gamma-band synchronization has been linked to attention and communication between brain regions, yet the underlying dynamical mechanisms are still unclear. How does the timing and amplitude of inputs to cells that generate an endogenously noisy gamma rhythm affect the network activity and rhythm? How does such "communication through coherence" (CTC) survive in the face of rhythm and input variability? We present a stochastic modelling approach to this question that yields a very fast computation of the effectiveness of inputs to cells involved in gamma rhythms. Our work is partly motivated by recent optogenetic experiments (Cardin et al. Nature, 459(7247), 663-667 2009) that tested the gamma phase-dependence of network responses by first stabilizing the rhythm with periodic light pulses to the interneurons (I). Our computationally efficient model E-I network of stochastic two-state neurons exhibits finite-size fluctuations. Using the Hilbert transform and Kuramoto index, we study how the stochastic phase of its gamma rhythm is entrained by external pulses. We then compute how this rhythmic inhibition controls the effectiveness of external input onto pyramidal (E) cells, and how variability shapes the window of firing opportunity. For transferring the time variations of an external input to the E cells, we find a tradeoff between the phase selectivity and depth of rate modulation. We also show that the CTC is sensitive to the jitter in the arrival times of spikes to the E cells, and to the degree of I-cell entrainment. We further find that CTC can occur even if the underlying deterministic system does not oscillate; quasicycle-type rhythms induced by the finite-size noise retain the basic CTC properties. Finally a resonance analysis confirms the relative importance of the I cell pacing for rhythm generation. Analysis of whole network behaviour, including computations of synchrony, phase and shifts in excitatory-inhibitory balance, can be further sped up by orders of magnitude using two coupled stochastic differential equations, one for each population. Our work thus yields a fast tool to numerically and analytically investigate CTC in a noisy context. It shows that CTC can be quite vulnerable to rhythm and input variability, which both decrease phase preference.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Effect of non-functional teeth on accumulation of supra-gingival calculus in children.

PubMed

Ashkenazi, M; Miller, R; Levin, L

2012-10-01

To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.

Matrix-Gla Protein rs4236 [A/G] gene polymorphism and serum and GCF levels of MGP in patients with subgingival dental calculus.

PubMed

Doğan, Gülnihal Emrem; Demir, Turgut; Aksoy, Hülya; Sağlam, Ebru; Laloğlu, Esra; Yildirim, Abdulkadir

2016-10-01

Matrix-Gla Protein (MGP) is one of the major Gla-containing protein associated with calcification process. It also has a high affinity for Ca 2+ and hydroxyapatite. In this study we aimed to evaluate the MGP rs4236 [A/G] gene polymorphism in association with subgingival dental calculus. Also a possible relationship between MGP gene polymorphism and serum and GCF levels of MGP were examined. MGP rs4236 [A/G] gene polymorphism was investigated in 110 patients with or without subgingival dental calculus, using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) techniques. Additionally, serum and GCF levels of MGP of the patients were compared according to subgingival dental calculus. Comparison of patients with and without subgingival dental calculus showed no statistically significant difference in MGP rs4236 [A/G] gene polymorphism (p=0.368). MGP concentrations in GCF of patients with subgingival dental calculus were statistically higher than those without subgingival dental calculus (p=0.032). However, a significant association was not observed between the genotypes of AA, AG and GG of the MGP rs4236 gene and the serum and GCF concentrations of MGP in subjects. In this study, it was found that MGP rs4236 [A/G] gene polymorphism was not to be associated with subgingival dental calculus. Also, that GCF MGP levels were detected higher in patients with subgingival dental calculus than those without subgingival dental calculus independently of polymorphism, may be the effect of adaptive mechanism to inhibit calculus formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Impact Analysis of Flow Shaping in Ethernet-AVB/TSN and AFDX from Network Calculus and Simulation Perspective

PubMed Central

He, Feng; Zhao, Lin; Li, Ershuai

2017-01-01

Ethernet-AVB/TSN (Audio Video Bridging/Time-Sensitive Networking) and AFDX (Avionics Full DupleX switched Ethernet) are switched Ethernet technologies, which are both candidates for real-time communication in the context of transportation systems. AFDX implements a fixed priority scheduling strategy with two priority levels. Ethernet-AVB/TSN supports a similar fixed priority scheduling with an additional Credit-Based Shaper (CBS) mechanism. Besides, TSN can support time-triggered scheduling strategy. One direct effect of CBS mechanism is to increase the delay of its flows while decreasing the delay of other priority ones. The former effect can be seen as the shaping restriction and the latter effect can be seen as the shaping benefit from CBS. The goal of this paper is to investigate the impact of CBS on different priority flows, especially on the intermediate priority ones, as well as the effect of CBS bandwidth allocation. It is based on a performance comparison of AVB/TSN and AFDX by simulation in an automotive case study. Furthermore, the shaping benefit is modeled based on integral operation from network calculus perspective. Combing with the analysis of shaping restriction and shaping benefit, some configuration suggestions on the setting of CBS bandwidth are given. Results show that the effect of CBS depends on flow loads and CBS configurations. A larger load of high priority flows in AVB tends to a better performance for the intermediate priority flows when compared with AFDX. Shaping benefit can be explained and calculated according to the changing from the permitted maximum burst. PMID:28531158

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

PubMed

Chen, Bor-Sen; Hsu, Chih-Yuan

2012-10-26

Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

PubMed Central

2012-01-01

Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. Conclusion If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks. PMID:23101662

Representing Micro-Macro Linkages by Actor-Based Dynamic Network Models

ERIC Educational Resources Information Center

Snijders, Tom A. B.; Steglich, Christian E. G.

2015-01-01

Stochastic actor-based models for network dynamics have the primary aim of statistical inference about processes of network change, but may be regarded as a kind of agent-based models. Similar to many other agent-based models, they are based on local rules for actor behavior. Different from many other agent-based models, by including elements of…

An AP Calculus Classroom Amusement Park

ERIC Educational Resources Information Center

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

A Historical Perspective on Teaching and Learning Calculus

ERIC Educational Resources Information Center

Doorman, Michiel; van Maanen, Jan

2008-01-01

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

Cash transportation vehicle routing and scheduling under stochastic travel times

NASA Astrophysics Data System (ADS)

Yan, Shangyao; Wang, Sin-Siang; Chang, Yu-Hsuan

2014-03-01

Stochastic disturbances occurring in real-world operations could have a significant influence on the planned routing and scheduling results of cash transportation vehicles. In this study, a time-space network flow technique is utilized to construct a cash transportation vehicle routing and scheduling model incorporating stochastic travel times. In addition, to help security carriers to formulate more flexible routes and schedules, a concept of the similarity of time and space for vehicle routing and scheduling is incorporated into the model. The test results show that the model could be useful for security carriers in actual practice.

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

NASA Technical Reports Server (NTRS)

Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.

1996-01-01

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

Stochastic availability analysis of operational data systems in the Deep Space Network

NASA Technical Reports Server (NTRS)

Issa, T. N.

1991-01-01

Existing availability models of standby redundant systems consider only an operator's performance and its interaction with the hardware performance. In the case of operational data systems in the Deep Space Network (DSN), in addition to an operator system interface, a controller reconfigures the system and links a standby unit into the network data path upon failure of the operating unit. A stochastic (Markovian) process technique is used to model and analyze the availability performance and occurrence of degradation due to partial failures are quantitatively incorporated into the model. Exact expressions of the steady state availability and proportion degraded performance measures are derived for the systems under study. The interaction among the hardware, operator, and controller performance parameters and that interaction's effect on data availability are evaluated and illustrated for an operational data processing system.

The behaviour of basic autocatalytic signalling modules in isolation and embedded in networks

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

Krishnan, J.; Mois, Kristina; Suwanmajo, Thapanar

2014-11-07

In this paper, we examine the behaviour of basic autocatalytic feedback modules involving a species catalyzing its own production, either directly or indirectly. We first perform a systematic study of the autocatalytic feedback module in isolation, examining the effect of different factors, showing how this module is capable of exhibiting monostable threshold and bistable switch-like behaviour. We then study the behaviour of this module embedded in different kinds of basic networks including (essentially) irreversible cycles, open and closed reversible chains, and networks with additional feedback. We study the behaviour of the networks deterministically and also stochastically, using simulations, analytical work,more » and bifurcation analysis. We find that (i) there are significant differences between the behaviour of this module in isolation and in a network: thresholds may be altered or destroyed and bistability may be destroyed or even induced, even when the ambient network is simple. The global characteristics and topology of this network and the position of the module in the ambient network can play important and unexpected roles. (ii) There can be important differences between the deterministic and stochastic dynamics of the module embedded in networks, which may be accentuated by the ambient network. This provides new insights into the functioning of such enzymatic modules individually and as part of networks, with relevance to other enzymatic signalling modules as well.« less

The behaviour of basic autocatalytic signalling modules in isolation and embedded in networks

NASA Astrophysics Data System (ADS)

Krishnan, J.; Mois, Kristina; Suwanmajo, Thapanar

2014-11-01

In this paper, we examine the behaviour of basic autocatalytic feedback modules involving a species catalyzing its own production, either directly or indirectly. We first perform a systematic study of the autocatalytic feedback module in isolation, examining the effect of different factors, showing how this module is capable of exhibiting monostable threshold and bistable switch-like behaviour. We then study the behaviour of this module embedded in different kinds of basic networks including (essentially) irreversible cycles, open and closed reversible chains, and networks with additional feedback. We study the behaviour of the networks deterministically and also stochastically, using simulations, analytical work, and bifurcation analysis. We find that (i) there are significant differences between the behaviour of this module in isolation and in a network: thresholds may be altered or destroyed and bistability may be destroyed or even induced, even when the ambient network is simple. The global characteristics and topology of this network and the position of the module in the ambient network can play important and unexpected roles. (ii) There can be important differences between the deterministic and stochastic dynamics of the module embedded in networks, which may be accentuated by the ambient network. This provides new insights into the functioning of such enzymatic modules individually and as part of networks, with relevance to other enzymatic signalling modules as well.

Asymptotic identity in min-plus algebra: a report on CPNS.

PubMed

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

PubMed Central

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

Subgingival calculus imaging based on swept-source optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

Dental calculus image based on optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

A probabilistic approach to quantifying spatial patterns of flow regimes and network-scale connectivity

NASA Astrophysics Data System (ADS)

Garbin, Silvia; Alessi Celegon, Elisa; Fanton, Pietro; Botter, Gianluca

2017-04-01

The temporal variability of river flow regime is a key feature structuring and controlling fluvial ecological communities and ecosystem processes. In particular, streamflow variability induced by climate/landscape heterogeneities or other anthropogenic factors significantly affects the connectivity between streams with notable implication for river fragmentation. Hydrologic connectivity is a fundamental property that guarantees species persistence and ecosystem integrity in riverine systems. In riverine landscapes, most ecological transitions are flow-dependent and the structure of flow regimes may affect ecological functions of endemic biota (i.e., fish spawning or grazing of invertebrate species). Therefore, minimum flow thresholds must be guaranteed to support specific ecosystem services, like fish migration, aquatic biodiversity and habitat suitability. In this contribution, we present a probabilistic approach aiming at a spatially-explicit, quantitative assessment of hydrologic connectivity at the network-scale as derived from river flow variability. Dynamics of daily streamflows are estimated based on catchment-scale climatic and morphological features, integrating a stochastic, physically based approach that accounts for the stochasticity of rainfall with a water balance model and a geomorphic recession flow model. The non-exceedance probability of ecologically meaningful flow thresholds is used to evaluate the fragmentation of individual stream reaches, and the ensuing network-scale connectivity metrics. A multi-dimensional Poisson Process for the stochastic generation of rainfall is used to evaluate the impact of climate signature on reach-scale and catchment-scale connectivity. The analysis shows that streamflow patterns and network-scale connectivity are influenced by the topology of the river network and the spatial variability of climatic properties (rainfall, evapotranspiration). The framework offers a robust basis for the prediction of the impact of land-use/land-cover changes and river regulation on network-scale connectivity.

Seasonal change of topology and resilience of ecological networks in wetlandscapes

NASA Astrophysics Data System (ADS)

Bin, Kim; Park, Jeryang

2017-04-01

Wetlands distributed in a landscape provide various ecosystem services including habitat for flora and fauna, hydrologic controls, and biogeochemical processes. Hydrologic regime of each wetland at a given landscape varies by hydro-climatic and geological conditions as well as the bathymetry, forming a certain pattern in the wetland area distribution and spatial organization. However, its large-scale pattern also changes over time as this wetland complex is subject to stochastic hydro-climatic forcing in various temporal scales. Consequently, temporal variation in the spatial structure of wetlands inevitably affects the dispersal ability of species depending on those wetlands as habitat. Here, we numerically show (1) the spatiotemporal variation of wetlandscapes by forcing seasonally changing stochastic rainfall and (2) the corresponding ecological networks which either deterministically or stochastically forming the dispersal ranges. We selected four vernal pool regions with distinct climate conditions in California. The results indicate that the spatial structure of wetlands in a landscape by measuring the wetland area frequency distribution changes by seasonal hydro-climatic condition but eventually recovers to the initial state. However, the corresponding ecological networks, which the structure and function change by the change of distances between wetlands, and measured by degree distribution and network efficiency, may not recover to the initial state especially in the regions with high seasonal dryness index. Moreover, we observed that the changes in both the spatial structure of wetlands in a landscape and the corresponding ecological networks exhibit hysteresis over seasons. Our analysis indicates that the hydrologic and ecological resilience of a wetlandcape may be low in a dry region with seasonal hydro-climatic forcing. Implications of these results for modelling ecological networks depending on hydrologic systems especially for conservation purposes are discussed.

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.; Koga, Dennis (Technical Monitor)

2003-01-01

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Stochastic resonance in feedforward acupuncture networks

NASA Astrophysics Data System (ADS)

Qin, Ying-Mei; Wang, Jiang; Men, Cong; Deng, Bin; Wei, Xi-Le; Yu, Hai-Tao; Chan, Wai-Lok

2014-10-01

Effects of noises and some other network properties on the weak signal propagation are studied systematically in feedforward acupuncture networks (FFN) based on FitzHugh-Nagumo neuron model. It is found that noises with medium intensity can enhance signal propagation and this effect can be further increased by the feedforward network structure. Resonant properties in the noisy network can also be altered by several network parameters, such as heterogeneity, synapse features, and feedback connections. These results may also provide a novel potential explanation for the propagation of acupuncture signal.

Dental calculus reveals Mesolithic foragers in the Balkans consumed domesticated plant foods.

PubMed

Cristiani, Emanuela; Radini, Anita; Edinborough, Marija; Borić, Dušan

2016-09-13

Researchers agree that domesticated plants were introduced into southeast Europe from southwest Asia as a part of a Neolithic "package," which included domesticated animals and artifacts typical of farming communities. It is commonly believed that this package reached inland areas of the Balkans by ∼6200 calibrated (cal.) BC or later. Our analysis of the starch record entrapped in dental calculus of Mesolithic human teeth at the site of Vlasac in the Danube Gorges of the central Balkans provides direct evidence that already by ∼6600 cal. BC, if not earlier, Late Mesolithic foragers of this region consumed domestic cereals, such as Triticum monococcum, Triticum dicoccum, and Hordeum distichon, which were also the main crops found among Early Neolithic communities of southeast Europe. We infer that "exotic" Neolithic domesticated plants were introduced to southern Europe independently almost half a millennium earlier than previously thought, through networks that enabled exchanges between inland Mesolithic foragers and early farming groups found along the Aegean coast of Turkey.

Dental calculus reveals Mesolithic foragers in the Balkans consumed domesticated plant foods

PubMed Central

Cristiani, Emanuela; Radini, Anita; Edinborough, Marija; Borić, Dušan

2016-01-01

Researchers agree that domesticated plants were introduced into southeast Europe from southwest Asia as a part of a Neolithic “package,” which included domesticated animals and artifacts typical of farming communities. It is commonly believed that this package reached inland areas of the Balkans by ∼6200 calibrated (cal.) BC or later. Our analysis of the starch record entrapped in dental calculus of Mesolithic human teeth at the site of Vlasac in the Danube Gorges of the central Balkans provides direct evidence that already by ∼6600 cal. BC, if not earlier, Late Mesolithic foragers of this region consumed domestic cereals, such as Triticum monococcum, Triticum dicoccum, and Hordeum distichon, which were also the main crops found among Early Neolithic communities of southeast Europe. We infer that “exotic” Neolithic domesticated plants were introduced to southern Europe independently almost half a millennium earlier than previously thought, through networks that enabled exchanges between inland Mesolithic foragers and early farming groups found along the Aegean coast of Turkey. PMID:27573829

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.

PubMed

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F

2017-01-01

Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.

Discrete gravity on random tensor network and holographic Rényi entropy

NASA Astrophysics Data System (ADS)

Han, Muxin; Huang, Shilin

2017-11-01

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study.

PubMed

Heron, Elizabeth A; Finkenstädt, Bärbel; Rand, David A

2007-10-01

In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.

Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control

NASA Astrophysics Data System (ADS)

Wang, Pengfei; Jin, Wei; Su, Huan

2018-04-01

This paper deals with the synchronization problem of a class of coupled stochastic complex-valued drive-response networks with time-varying delays via aperiodically intermittent adaptive control. Different from the previous works, the intermittent control is aperiodic and adaptive, and the restrictions on the control width and time delay are removed, which lead to a larger application scope for this control strategy. Then, based on the Lyapunov method and Kirchhoff's Matrix Tree Theorem as well as differential inequality techniques, several novel synchronization conditions are derived for the considered model. Specially, impulsive control is also considered, which can be seen as a special case of the aperiodically intermittent control when the control width tends to zero. And the corresponding synchronization criteria are given as well. As an application of the theoretical results, a class of stochastic complex-valued coupled oscillators with time-varying delays is studied, and the numerical simulations are also given to demonstrate the effectiveness of the control strategies.

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

ERIC Educational Resources Information Center

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

The Path to College Calculus: The Impact of High School Mathematics Coursework

ERIC Educational Resources Information Center

Sadler, Philip; Sonnert, Gerhard

2018-01-01

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

The Development and Nature of Problem-Solving among First-Semester Calculus Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

ERIC Educational Resources Information Center

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

The History of the Calculus

ERIC Educational Resources Information Center

Harding, Simon; Scott, Paul

2004-01-01

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

ERIC Educational Resources Information Center

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Calculus ABCs: A Gateway for Freshman Calculus

ERIC Educational Resources Information Center

Fulton, Scott R.

2003-01-01

This paper describes a gateway testing program designed to ensure that students acquire basic skills in freshman calculus. Students must demonstrate they have mastered standards for "Absolutely Basic Competency"--the Calculus ABCs--in order to pass the course with a grade of C or better. We describe the background, standards, and testing program.…

Unusual Case of Calculus in Floor of Mouth: A Case Report

PubMed Central

Thosar, Nilima; Jain, Eesha S

2012-01-01

Abstract Calculus consists of mineralized bacterial plaque that forms on the surfaces of natural teeth. It is supragingival or subgingival depending upon its relation with gingival margin. The two most common locations for supragingival calculus are the buccal surfaces of maxillary molars and lingual surfaces of mandibular anterior teeth. It is very important to rule out the predisposing factor for calculus formation. In the present case of an 11-year- old female child, 1.2 × 1.5 cm large indurated mass suggestive of calculus in the left side of floor of mouth was observed. After surgical removal, along with indurated mass, an embedded root fragment was seen. Biochemical analysis of the specimen detected the calcium and phosphate ions approximately equals to the level in calculus. Thus, we diagnosed it as a calculus. Oral hygiene instructions and regular follow-up was advised. How to cite this article: Bahadure RN, Thosar N, Jain ES. Unusual Case of Calculus in Floor of Mouth: A Case Report. Int J Clin Pediatr Dent 2012;5(3):223-225. PMID:25206174

Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.

PubMed

Baris, O; Demir, T; Gulluce, M

2017-12-01

Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.

Dental calculus formation in children and adolescents undergoing hemodialysis.

PubMed

Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães

2012-10-01

This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p < 0.01). Correlation was observed between rate of dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p < 0.05). The presence of dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p < 0.05). In conclusion, patients undergoing hemodialysis presented accelerated dental calculus formation, probably due to salivary variables.

The Case for Biocalculus: Design, Retention, and Student Performance

PubMed Central

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. PMID:28450445

Improving student learning in calculus through applications

NASA Astrophysics Data System (ADS)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Stochastic Control of Multi-Scale Networks: Modeling, Analysis and Algorithms

DTIC Science & Technology

2014-10-20

Theory, (02 2012): 0. doi: B. T. Swapna, Atilla Eryilmaz, Ness B. Shroff. Throughput-Delay Analysis of Random Linear Network Coding for Wireless ... Wireless Sensor Networks and Effects of Long-Range Dependent Data, Sequential Analysis , (10 2012): 0. doi: 10.1080/07474946.2012.719435 Stefano...Sequential Analysis , (10 2012): 0. doi: John S. Baras, Shanshan Zheng. Sequential Anomaly Detection in Wireless Sensor Networks andEffects of Long

Value of Information for Optimal Adaptive Routing in Stochastic Time-Dependent Traffic Networks: Algorithms and Computational Tools

DOT National Transportation Integrated Search

2010-10-25

Real-time information is important for travelers' routing decisions in uncertain networks by enabling online adaptation to revealed traffic conditions. Usually there are spatial and/or temporal limitations in traveler information. In this research, a...

Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks.

PubMed

Thanh, Vo Hong; Zunino, Roberto; Priami, Corrado

2017-01-01

Exact stochastic simulation is an indispensable tool for a quantitative study of biochemical reaction networks. The simulation realizes the time evolution of the model by randomly choosing a reaction to fire and update the system state according to a probability that is proportional to the reaction propensity. Two computationally expensive tasks in simulating large biochemical networks are the selection of next reaction firings and the update of reaction propensities due to state changes. We present in this work a new exact algorithm to optimize both of these simulation bottlenecks. Our algorithm employs the composition-rejection on the propensity bounds of reactions to select the next reaction firing. The selection of next reaction firings is independent of the number reactions while the update of propensities is skipped and performed only when necessary. It therefore provides a favorable scaling for the computational complexity in simulating large reaction networks. We benchmark our new algorithm with the state of the art algorithms available in literature to demonstrate its applicability and efficiency.

Stochastic dynamics of genetic broadcasting networks

NASA Astrophysics Data System (ADS)

Potoyan, Davit A.; Wolynes, Peter G.

2017-11-01

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

Dual adaptive dynamic control of mobile robots using neural networks.

PubMed

Bugeja, Marvin K; Fabri, Simon G; Camilleri, Liberato

2009-02-01

This paper proposes two novel dual adaptive neural control schemes for the dynamic control of nonholonomic mobile robots. The two schemes are developed in discrete time, and the robot's nonlinear dynamic functions are assumed to be unknown. Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are used for function approximation. In each scheme, the unknown network parameters are estimated stochastically in real time, and no preliminary offline neural network training is used. In contrast to other adaptive techniques hitherto proposed in the literature on mobile robots, the dual control laws presented in this paper do not rely on the heuristic certainty equivalence property but account for the uncertainty in the estimates. This results in a major improvement in tracking performance, despite the plant uncertainty and unmodeled dynamics. Monte Carlo simulation and statistical hypothesis testing are used to illustrate the effectiveness of the two proposed stochastic controllers as applied to the trajectory-tracking problem of a differentially driven wheeled mobile robot.

Optimal route discovery for soft QOS provisioning in mobile ad hoc multimedia networks

NASA Astrophysics Data System (ADS)

Huang, Lei; Pan, Feng

2007-09-01

In this paper, we propose an optimal routing discovery algorithm for ad hoc multimedia networks whose resource keeps changing, First, we use stochastic models to measure the network resource availability, based on the information about the location and moving pattern of the nodes, as well as the link conditions between neighboring nodes. Then, for a certain multimedia packet flow to be transmitted from a source to a destination, we formulate the optimal soft-QoS provisioning problem as to find the best route that maximize the probability of satisfying its desired QoS requirements in terms of the maximum delay constraints. Based on the stochastic network resource model, we developed three approaches to solve the formulated problem: A centralized approach serving as the theoretical reference, a distributed approach that is more suitable to practical real-time deployment, and a distributed dynamic approach that utilizes the updated time information to optimize the routing for each individual packet. Examples of numerical results demonstrated that using the route discovered by our distributed algorithm in a changing network environment, multimedia applications could achieve better QoS statistically.

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

NASA Astrophysics Data System (ADS)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

The development and nature of problem-solving among first-semester calculus students

NASA Astrophysics Data System (ADS)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

In vitro performance of DIAGNOdent laser fluorescence device for dental calculus detection on human tooth root surfaces.

PubMed

Rams, Thomas E; Alwaqyan, Abdulaziz Y

2017-10-01

This study assessed the reproducibility of a red diode laser device, and its capability to detect dental calculus in vitro on human tooth root surfaces. On each of 50 extracted teeth, a calculus-positive and calculus-free root surface was evaluated by two independent examiners with a low-power indium gallium arsenide phosphide diode laser (DIAGNOdent) fitted with a periodontal probe-like sapphire tip and emitting visible red light at 655 nm wavelength. Laser autofluorescence intensity readings of examined root surfaces were scored on a 0-99 scale, with duplicate assessments performed using the laser probe tip directed both perpendicular and parallel to evaluated tooth root surfaces. Pearson correlation coefficients of untransformed measurements, and kappa analysis of data dichotomized with a >40 autofluorescence intensity threshold, were calculated to assess intra- and inter-examiner reproducibility of the laser device. Mean autofluorescence intensity scores of calculus-positive and calculus-free root surfaces were evaluated with the Student's t -test. Excellent intra- and inter-examiner reproducibility was found for DIAGNOdent laser autofluorescence intensity measurements, with Pearson correlation coefficients above 94%, and kappa values ranging between 0.96 and 1.0, for duplicate readings taken with both laser probe tip orientations. Significantly higher autofluorescence intensity values were measured when the laser probe tip was directed perpendicular, rather than parallel, to tooth root surfaces. However, calculus-positive roots, particularly with calculus in markedly-raised ledges, yielded significantly greater mean DIAGNOdent laser autofluorescence intensity scores than calculus-free surfaces, regardless of probe tip orientation. DIAGNOdent autofluorescence intensity values >40 exhibited a stronger association with calculus (36.6 odds ratio) then measurements of ≥5 (20.1 odds ratio) when the laser probe tip was advanced parallel to root surfaces. Excellent intra- and inter-examiner reproducibility of autofluorescence intensity measurements was obtained with the DIAGNOdent laser fluorescence device on human tooth roots. Calculus-positive root surfaces exhibited significantly greater DIAGNOdent laser autofluorescence than calculus-free tooth roots, even with the laser probe tip directed parallel to root surfaces. These findings provide further in vitro validation of the potential utility of a DIAGNOdent laser fluorescence device for identifying dental calculus on human tooth root surfaces.

Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.

PubMed

Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y

2018-06-01

Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental calculus was significantly inhibited by cytochalasin D, z-YVAD-fmk and glyburide, indicating NLRP3 inflammasome involvement. In permeability assays, dental calculus attenuated the barrier function of HSC-2 cell monolayers. Dental calculus induces pyroptotic cell death in human oral epithelial cells and the crystalline structure plays a major role in this process. Oral epithelial cell death induced by dental calculus might be important for the etiology of periodontitis. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

Fast and Precise Emulation of Stochastic Biochemical Reaction Networks With Amplified Thermal Noise in Silicon Chips.

PubMed

Kim, Jaewook; Woo, Sung Sik; Sarpeshkar, Rahul

2018-04-01

The analysis and simulation of complex interacting biochemical reaction pathways in cells is important in all of systems biology and medicine. Yet, the dynamics of even a modest number of noisy or stochastic coupled biochemical reactions is extremely time consuming to simulate. In large part, this is because of the expensive cost of random number and Poisson process generation and the presence of stiff, coupled, nonlinear differential equations. Here, we demonstrate that we can amplify inherent thermal noise in chips to emulate randomness physically, thus alleviating these costs significantly. Concurrently, molecular flux in thermodynamic biochemical reactions maps to thermodynamic electronic current in a transistor such that stiff nonlinear biochemical differential equations are emulated exactly in compact, digitally programmable, highly parallel analog "cytomorphic" transistor circuits. For even small-scale systems involving just 80 stochastic reactions, our 0.35-μm BiCMOS chips yield a 311× speedup in the simulation time of Gillespie's stochastic algorithm over COPASI, a fast biochemical-reaction software simulator that is widely used in computational biology; they yield a 15 500× speedup over equivalent MATLAB stochastic simulations. The chip emulation results are consistent with these software simulations over a large range of signal-to-noise ratios. Most importantly, our physical emulation of Poisson chemical dynamics does not involve any inherently sequential processes and updates such that, unlike prior exact simulation approaches, they are parallelizable, asynchronous, and enable even more speedup for larger-size networks.

Input reconstruction for networked control systems subject to deception attacks and data losses on control signals

NASA Astrophysics Data System (ADS)

Keller, J. Y.; Chabir, K.; Sauter, D.

2016-03-01

State estimation of stochastic discrete-time linear systems subject to unknown inputs or constant biases has been widely studied but no work has been dedicated to the case where a disturbance switches between unknown input and constant bias. We show that such disturbance can affect a networked control system subject to deception attacks and data losses on the control signals transmitted by the controller to the plant. This paper proposes to estimate the switching disturbance from an augmented state version of the intermittent unknown input Kalman filter recently developed by the authors. Sufficient stochastic stability conditions are established when the arrival binary sequence of data losses follows a Bernoulli random process.

Bounded-Degree Approximations of Stochastic Networks

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

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less

A Transition Course from Advanced Placement to College Calculus

ERIC Educational Resources Information Center

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Improving Calculus II and III through the Redistribution of Topics

ERIC Educational Resources Information Center

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

ERIC Educational Resources Information Center

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Computer Managed Instruction Homework Modules for Calculus I.

ERIC Educational Resources Information Center

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

Subgingival calculus imaging based on swept-source optical coherence tomography.

PubMed

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 ± 0.024, 1.534 ± 0.029, 1.570 ± 0.021, and 2.097 ± 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

A new proof of the generalized Hamiltonian–Real calculus

PubMed Central

Gao, Hua; Mandic, Danilo P.

2016-01-01

The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing. In this paper, we introduce novel dual relationships between the GHR calculus and multivariate real calculus, in order to provide a new, simpler proof of the GHR derivative rules. This further reinforces the theoretical foundation of the GHR calculus and provides a convenient methodology for generic extensions of real- and complex-valued learning algorithms to the quaternion domain.

Calculus detection technologies: where do we stand now?

PubMed Central

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Calculus detection technologies: where do we stand now?

PubMed

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

A FRAMEWORK FOR ATTRIBUTE-BASED COMMUNITY DETECTION WITH APPLICATIONS TO INTEGRATED FUNCTIONAL GENOMICS.

PubMed

Yu, Han; Hageman Blair, Rachael

2016-01-01

Understanding community structure in networks has received considerable attention in recent years. Detecting and leveraging community structure holds promise for understanding and potentially intervening with the spread of influence. Network features of this type have important implications in a number of research areas, including, marketing, social networks, and biology. However, an overwhelming majority of traditional approaches to community detection cannot readily incorporate information of node attributes. Integrating structural and attribute information is a major challenge. We propose a exible iterative method; inverse regularized Markov Clustering (irMCL), to network clustering via the manipulation of the transition probability matrix (aka stochastic flow) corresponding to a graph. Similar to traditional Markov Clustering, irMCL iterates between "expand" and "inflate" operations, which aim to strengthen the intra-cluster flow, while weakening the inter-cluster flow. Attribute information is directly incorporated into the iterative method through a sigmoid (logistic function) that naturally dampens attribute influence that is contradictory to the stochastic flow through the network. We demonstrate advantages and the exibility of our approach using simulations and real data. We highlight an application that integrates breast cancer gene expression data set and a functional network defined via KEGG pathways reveal significant modules for survival.

Modeling heterogeneous responsiveness of intrinsic apoptosis pathway

PubMed Central

2013-01-01

Background Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism’s survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level. Results To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway. Conclusions Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness. PMID:23875784

Enabling congestion avoidance and reduction in the Michigan-Ohio transportation network to improve supply chain efficiency : freight ATIS.

DOT National Transportation Integrated Search

2010-01-01

We consider dynamic vehicle routing under milk-run tours with time windows in congested : transportation networks for just-in-time (JIT) production. The arc travel times are considered : stochastic and time-dependent. The problem integrates TSP with ...

Dynamic analysis of a stochastic delayed rumor propagation model

NASA Astrophysics Data System (ADS)

Jia, Fangju; Lv, Guangying; Wang, Shuangfeng; Zou, Guang-an

2018-02-01

The rapid development of the Internet, especially the emergence of the social networks, has led rumor propagation into a new media era. In this paper, we are concerned with a stochastic delayed rumor propagation model. Firstly, we obtain the existence of the global solution. Secondly, sufficient conditions for extinction of the rumor are established. Lastly, the boundedness of solution is proved and some simulations are given to verify our results.

Event-Based Variance-Constrained ${\\mathcal {H}}_{\\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2018-03-01

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Simulated maximum likelihood method for estimating kinetic rates in gene expression.

PubMed

Tian, Tianhai; Xu, Songlin; Gao, Junbin; Burrage, Kevin

2007-01-01

Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Comparative clinical efficacy of three toothpastes in the control of supragingival calculus formation.

PubMed

Kraivaphan, Petcharat; Amornchat, Cholticha

2017-01-01

The purpose of this double-blind, parallel clinical study was to assess clinical efficacy in supragingival calculus formation reduction using Abhaibhubejhr Herbal Toothpaste compared to Colgate Total and Colgate Cavity Protection toothpastes. A total of 150 subjects participated in the pretest phase. All subjects were given oral soft/hard tissue evaluation, calculus examination using Volpe-Manhold calculus, and whole mouth oral prophylaxis. They received noncalculus control fluoride toothpaste and a soft-bristled toothbrush to brush for 1 min two times daily for 8 weeks. After which, subjects were given a test phase oral soft/hard tissue evaluation and calculus examination and were randomized into one of the three toothpaste groups. All subjects in the test phase received a whole mouth oral prophylaxis and were given their assigned toothpaste and a soft-bristled toothbrush to brush for 1 min two times a day for 12 weeks. Thereafter, subjects were assessed for their oral soft/hard tissue and calculus formation. Mean Volpe-Manhold calculus index scores for the Cavity Protection, Abhaibhubejhr, and Total toothpaste groups were 0.78, 0.62, and 0.48, respectively, at the 12-week test phase evaluation. Abhaibhubejhr and Total toothpaste groups show 20.51% and 38.46% significantly less calculus formation than the Cavity Protection toothpaste group ( P < 0.05). Total toothpaste group also show 22.58% significantly less calculus formation than the Abhaibhubejhr toothpaste group ( P < 0.05). The use of Colgate Total toothpaste over a 12-week period was clinically more effective than either Abhaibhubejhr or Colgate Cavity Protection toothpastes in controlling supragingival calculus formation.

Endoscopic vs. tactile evaluation of subgingival calculus.

PubMed

Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M

2014-08-01

Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (p<0.005). Mean changes (reduction) in calculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (p<0.0001). However, further reductions in calculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (p<0.025), indicating that this methodology was able to more precisely detect calculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.

A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

PubMed

Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Spreading dynamics on complex networks: a general stochastic approach.

PubMed

Noël, Pierre-André; Allard, Antoine; Hébert-Dufresne, Laurent; Marceau, Vincent; Dubé, Louis J

2014-12-01

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

Stochastic dynamics of genetic broadcasting networks

NASA Astrophysics Data System (ADS)

Potoyan, Davit; Wolynes, Peter

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

Stochastic dynamics for idiotypic immune networks

NASA Astrophysics Data System (ADS)

Barra, Adriano; Agliari, Elena

2010-12-01

In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker-Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-of-equilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.

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

A moment-convergence method for stochastic analysis of biochemical reaction networks.

PubMed

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou

2016-05-21

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Science 101: How Do We Use Calculus in Science?

ERIC Educational Resources Information Center

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

An Analysis of College Mathematics Departments' Credit Granting Policies for Students with High School Calculus Experience

ERIC Educational Resources Information Center

Laurent, Theresa A.

2009-01-01

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

A Study of Calculus Instructors' Perceptions of Approximation as a Unifying Thread of the First-Year Calculus

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Swaminathan, Hariharan; Gorgievski, Nicholas; Vinsonhaler, Charles; Wiseman, Brianna; Escolas, Samuel

2015-01-01

This paper discusses findings from a research study designed to investigate calculus instructors' perceptions of approximation as a central concept and possible unifying thread of the first-year calculus. The study also examines the role approximation plays in participants' self-reported instructional practices. A survey was administered to 279…

What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris

2011-01-01

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Examining related influential factors for dental calculus scaling utilization among people with disabilities in Taiwan, a nationwide population-based study.

PubMed

Lai, Hsien-Tang; Kung, Pei-Tseng; Su, Hsun-Pi; Tsai, Wen-Chen

2014-09-01

Limited studies with large samples have been conducted on the utilization of dental calculus scaling among people with physical or mental disabilities. This study aimed to investigate the utilization of dental calculus scaling among the national disabled population. This study analyzed the utilization of dental calculus scaling among the disabled people, using the nationwide data between 2006 and 2008. Descriptive analysis and logistic regression were performed to analyze related influential factors for dental calculus scaling utilization. The dental calculus scaling utilization rate among people with physical or mental disabilities was 16.39%, and the annual utilization frequency was 0.2 times. Utilization rate was higher among the female and non-aboriginal samples. Utilization rate decreased with increased age and disability severity while utilization rate increased with income, education level, urbanization of residential area and number of chronic illnesses. Related influential factors for dental calculus scaling utilization rate were gender, age, ethnicity (aboriginal or non-aboriginal), education level, urbanization of residence area, income, catastrophic illnesses, chronic illnesses, disability types, and disability severity significantly influenced the dental calculus scaling utilization rate. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

PubMed

Touboul, Jonathan D; Faugeras, Olivier D

2011-11-01

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

The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.

PubMed

Caravagna, Giulio; Mauri, Giancarlo; d'Onofrio, Alberto

2013-01-01

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i) the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii) a model of enzymatic futile cycle and (iii) a genetic toggle switch. In (ii) and (iii) we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.

Dental calculus detection using the VistaCam.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  < .05). The readings for calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.