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Sample records for nonlinear stochastic process

  1. Stochastic Growth and Nonlinear Processes in Earth's Foreshock

    NASA Astrophysics Data System (ADS)

    Cairns, Iver; Robinson, P. A.; Connors, Timothy

    2000-10-01

    Langmuir-like waves driven by electron beams in Earth's foreshock have been observed for many years. The foreshock is also a source of radiation near the electron plasma frequency fp and near 2f_p, long interpreted in terms of Langmuir waves undergoing nonlinear processes. However, standard plasma theory, in which homogeneous waves grow exponentially until saturated by a nonlinear process, encounters great difficulties explaining the burstiness, widely varying fields, and persistence far from the bow shock of the foreshock Langmuir waves Recently, however, stochastic growth theory (SGT) has been shown to provide a detailed explanation for the burstiness, field statistics, persistence, and spatial evolution of Langmuir waves in Earth's foreshock. This paper reviews this evidence for SGT and then presents a new, strong argument based on SGT that a nonlinear Langmuir process occurs near the upstream edge of Earth's foreshock. The argument involves the SGT prediction that the probability distribution P(log E) of wave electric fields E should suffer an abrupt fall-off at fields higher than the threshold field of an active nonlinear process. For two intervals of ISEE-1 data it is shown that the P(log E) distributions are well described by SGT with an active nonlinear process at fields of a few mV m-1. Based on calculated thresholds for foreshock beam parameters, the nonlinear process is most likely the electrostatic decay L arrow L' + S (L, L' and S denote Langmuir, Langmuir, and ion acoustic waves, respectively). Accordingly, these data are consistent with stochastic growth physics dominating the evolution of the Langmuir waves, and electrostatic decay occurring only near the foreshock's edge for the most intense Langmuir waves, similar to previous results for type III radio sources.

  2. Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

    SciTech Connect

    Yang, Hui Chen, Yun

    2014-03-15

    Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

  3. Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

    SciTech Connect

    Yang, Hui Chen, Yun

    2014-03-15

    Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

  4. Nonlinear Stochastic Markov Processes and Modeling Uncertainty in Populations

    DTIC Science & Technology

    2011-07-06

    growth rate g(x) = rx ( 1− x κ ) and the general tran- sition rates g(x, t) = (a0(t) − a1(t) ln x)x of which the standard Gompertz growth rates g(x) = r...probabilistic formulation (5.4) and the stochastic formulation (5.5), which nicely illustrates our earlier theoretical results. Example 5.3 ( Gompertz ...stochastic version of the generalized Gompertz model ẋ = (a0(t)− a1(t) lnx)x, which has been extensively used in biological and medical research to describe

  5. Research in Stochastic Processes.

    DTIC Science & Technology

    1985-09-01

    appear. G. Kallianpur, Finitely additive approach to nonlinear filtering, Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to...Nov. 85, in Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to appear. i. Preparation T. Hsing, Extreme value theory for...1507 Carroll, R.J., Spiegelman, C.H., Lan, K.K.G., Bailey , K.T. and Abbott, R.D., Errors in-variables for binary regression models, Aug.82. 1508

  6. Modeling scaled processes and 1/fβ noise using nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Kaulakys, B; Alaburda, M

    2009-02-01

    We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/fβ noise, power-law autocorrelations and second-order structural (height-height correlation) functions. Analytical expressions for such characteristics are derived and a comparison with numerical calculations is presented. The numerical calculations reveal links between the proposed model and models where signals consist of bursts characterized by power-law distributions of burst size, burst duration and interburst time, as in the case of avalanches in self-organized critical models and the extreme event return times in long-term memory processes. The approach presented may be useful for modeling long-range scaled processes exhibiting 1/f noise and power-law distributions.

  7. Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes.

    PubMed

    Ohkubo, Jun

    2015-10-01

    An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.

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

    NASA Astrophysics Data System (ADS)

    Balaji, Bhashyam

    2016-05-01

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

  9. Nonlinear Stochastic PDEs: Analysis and Approximations

    DTIC Science & Technology

    2016-05-23

    3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations We compare Wiener chaos and stochastic collocation methods for linear advection-reaction...ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 nonlinear stochastic PDEs (SPDEs), nonlocal SPDEs, Navier...3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations Report Title We compare Wiener chaos and stochastic collocation methods for linear

  10. Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

    NASA Astrophysics Data System (ADS)

    Timmer, Jens; Häußler, Siegfried; Lauk, Michael; Lücking, Carl

    2000-02-01

    Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic second order processes.

  11. Stochastic Nonlinear Aeroelasticity

    DTIC Science & Technology

    2009-01-01

    aeroelasticity. The work was divided into different project areas, including: accurate analysis of limit- cycle oscillations for simple aeroelastic systems...vehicles, limit-cycle oscillation 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 18. NUMBER OF PAGES 44 19a. NAME OF...susceptible to nonlinear oscillations (for the purpose of avoiding dangerous oscillations ), and (2) multidisciplinary design optimization of flapping wing

  12. On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

    PubMed

    Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

    2017-02-01

    Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a

  13. On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

    PubMed Central

    Truccolo, Wilson

    2017-01-01

    Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a

  14. Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion

    PubMed Central

    Sun, Fuqiang; Liu, Le; Li, Xiaoyang; Liao, Haitao

    2016-01-01

    Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product’s performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner’s ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters. PMID:27509499

  15. Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Kaulakys, B.; Alaburda, M.; Ruseckas, J.

    2016-05-01

    A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

  16. Forward Stochastic Nonlinear Adaptive Control Method

    NASA Technical Reports Server (NTRS)

    Bayard, David S.

    1990-01-01

    New method of computation for optimal stochastic nonlinear and adaptive control undergoing development. Solves systematically stochastic dynamic programming equations forward in time, using nested-stochastic-approximation technique. Main advantage, simplicity of programming and reduced complexity with clear performance/computation trade-offs.

  17. Nonlinear Stochastic Interaction in Aeroelastic Structures.

    DTIC Science & Technology

    1988-01-29

    Frangopol. D NI (1985ai Sensiti-ts of reltabiltIisbaed optimum de Boyce. W E (1966). Stochastic nonthomogeneous Sturm - Liouville problem. Strut, Dig 111. 1703...It is known that 4,2 =- qlql -q11+- q2 4j the result of any linear operator , with constant coefficients, , 1 = 3E,- - 2 q) applied to a random...Gaussian process results in a Gaussian k. - 3EIIP (2) process. However. if the operator is nonlinear, the resulting It is seen that the left-hand side of

  18. Quantum Stochastic Processes

    SciTech Connect

    Spring, William Joseph

    2009-04-13

    We consider quantum analogues of n-parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].

  19. Introduction to Focus Issue: nonlinear and stochastic physics in biology.

    PubMed

    Bahar, Sonya; Neiman, Alexander B; Jung, Peter; Kurths, Jürgen; Schimansky-Geier, Lutz; Showalter, Kenneth

    2011-12-01

    Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

  20. Nonlinear optimization for stochastic simulations.

    SciTech Connect

    Johnson, Michael M.; Yoshimura, Ann S.; Hough, Patricia Diane; Ammerlahn, Heidi R.

    2003-12-01

    This report describes research targeting development of stochastic optimization algorithms and their application to mission-critical optimization problems in which uncertainty arises. The first section of this report covers the enhancement of the Trust Region Parallel Direct Search (TRPDS) algorithm to address stochastic responses and the incorporation of the algorithm into the OPT++ optimization library. The second section describes the Weapons of Mass Destruction Decision Analysis Center (WMD-DAC) suite of systems analysis tools and motivates the use of stochastic optimization techniques in such non-deterministic simulations. The third section details a batch programming interface designed to facilitate criteria-based or algorithm-driven execution of system-of-system simulations. The fourth section outlines the use of the enhanced OPT++ library and batch execution mechanism to perform systems analysis and technology trade-off studies in the WMD detection and response problem domain.

  1. The Stochastic Nonlinear Damped Wave Equation

    SciTech Connect

    Barbu, V. Da Prato, G.

    2002-12-19

    We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in R{sup n} of the Klein-Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied.

  2. Stochastic Nonlinear Dynamics of Floating Structures

    DTIC Science & Technology

    1994-08-03

    examples of colored noise filters exist in the literature. Billah and Shinozuka [4] use the following Tr/(t) = -y(t) + F(t), (8) where rc is the...several sources such as Billah and Shinozuka [6]. Because the Fokker-Planck equation requires that the governing equations be cast as a series of first...Nonlinear Stochastic Dynamics Engineering systems, pages 87- 100, New York, 1987. IUTAM, Springer-Verlag. [6] K.Y.R. Billah and M. Shinozuka

  3. Fully nonlinear dynamics of stochastic thin-film dewetting

    NASA Astrophysics Data System (ADS)

    Nesic, S.; Cuerno, R.; Moro, E.; Kondic, L.

    2015-12-01

    The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.

  4. Research in Stochastic Processes

    DTIC Science & Technology

    1988-10-10

    26 L. Gorostiza ................................................. 25 G. Hardy...Technical Report No. 219, Dec. 1987. Sequential Anat., 7. 1988, 111-126 25 DONALD DAWSON and LUIS G. GOROSTIZA The work of Professors Dawson and Gorostiza ... Gorostiza , Generalized solutions of a class of nuclear space valued stochastic evolution equations. University of North Carolina Center for Stochastic

  5. Stochastic resonance-a nonlinear control theory interpretation

    NASA Astrophysics Data System (ADS)

    Repperger, D. W.; Farris, K. A.

    2010-07-01

    Stochastic resonance (SR) is an effect that has been known (Benzi, R., Sutera, A., and Vulpiani, A. (1981), 'The Mechanism of Stochastic Resonance', Journal of Physics, A14, L453-L457) for almost three decades and has been extensively studied in biology, statistics, signal processing and in numerous other eclectic areas (Wiesenfeld, K., and Moss, F. (1995), 'Stochastic Resonance and the Benefits of Noise: From Ice Ages to Crayfish and Squids', Nature, 373, 33-36). Herein, a nonlinear control theory analysis is conducted on how to better understand the class of systems that may exhibit the SR effect. Using nonlinear control theory methods, equilibrium points are manipulated to create the SR response (similar to shaping dynamical response in a phase plane). From this approach, a means of synthesising and designing the appropriate class of nonlinear systems is introduced. New types of nonlinear dynamics that demonstrate the SR effects are discovered, which may have utility in control theory as well as in many diverse applications. A numerical simulation illustrates some powerful attributes of these systems.

  6. Deterministic and stochastic responses of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Abou-Rayan, Ashraf Mohamed

    The responses of nonlinear systems to both deterministic and stochastic excitations are discussed. For a single degree of freedom system, the response of a simply supported buckled beam to parametric excitations is investigated. Two types of excitations are examined: deterministic and random. For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude and phase modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics. The results are compared with those obtained from real-time analysis (analog-computer simulation). The normality assumption is examined. A comparison between the responses to deterministic and random excitation is presented. For two degree of freedom systems, two methods are used to study the response under the action of broad-band random excitations. The first method is applicable to systems having cubic nonlinearities. It involves an averaging approach to reduce the number of moment equations for the non-Gaussian closure scheme from 69 to 14 equations. The results are compared with those obtained from numerical integrations of the moment equations and the exact stationary solution of the Fokker-Planck-Komologorov equation. The second method is applicable to systems having quadratic and cubic nonlinearities. Stationary solutions of the moment equations are determined and their stability is ascertained by examining the

  7. A data driven nonlinear stochastic model for blood glucose dynamics.

    PubMed

    Zhang, Yan; Holt, Tim A; Khovanova, Natalia

    2016-03-01

    The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

  8. Research in Stochastic Processes.

    DTIC Science & Technology

    1982-10-31

    locally convex spaces is studied. We obtain a general form of convergent p-cylindrical martingales in barrelled spaces. Using the locally convex space...topology of certain Orlicz and Lorentz spaces. References 1. Z. Suchanecki and A. Weron, Decomposability of p-cylindrical martingales, Center for Stochastic

  9. Research in Stochastic Processes

    DTIC Science & Technology

    1988-08-31

    25 L. de Haan ................................................... 26 L. Gorostiza ...DAISON and LUIS C. COROSTIZA The work of Professors Dawson and Gorostiza is concerned with obtaining a Langevin equation for the fluctuation limit of a...its uniqueness established. Reference 1. D.A. Dawson and L.G. Gorostiza , Generalized solutions of a class of nuclear space valued stochastic

  10. 1/f noise from nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Ruseckas, J.; Kaulakys, B.

    2010-03-01

    We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fβ noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fβ noise, and provides further insights into the origin of 1/fβ noise.

  11. Nonlinear and Stochastic Dynamics in the Heart.

    PubMed

    Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N

    2014-10-10

    In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

  12. Nonlinear and Stochastic Dynamics in the Heart

    PubMed Central

    Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

    2014-01-01

    In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

  13. Stochastic processes in cosmology

    NASA Astrophysics Data System (ADS)

    Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.

    1987-08-01

    The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.

  14. STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.

    DTIC Science & Technology

    A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest...converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)

  15. Stochastic processes in gravitropism.

    PubMed

    Meroz, Yasmine; Bastien, Renaud

    2014-01-01

    In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles) to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i) dynamic sensing, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification, and integration of the signal. (ii) The role of the cytoskeleton in signal-to-noise modulation and (iii) in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.

  16. Nonlinear dynamic characteristics of SMA intravascular stent under radial stochastic loads.

    PubMed

    Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia

    2014-01-01

    Nonlinear dynamic characteristics of shape memory alloy (SMA) intravascular stent under radial stochastic loads were studied in this paper. Von de Pol item was improved to interpret the hysteretic phenomena of SMA, and the nonlinear dynamic model of SMA intravascular stent under radial stochastic loads was developed. The conditions of stochastic stability of the system were obtained in singular boundary theory. The steady-state probability density function of the dynamic response of the system was given, and the stochastic Hopf bifurcation characteristics of the system were analyzed. Theoretical analysis and numerical simulation show that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process, which can cause stent fracture or loss. The results of this paper are helpful to application of SMA intravascular stent in biomedical engineering fields.

  17. Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators

    NASA Technical Reports Server (NTRS)

    Tsitsiklis, J. N.; Athans, M.

    1983-01-01

    The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

  18. Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

    PubMed

    Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

    2016-11-14

    In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

  19. Stochastic Process Creation

    NASA Astrophysics Data System (ADS)

    Esparza, Javier

    In many areas of computer science entities can “reproduce”, “replicate”, or “create new instances”. Paramount examples are threads in multithreaded programs, processes in operating systems, and computer viruses, but many others exist: procedure calls create new incarnations of the callees, web crawlers discover new pages to be explored (and so “create” new tasks), divide-and-conquer procedures split a problem into subproblems, and leaves of tree-based data structures become internal nodes with children. For lack of a better name, I use the generic term systems with process creation to refer to all these entities.

  20. Accelerated stochastic diffusion processes

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr

    1990-07-01

    We give a purely probabilistic demonstration that all effects of non-random (external, conservative) forces on the diffusion process can be encoded in the Nelson ansatz for the second Newton law. Each random path of the process together with a probabilistic weight carries a phase accumulation (complex valued) weight. Random path summation (integration) of these weights leads to the transition probability density and transition amplitude respectively between two spatial points in a given time interval. The Bohm-Vigier, Fenyes-Nelson-Guerra and Feynman descriptions of the quantum particle behaviours are in fact equivalent.

  1. Research in Stochastic Processes.

    DTIC Science & Technology

    1984-10-01

    of stable processes: Spectral and moving average representations." S. Cambanis and A. Soltani , Z. Wahrsch. verw. Geb., 66, 1984, 593-612. "Comparisons...average representation for stationary random fields and Beurling’s theorem." A. Soltani , Ann. Probabilit, 12, 1984, 120-132. S "Decomposability of p

  2. Research in Stochastic Processes.

    DTIC Science & Technology

    1982-12-01

    the Statistics Department, involving permaner.c faculty, visitors and students. UNCLASSIFIED/UNLIMITED SAME AS RP-T EO TIC USERS ED 22a NAME OF...possible extensions of large deviation thoery (see (l] and references therein). For the case of Markov processes we attempted to derive the results of...homoscedastic errors, several classes of efficient, balanced designs for factorial experiments were constructed in [2]. In this project, the author has

  3. Wavelet entropy of stochastic processes

    NASA Astrophysics Data System (ADS)

    Zunino, L.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.

    2007-06-01

    We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise ( -1<α< 1) and fractional Brownian motion ( 1<α< 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.

  4. Stochastic processes, slaves and supersymmetry

    NASA Astrophysics Data System (ADS)

    Drummond, I. T.; Horgan, R. R.

    2012-03-01

    We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for slave variables. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements, together with the associated surface and volume elements constructed from them, provide the basis of the supersymmetry properties of the theory. For ease of visualization, and in order to emphasize a helpful electromagnetic analogy, we work in three dimensions. The results are all generalizable to higher dimensions and can be specialized to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities.

  5. Reaching Nonlinear Consensus via Non-Autonomous Polynomial Stochastic Operators

    NASA Astrophysics Data System (ADS)

    Saburov, Mansoor; Saburov, Khikmat

    2017-03-01

    This paper is a continuation of our previous studies on nonlinear consensus which unifies and generalizes all previous results. We consider a nonlinear protocol for a structured time-varying synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of non-autonomous polynomial stochastic operators associated with multidimensional stochastic hyper-matrices. We show that the multi-agent system eventually reaches to a nonlinear consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective distribution on the given task after some revision steps or (ii) all entries of some multidimensional stochastic hyper-matrix are positive.

  6. A Stochastic Diffusion Process for the Dirichlet Distribution

    DOE PAGES

    Bakosi, J.; Ristorcelli, J. R.

    2013-03-01

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

  7. Stochastic nonlinear mixed effects: a metformin case study.

    PubMed

    Matzuka, Brett; Chittenden, Jason; Monteleone, Jonathan; Tran, Hien

    2016-02-01

    In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi for their stochastic deconvolution.

  8. Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients

    NASA Astrophysics Data System (ADS)

    Rifhat, Ramziya; Wang, Lei; Teng, Zhidong

    2017-09-01

    In this paper, we investigate the dynamics of a class of periodic stochastic SIS epidemic models with general nonlinear incidence f(S , I) . Some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established. By using the Khasminskii's boundary periodic Markov processes, the existence of stochastic nontrivial periodic solution for the models is also obtained. The numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented.

  9. Stochastic thermodynamics of information processing

    NASA Astrophysics Data System (ADS)

    Cardoso Barato, Andre

    2015-03-01

    We consider two recent advancements on theoretical aspects of thermodynamics of information processing. First we show that the theory of stochastic thermodynamics can be generalized to include information reservoirs. These reservoirs can be seen as a sequence of bits which has its Shannon entropy changed due to the interaction with the system. Second we discuss bipartite systems, which provide a convenient description of Maxwell's demon. Analyzing a special class of bipartite systems we show that they can be used to study cellular information processing, allowing for the definition of an entropic rate that quantifies how much a cell learns about a fluctuating external environment and that is bounded by the thermodynamic entropy production.

  10. Adaptive Control of Nonlinear and Stochastic Systems

    DTIC Science & Technology

    1991-01-14

    Hernmndez-Lerma and S.I. Marcus, Nonparametric adaptive control of dis- crete time partially observable stochastic systems, Journal of Mathematical Analysis and Applications 137... Journal of Mathematical Analysis and Applications 137 (1989), 485-514. [19] A. Arapostathis and S.I. Marcus, Analysis of an identification algorithm

  11. Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems

    NASA Technical Reports Server (NTRS)

    Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.

    2004-01-01

    A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.

  12. Filtering nonlinear dynamical systems with linear stochastic models

    NASA Astrophysics Data System (ADS)

    Harlim, J.; Majda, A. J.

    2008-06-01

    2007 Proc. Natl Acad. Sci. 104 1124-9 Castronovo et al 2008 J. Comput. Phys. 227 3678-714) for the linear stochastically forced partial differential equations with constant coefficients such as in (Castronovo et al 2008 J. Comput. Phys. 227 3678-714), this Fourier diagonal decoupling is a natural approach provided that the system noise is chosen to be independent in the Fourier space; for a nonlinear problem, however, there is a strong mixing and correlations between different Fourier modes. Our strategy is to radically assume for the purposes of filtering that different Fourier modes are uncorrelated. In particular, we introduce physical model errors by replacing the nonlinearity in the original model with a suitable Ornstein-Uhlenbeck process. We show that even with this 'poor-man's' stochastic model, when the appropriate parametrization strategy is guided by mathematical offline test criteria, it is able to produce reasonably skilful filtered solutions. In the highly turbulent regime with infrequent observation time, this approach is at least as good as trusting the observations while the ensemble Kalman filter implemented in a perfect model scenario diverges. Since these Fourier diagonal linear filters have large model error compared with the nonlinear dynamics, an essential part of the study below is the interplay between this error and the mathematical criteria for a given linear filter in order to produce skilful filtered solutions through the radical strategy.

  13. Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

    PubMed

    Herzallah, Randa

    2013-06-01

    Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

  14. A forward method for optimal stochastic nonlinear and adaptive control

    NASA Technical Reports Server (NTRS)

    Bayard, David S.

    1988-01-01

    A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.

  15. NONLINEAR EFFECTS IN PARTICLE TRANSPORT IN STOCHASTIC MAGNETIC FIELDS

    SciTech Connect

    Vlad, M.; Spineanu, F.; Croitoru, A.

    2015-12-10

    Collisional particle transport in stochastic magnetic fields is studied using a semi-analytical method. The aim is to determine the influence of the nonlinear effects that occur in the magnetic field line random walk on particle transport. We show that particle transport coefficients can be strongly influenced by the magnetic line trapping. The conditions that correspond to these nonlinear regimes are determined. We also analyze the effects produced by the space variation of the large-scale magnetic field. We show that an average drift is generated by the gradient of the magnetic field, which strongly increases and reverses its orientation in the nonlinear regime.

  16. Representation of nonlinear random transformations by non-gaussian stochastic neural networks.

    PubMed

    Turchetti, Claudio; Crippa, Paolo; Pirani, Massimiliano; Biagetti, Giorgio

    2008-06-01

    The learning capability of neural networks is equivalent to modeling physical events that occur in the real environment. Several early works have demonstrated that neural networks belonging to some classes are universal approximators of input-output deterministic functions. Recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks (SNN). In the language of system theory, the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no-memory systems. However, all the results presented so far are restricted to the case of Gaussian stochastic processes (SPs) only, or to linear transformations that guarantee this property. This paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input-output random transformations, thus widening the range of applicability of these networks to nonlinear systems with memory. In particular, this study shows that networks belonging to a class named non-Gaussian stochastic approximate identity neural networks (SAINNs) are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations. The effectiveness of this approach is demonstrated and discussed by some application examples.

  17. Non-linear stochastic growth rates and redshift space distortions

    SciTech Connect

    Jennings, Elise; Jennings, David

    2015-04-09

    The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at k ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.

  18. Non-linear stochastic growth rates and redshift space distortions

    DOE PAGES

    Jennings, Elise; Jennings, David

    2015-04-09

    The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at kmore » ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M⊙ h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.« less

  19. Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

    SciTech Connect

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

    2014-05-30

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

  20. Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation

    NASA Astrophysics Data System (ADS)

    Gomes, S. N.; Kalliadasis, S.; Papageorgiou, D. T.; Pavliotis, G. A.; Pradas, M.

    2017-06-01

    We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.

  1. Equilibrium thermodynamics and stochastic nonlinear acoustic fields. [in crystalline lattices

    NASA Technical Reports Server (NTRS)

    Cantrell, J. H.

    1985-01-01

    A crystalline solid is considered to consist of a large number of incoherent nonlinear acoustic radiation sources identified with the vibrating particles of the crystalline lattice. Randomization of the field, together with the assumption of a stochastically independent, fluctuating, radiation field at the absolue zero of temperature, leads to an expression of the temperature-dependent radiation field in terms of the zero-point field. The equation is identified with the Planck distribution formula of quantum mechanics in the linear field limit. The thermodynamic state functions are also obtained in terms of the nonlinear acoustic modal energies per unit mass and reduce to the results of the Debye-Einstein stochastic quantum oscillator model in the linear field limit.

  2. Nonlinear Aeroelastic Analysis of UAVs: Deterministic and Stochastic Approaches

    NASA Astrophysics Data System (ADS)

    Sukut, Thomas Woodrow

    Aeroelastic aspects of unmanned aerial vehicles (UAVs) is analyzed by treatment of a typical section containing geometrical nonlinearities. Equations of motion are derived and numerical integration of these equations subject to quasi-steady aerodynamic forcing is performed. Model properties are tailored to a high-altitude long-endurance unmanned aircraft. Harmonic balance approximation is employed based on the steady-state oscillatory response of the aerodynamic forcing. Comparisons are made between time integration results and harmonic balance approximation. Close agreement between forcing and displacement oscillatory frequencies is found. Amplitude agreement is off by a considerable margin. Additionally, stochastic forcing effects are examined. Turbulent flow velocities generated from the von Karman spectrum are applied to the same nonlinear structural model. Similar qualitative behavior is found between quasi-steady and stochastic forcing models illustrating the importance of considering the non-steady nature of atmospheric turbulence when operating near critical flutter velocity.

  3. Stochastic Nonlinear Response of Woven CMCs

    NASA Technical Reports Server (NTRS)

    Kuang, C. Liu; Arnold, Steven M.

    2013-01-01

    It is well known that failure of a material is a locally driven event. In the case of ceramic matrix composites (CMCs), significant variations in the microstructure of the composite exist and their significance on both deformation and life response need to be assessed. Examples of these variations include changes in the fiber tow shape, tow shifting/nesting and voids within and between tows. In the present work, the influence of scale specific architectural features of woven ceramic composite are examined stochastically at both the macroscale (woven repeating unit cell (RUC)) and structural scale (idealized using multiple RUCs). The recently developed MultiScale Generalized Method of Cells methodology is used to determine the overall deformation response, proportional elastic limit (first matrix cracking), and failure under tensile loading conditions and associated probability distribution functions. Prior results showed that the most critical architectural parameter to account for is weave void shape and content with other parameters being less in severity. Current results show that statistically only the post-elastic limit region (secondary hardening modulus and ultimate tensile strength) is impacted by local uncertainties both at the macro and structural level.

  4. Analytical Methods in Stochastic Control and Nonlinear Filtering.

    DTIC Science & Technology

    1987-12-31

    one puts further restrictions on the type of nonlinearities considered. IConsider the one dimensional Ito stochastic differential equation dxt = g(t, xt...derivatives to obtain lower and upper bounds involving ordinary differential equations of the Riccati type. The upper bound is obtained in subsection 1.2.2...filters approaches the optimal oneI asymptotically. The upper and lower bounds satisfy ordinary differential equations of the Riccati type. In

  5. Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Williams Colin P.

    1999-01-01

    Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

  6. Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Williams Colin P.

    1999-01-01

    Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

  7. An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

    SciTech Connect

    Heydari, M.H.; Hooshmandasl, M.R.; Cattani, C.; Maalek Ghaini, F.M.

    2015-02-15

    Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.

  8. Stochastic differential equation model to Prendiville processes

    NASA Astrophysics Data System (ADS)

    Granita, Bahar, Arifah

    2015-10-01

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  9. Stochastic differential equation model to Prendiville processes

    SciTech Connect

    Granita; Bahar, Arifah

    2015-10-22

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  10. Multiple Stochastic Point Processes in Gene Expression

    NASA Astrophysics Data System (ADS)

    Murugan, Rajamanickam

    2008-04-01

    We generalize the idea of multiple-stochasticity in chemical reaction systems to gene expression. Using Chemical Langevin Equation approach we investigate how this multiple-stochasticity can influence the overall molecular number fluctuations. We show that the main sources of this multiple-stochasticity in gene expression could be the randomness in transcription and translation initiation times which in turn originates from the underlying bio-macromolecular recognition processes such as the site-specific DNA-protein interactions and therefore can be internally regulated by the supra-molecular structural factors such as the condensation/super-coiling of DNA. Our theory predicts that (1) in case of gene expression system, the variances ( φ) introduced by the randomness in transcription and translation initiation-times approximately scales with the degree of condensation ( s) of DNA or mRNA as φ ∝ s -6. From the theoretical analysis of the Fano factor as well as coefficient of variation associated with the protein number fluctuations we predict that (2) unlike the singly-stochastic case where the Fano factor has been shown to be a monotonous function of translation rate, in case of multiple-stochastic gene expression the Fano factor is a turn over function with a definite minimum. This in turn suggests that the multiple-stochastic processes can also be well tuned to behave like a singly-stochastic point processes by adjusting the rate parameters.

  11. Sequential decision analysis for nonstationary stochastic processes

    NASA Technical Reports Server (NTRS)

    Schaefer, B.

    1974-01-01

    A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.

  12. Nonlinear stochastic system identification of skin using volterra kernels.

    PubMed

    Chen, Yi; Hunter, Ian W

    2013-04-01

    Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy.

  13. Stochastic cooperativity in non-linear dynamics of genetic regulatory networks.

    PubMed

    Rosenfeld, Simon

    2007-11-01

    Two major approaches are known in the field of stochastic dynamics of genetic regulatory networks (GRN). The first one, referred here to as the Markov Process Paradigm (MPP), places the focus of attention on the fact that many biochemical constituents vitally important for the network functionality are present only in small quantities within the cell, and therefore the regulatory process is essentially discrete and prone to relatively big fluctuations. The Master Equation of Markov Processes is an appropriate tool for the description of this kind of stochasticity. The second approach, the Non-linear Dynamics Paradigm (NDP), treats the regulatory process as essentially continuous. A natural tool for the description of such processes are deterministic differential equations. According to NDP, stochasticity in such systems occurs due to possible bistability and oscillatory motion within the limit cycles. The goal of this paper is to outline a third scenario of stochasticity in the regulatory process. This scenario is only conceivable in high-dimensional, highly non-linear systems, and thus represents an adequate framework for conceptually modeling the GRN. We refer to this framework as the Stochastic Cooperativity Paradigm (SCP). In this approach, the focus of attention is placed on the fact that in systems with the size and link density of GRN ( approximately 25000 and approximately 100, respectively), the confluence of all the factors which are necessary for gene expression is a comparatively rare event, and only massive redundancy makes such events sufficiently frequent. An immediate consequence of this rareness is 'burstiness' in mRNA and protein concentrations, a well known effect in intracellular dynamics. We demonstrate that a high-dimensional non-linear system, despite the absence of explicit mechanisms for suppressing inherent instability, may nevertheless reside in a state of stationary pseudo-random fluctuations which for all practical purposes may be

  14. Stochastic theory of an optical vortex in nonlinear media.

    PubMed

    Kuratsuji, Hiroshi

    2013-07-01

    A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.

  15. Stochastic theory of an optical vortex in nonlinear media

    NASA Astrophysics Data System (ADS)

    Kuratsuji, Hiroshi

    2013-07-01

    A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.

  16. System Identification and Filtering of Nonlinear Controlled Markov Processes by Canonical Variate Analysis

    DTIC Science & Technology

    1989-10-30

    In this Phase I SBIR study, new methods are developed for the system identification and stochastic filtering of nonlinear controlled Markov processes...state space Markov process models and canonical variate analysis (CVA) for obtaining optimal nonlinear procedures for system identification and stochastic

  17. Dynamic similarity approach for more robust structural health monitoring in nonlinear, nonstationary and stochastic systems

    NASA Astrophysics Data System (ADS)

    Nataraju, Madhura; Johnson, Timothy J.; Adams, Douglas E.

    2003-07-01

    Environmental and operational variability due to changes in the excitation or any other variable can mimic or altogether obscure evidence of structural defects in measured data leading to false positive/negative diagnoses of damage and conservative/tolerant predictions of remaining useful life in structural health monitoring system. Diagnostic and prognostic errors like these in many types of commercial and defense-related applications must be eliminated if health monitoring is to be widely implemented in these applications. A theoretical framework of "dynamic similiarity" in which two sets of mathematical operators are utilized in one system/data model to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish abnormal from normal nonlinear dynamics, which are accentuated by physically or statistically non-stationary events in the operating environment. After discussing several examples of structural diagnosis and prognosis involving dynamic similarity, a simplifeid numerical finite element model of a helicopter blade with time-varying flexural stiffness on a nonlinear aerodynamic elastic foundation that is subjected to a stochastic base excitation is utilized to introduce and examine the effects of dynamic similarity on health monitoring systems. It is shown that environmental variability can be distinguished from structural damage using a physics-based model in conjunction with the dynamic similarity operators to develop more robust damage detection algorithms, which may prove to be more accurate and precise when operating conditions fluctuate.

  18. Stochastic resonance during a polymer translocation process

    NASA Astrophysics Data System (ADS)

    Mondal, Debasish; Muthukumar, Murugappan

    We study the translocation of a flexible polymer in a confined geometry subjected to a time-periodic external drive to explore stochastic resonance. We describe the equilibrium translocation process in terms of a Fokker-Planck description and use a discrete two-state model to describe the effect of the external driving force on the translocation dynamics. We observe that no stochastic resonance is possible if the associated free-energy barrier is purely entropic in nature. The polymer chain experiences a stochastic resonance effect only in presence of an energy threshold in terms of polymer-pore interaction. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

  19. Stochastic modular analysis for gene circuits: interplay among retroactivity, nonlinearity, and stochasticity.

    PubMed

    Kim, Kyung Hyuk; Sauro, Herbert M

    2015-01-01

    This chapter introduces a computational analysis method for analyzing gene circuit dynamics in terms of modules while taking into account stochasticity, system nonlinearity, and retroactivity. (1) ANALOG ELECTRICAL CIRCUIT REPRESENTATION FOR GENE CIRCUITS: A connection between two gene circuit components is often mediated by a transcription factor (TF) and the connection signal is described by the TF concentration. The TF is sequestered to its specific binding site (promoter region) and regulates downstream transcription. This sequestration has been known to affect the dynamics of the TF by increasing its response time. The downstream effect-retroactivity-has been shown to be explicitly described in an electrical circuit representation, as an input capacitance increase. We provide a brief review on this topic. (2) MODULAR DESCRIPTION OF NOISE PROPAGATION: Gene circuit signals are noisy due to the random nature of biological reactions. The noisy fluctuations in TF concentrations affect downstream regulation. Thus, noise can propagate throughout the connected system components. This can cause different circuit components to behave in a statistically dependent manner, hampering a modular analysis. Here, we show that the modular analysis is still possible at the linear noise approximation level. (3) NOISE EFFECT ON MODULE INPUT-OUTPUT RESPONSE: We investigate how to deal with a module input-output response and its noise dependency. Noise-induced phenotypes are described as an interplay between system nonlinearity and signal noise. Lastly, we provide the comprehensive approach incorporating the above three analysis methods, which we call "stochastic modular analysis." This method can provide an analysis framework for gene circuit dynamics when the nontrivial effects of retroactivity, stochasticity, and nonlinearity need to be taken into account.

  20. A Nonlinear Stochastic Filter for Continuous-Time State Estimation

    PubMed Central

    Ghoreyshi, Atiyeh; Sanger, Terence D.

    2015-01-01

    Nonlinear filters produce a nonparametric estimate of the probability density of state at each point in time. Currently-known nonlinear filters include Particle Filters and the Kushner equation (and its un-normalized version: the Zakai equation). However, these filters have limited measurement models: Particle Filters require measurement at discrete times, and the Kushner and Zakai equations only apply when the measurement can be represented as a function of the state. We present a new nonlinear filter for continuous-time measurements with a much more general stochastic measurement model. It integrates to Bayes’ rule over short time intervals and provides Bayes-optimal estimates from quantized, intermittent, or ambiguous sensor measurements. The filter has a close link to Information Theory, and we show that the rate of change of entropy of the density estimate is equal to the mutual information between the measurement and the state and thus the maximum achievable. This is a fundamentally new class of filter that is widely applicable to nonlinear estimation for continuous-time control. PMID:26412871

  1. Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

    NASA Astrophysics Data System (ADS)

    Zhu, Z. W.; Zhang, W. D.; Xu, J.

    2014-03-01

    The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

  2. Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

    SciTech Connect

    Zhu, Z. W.; Zhang, W. D. Xu, J.

    2014-03-15

    The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

  3. Stochastic model for supersymmetric particle branching process

    NASA Astrophysics Data System (ADS)

    Zhang, Yuanyuan; Chan, Aik Hui; Oh, Choo Hiap

    2017-01-01

    We develop a stochastic branching model to describe the jet evolution of supersymmetric (SUSY) particles. This model is a modified two-phase branching process, or more precisely, a two-phase simple birth process plus Poisson process. Both pure SUSY partons initiated jets and SUSY plus ordinary partons initiated jets scenarios are considered. The stochastic branching equations are established and the Multiplicity Distributions (MDs) are derived for these two scenarios. We also fit the distribution of the general case (SUSY plus ordinary partons initiated jets) with experimental data. The fitting shows the SUSY particles have not participated in branching at current collision energy yet.

  4. Nonlinear system stochastic response determination via fractional equivalent linearization and Karhunen-Loève expansion

    NASA Astrophysics Data System (ADS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-08-01

    In this paper, a novel fractional equivalent linearization (EL) approach is developed by incorporating a fractional derivative term into the classical linearization equation. Due to the introduction of the fractional derivative term, the accuracy of the new linearization is improved, illustrated by a Duffing oscillator that is subjected to a harmonic excitation. Furthermore, a new method for solving stochastic response of nonlinear SDOF system is developed by combining Karhunen-Loève (K-L) expansion and fractional EL. The method firstly decomposes the stochastic excitation in terms of a set of random variables and deterministic sub-excitations using K-L expansion, and then construct sub-fractional equivalent linear system according to each sub-excitation by fractional EL, the response of the original nonlinear system is finally approximated as the weighed summation of the deterministic response of each sub-system multiplied by the corresponding random variable. The random nature of the final response comes from the set of random variables that is obtained in K-L expansion. In this way, the stochastic response computation is converted to a set of deterministic response analysis problems. The effectiveness of the developed method is demonstrated by a Duffing oscillator that is subjected to stochastic excitation modeled by Winner process. The results are compared with the numerical method and Monte Carlo simulation (MCS).

  5. Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

    PubMed

    Ding, Bo; Fang, Huajing

    2017-03-31

    This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system.

  6. Robust H∞ filtering for discrete nonlinear delayed stochastic systems with missing measurements and randomly occurring nonlinearities

    NASA Astrophysics Data System (ADS)

    Liu, Yurong; Alsaadi, Fuad E.; Yin, Xiaozhou; Wang, Yamin

    2015-02-01

    In this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed ? disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.

  7. Functional integral approach for multiplicative stochastic processes.

    PubMed

    Arenas, Zochil González; Barci, Daniel G

    2010-05-01

    We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green's functions in the Grassman sector of the theory. We also study nonperturbative constraints imposed by Becchi, Rouet and Stora symmetry (BRS) and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory, the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.

  8. Minimum Entropy Rate Simplification of Stochastic Processes.

    PubMed

    Henter, Gustav Eje; Kleijn, W Bastiaan

    2016-02-23

    This document contains supplemental material for the IEEE Transactions on Pattern Analysis and Machine Intelligence article "Minimum Entropy Rate Simplification of Stochastic Processes." The supplement is divided into three appen- dices: the first on MERS for Gaussian processes, and the remaining two on, respectively, the theory and the experimental results of MERS for Markov chains.

  9. A Note on Boolean Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Fidaleo, Francesco

    2015-03-01

    For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.

  10. On doubly stochastic rarefaction of renewal processes

    NASA Astrophysics Data System (ADS)

    Korolev, V. Yu.; Korchagin, A. Yu.; Zeifman, A. I.

    2017-07-01

    In the paper, the concepts of π-mixed geometric and π-mixed binomial distributions are introduced within the setting of Bernoulli trials with a random probability of success. A generalization of the Rényi theorem concerning the asymptotic behavior of rarefied renewal processes is proved for doubly stochastic rarefaction resulting in that the limit process is mixed Poisson.

  11. Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case.

    PubMed

    Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem

    2015-01-01

    In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing-van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance.

  12. Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case

    PubMed Central

    Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem

    2015-01-01

    In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756

  13. On a class of nonstationary stochastic processes

    NASA Technical Reports Server (NTRS)

    Miamee, A. G.; Hardin, Jay C.

    1989-01-01

    A new class of nonstationary stochastic processes is introduced and some of the essential properties of its members are investigated. This class is richer than the class of stationary processes and has the potential of modeling some nonstationary time series. The relation between these newly defined processes with other important classes of nonstationary processes is investigated. Several examples of linearly correlated processes which are not stationary, periodically correlated, or harmonizable are given.

  14. Stochastic processes in muon ionization cooling

    NASA Astrophysics Data System (ADS)

    Errede, D.; Makino, K.; Berz, M.; Johnstone, C. J.; Van Ginneken, A.

    2004-02-01

    A muon ionization cooling channel consists of three major components: the magnet optics, an acceleration cavity, and an energy absorber. The absorber of liquid hydrogen contained by thin aluminum windows is the only component which introduces stochastic processes into the otherwise deterministic acceleration system. The scattering dynamics of the transverse coordinates is described by Gaussian distributions. The asymmetric energy loss function is represented by the Vavilov distribution characterized by the minimum number of collisions necessary for a particle undergoing loss of the energy distribution average resulting from the Bethe-Bloch formula. Examples of the interplay between stochastic processes and deterministic beam dynamics are given.

  15. Regeneration of stochastic processes: an inverse method

    NASA Astrophysics Data System (ADS)

    Ghasemi, F.; Peinke, J.; Sahimi, M.; Rahimi Tabar, M. R.

    2005-10-01

    We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.

  16. Stochastic bifurcation for a white-noise perturbed nonlinear oscillator

    NASA Astrophysics Data System (ADS)

    Baxendale, Peter

    2005-03-01

    Consider the vibrations of a thin beam excited by longitudinal white noise. The amplitude of the first mode of vibration evolves according to a 2-dimensional nonlinear stochastic differential equation. The white noise enters in a multiplicative fashion and so the origin is a fixed point for the system. When the noise intensity is sufficiently small relative to the coefficient of linear dissipation the origin is almost surely stable; however as the noise intensity is increased beyond a critical level the origin becomes almost surely unstable and the system evolves as a recurrent diffusion on the rest of the 2-dimensional space. We will discuss rigorous results on the changes in behavior of the system, and in particular the nature of its stationary measures, as the noise intensity passes through its critical level. In particular we identify the critical noise level, and the scaling of stationary moments just above the critical level. These results validate earlier numerical simulations of Wedig, Springer Lect. Notes Math., Vol 1486 (1991). The techniques used extend to a wide class of finite dimensional stochastic differential equations with a fixed point.

  17. Stochastic processes, estimation theory and image enhancement

    NASA Technical Reports Server (NTRS)

    Assefi, T.

    1978-01-01

    An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.

  18. Stochastic Processes and the Guttman Simplex

    ERIC Educational Resources Information Center

    Groen, Guy J.

    1971-01-01

    The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…

  19. Empirical method to measure stochasticity and multifractality in nonlinear time series.

    PubMed

    Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

    2013-12-01

    An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

  20. Empirical method to measure stochasticity and multifractality in nonlinear time series

    NASA Astrophysics Data System (ADS)

    Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

    2013-12-01

    An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

  1. Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

    SciTech Connect

    Kushner, Harold J.

    2012-08-15

    This two-part paper deals with 'foundational' issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.

  2. On strongly GA-convex functions and stochastic processes

    NASA Astrophysics Data System (ADS)

    Bekar, Nurgül Okur; Akdemir, Hande Günay; Işcan, Imdat

    2014-08-01

    In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.

  3. On strongly GA-convex functions and stochastic processes

    SciTech Connect

    Bekar, Nurgül Okur; Akdemir, Hande Günay; İşcan, İmdat

    2014-08-20

    In this study, we introduce strongly GA-convex functions and stochastic processes. We provide related well-known Kuhn type results and Hermite-Hadamard type inequality for strongly GA-convex functions and stochastic processes.

  4. Robust transport by multiple motors with nonlinear force-velocity relations and stochastic load sharing

    NASA Astrophysics Data System (ADS)

    Kunwar, Ambarish; Mogilner, Alexander

    2010-03-01

    Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force-velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the 'tug-of-war' of the multiple opposing motors.

  5. Robust transport by multiple motors with nonlinear force-velocity relations and stochastic load sharing.

    PubMed

    Kunwar, Ambarish; Mogilner, Alexander

    2010-02-10

    Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force-velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the 'tug-of-war' of the multiple opposing motors.

  6. Robust transport by multiple motors with nonlinear force–velocity relations and stochastic load sharing

    PubMed Central

    Kunwar, Ambarish; Mogilner, Alexander

    2010-01-01

    Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force–velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the ‘tug-of-war’ of the multiple opposing motors. PMID:20147778

  7. External Theory for Stochastic Processes.

    DTIC Science & Technology

    1985-11-01

    8217’ which are roughly of the order 1/n for p _ 0. n By using an embedding technique, these rates are extended also to Mkn and to point processes of...increasing, then (tl,., and (.T. (),..., Td ( d)) have the same dependence function. Hsing also extends these results to stationary dependent sequences {in

  8. Agent based reasoning for the non-linear stochastic models of long-range memory

    NASA Astrophysics Data System (ADS)

    Kononovicius, A.; Gontis, V.

    2012-02-01

    We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

  9. Finite-time H∞ filtering for non-linear stochastic systems

    NASA Astrophysics Data System (ADS)

    Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

    2016-09-01

    This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

  10. Diffusive processes in a stochastic magnetic field

    SciTech Connect

    Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R. |

    1995-05-01

    The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.

  11. Chromatography as Lévy stochastic process.

    PubMed

    Dondi, Francesco; Cavazzini, Alberto; Pasti, Luisa

    2006-09-08

    The Stochastic Theory of Chromatography has been revised in light of some of the most relevant Lévy's findings in Theory of Probability, including the so-called Lévy's distance, the characteristic function and the theory of infinitesimally divisible distributions. These concepts represent the key to exploit and understand, at a molecular basis, phenomena typical of chromatographic separations under linear conditions, such as peak tailing and splitting. In particular, Lévy's distance has been used to quantify the degree of convergence of real peaks towards an ideal Gaussian shape; the characteristic function properties, introduced by Lévy to deal with the problem of the addition of independent random variables, have been employed to solve a wide variety of chromatographic models (including adsorption on heterogeneous surfaces) and to interpret mobile phase dispersion from a probabilistic point of view. Finally, Lévy's studies concerning infinitesimally divisible distributions have allowed to introduce in the stochastic description of chromatography, effects associated to dispersion in mobile phase. It has been demonstrated that, according to Lévy's canonical representation of stochastic processes, the basis of chromatography is a mobile phase Poisson Process. Represented as a Lévy's process, the microscopic-probabilistic model of chromatography permits the establishment of a connection between single-molecule properties and their statistical fluctuations and shapes of real chromatographic peaks allowing, at the same time, for the constitution of a link between different branches of physical sciences.

  12. Prospect of Nonlinear Freak Tsunami Waves from Stochastic Earthquake Sources

    NASA Astrophysics Data System (ADS)

    Geist, E. L.

    2014-12-01

    The prospect of freak (or rogue) tsunami edge waves from continental subduction zone earthquakes is examined. Although the hydrodynamics that govern tsunamis are formulated from the shallow-water wave equations, the dispersion relation for edge waves is similar to that for deep-water waves. As a result, freak waves can result from many of the same mechanisms as for deep-water waves: spatial focusing, dispersive (temporal) focusing, modulation instability, and mode coupling from resonant interaction. The focus of this study is on determining the likelihood of freak edge waves from the two nonlinear mechanisms: modulation instability and mode coupling. The initial conditions are provided by coseismic vertical displacement from a subduction thrust earthquake. A two-dimensional stochastic slip model is used to generate a range of coseismic displacement realizations. The slip model is defined by a power-law wavenumber spectrum and Lévy-law distributed random variables. Tsunami edge waves produced by this source model have a broader spectrum with energy distributed across many more modes compared to edge waves derived from the simplified earthquake sources used in the past. To characterize modulation instability, methods developed for a random sea are modified for seismogenic edge waves. The Benjamin-Feir parameter constrains how many unstable wave packets are possible in a time series of finite length. In addition, because seismogenic tsunami edge wave energy is distributed across a number of modes, nonlinear mode coupling can result both in the collinear case and in the counter-propagating case where edge waves are reflected by coastline irregularities. Mode coupling results in the appearance of a third edge wave mode that can greatly increase the variability in wave heights. Determination of possible freak tsunami edge waves is important for assessing the tsunami hazard at longshore locations distant from the rupture zone of continental subduction zone earthquakes.

  13. Nonlinear high-order mode locking in stochastic sensory neurons

    NASA Astrophysics Data System (ADS)

    Rowe, Michael; Afghan, Muhammad; Neiman, Alexander

    2004-03-01

    Excitable systems demonstrate various mode locking regimes when driven by periodic external signals. With noise taken into account, such regimes represent complex nonlinear responses which depend crucially on the frequency and amplitude of the periodic drive as well as on the noise intensity. We study this using a computational model of a stochastic Hodgkin-Huxley neuron in combination with the turtle vestibular sensory system as an experimental model. A bifurcation analysis of the model is performed. Extracellular recordings from primary vestibular afferent neurons with two types of stimuli are used in the experimental study. First, mechanical stimuli applied to the labyrinth allow us to study the responses of the entire system, including transduction by the hair cells and spike generation in the primary afferents. Second, a galvanic stimuli applied directly to an afferent are used to study the responses of afferent spike generator directly. The responses to galvanic stimuli reveal multiple high-order mode locking regimes which are well reproduced in numerical simulation. Responses to mechanical stimulation are characterized by larger variability so that fewer mode-locking regimes can be observed.

  14. Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  15. 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

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

    NASA Astrophysics Data System (ADS)

    Scarpa, Luca

    2017-08-01

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

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

    SciTech Connect

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-06-20

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

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

    NASA Astrophysics Data System (ADS)

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-06-01

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

  19. Aperiodic signals processing via parameter-tuning stochastic resonance in a photorefractive ring cavity

    SciTech Connect

    Li, Xuefeng; Cao, Guangzhan; Liu, Hongjun

    2014-04-15

    Based on solving numerically the generalized nonlinear Langevin equation describing the nonlinear dynamics of stochastic resonance by Fourth-order Runge-Kutta method, an aperiodic stochastic resonance based on an optical bistable system is numerically investigated. The numerical results show that a parameter-tuning stochastic resonance system can be realized by choosing the appropriate optical bistable parameters, which performs well in reconstructing aperiodic signals from a very high level of noise background. The influences of optical bistable parameters on the stochastic resonance effect are numerically analyzed via cross-correlation, and a maximum cross-correlation gain of 8 is obtained by optimizing optical bistable parameters. This provides a prospective method for reconstructing noise-hidden weak signals in all-optical signal processing systems.

  20. A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow

    NASA Astrophysics Data System (ADS)

    Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.

    2014-12-01

    Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.

  1. Function projective synchronization between integer-order and stochastic fractional-order nonlinear systems.

    PubMed

    Geng, Lingling; Yu, Yongguang; Zhang, Shuo

    2016-09-01

    In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.

  2. Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

    PubMed

    Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

    2014-12-01

    In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

  3. Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity

    NASA Astrophysics Data System (ADS)

    Florchinger, Patrick

    2016-07-01

    The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.

  4. Switching of bound vector solitons for the coupled nonlinear Schroedinger equations with nonhomogenously stochastic perturbations

    SciTech Connect

    Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian

    2012-12-15

    We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schroedinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

  5. Analysis of bilinear stochastic systems. [involving multiplicative noise processes

    NASA Technical Reports Server (NTRS)

    Willsky, A. S.; Marcus, S. I.; Martin, D. N.

    1974-01-01

    Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

  6. Stochastic functionals and fluctuation theorem for multikangaroo processes.

    PubMed

    Van den Broeck, C; Toral, R

    2014-06-01

    We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.

  7. On using block pulse transform to perform equivalent linearization for a nonlinear Van der Pol oscillator under stochastic excitation

    NASA Astrophysics Data System (ADS)

    Younespour, Amir; Ghaffarzadeh, Hosein

    2016-06-01

    This paper applied the idea of block pulse (BP) transform in the equivalent linearization of a nonlinear system. The BP transform gives effective tools to approximate complex problems. The main goal of this work is on using BP transform properties in process of linearization. The accuracy of the proposed method compared with the other equivalent linearization including the stochastic equivalent linearization and the regulation linearization methods. Numerical simulations are applied to the nonlinear Van der Pol oscillator system under Gaussian white noise excitation to demonstrate the feasibility of the present method. Different values of nonlinearity are considered to show the effectiveness of the present method. Besides, by comparing the mean-square responses for divers values of nonlinearity and excitation intensity depicted the present method is able to approximate the behavior of nonlinear system and is in agreement with other methods.

  8. Nonlinear electric properties in biological system for stochastic computing (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Sumida, Saki; Yamaguchi, Harumasa; Ohyama, Hiroshi; Otsuka, Yoichi; Che, Dock-Chil; Matsumoto, Takuya

    2016-09-01

    Nonlinearity is the vital factor for stochastic computing. Toward the realization of brain-mimetic function using molecular network, the nonlinear electric properties of molecular systems are investigated in nanoscale with atomic force microscopy and nano-gap electrodes. Nonlinear current-voltage characteristics were observed for {Mo154/152}-ring, cytochorome c, and cytochrome c/DNA networks where the conduction paths include electron injection into weakly coupled discrete energy levels, electron tunneling through potential well, and electron hopping via Coulomb-blockade network. Stochastic resonance was observed in Cytochrome c/DNA network.

  9. On a theory of stability for nonlinear stochastic chemical reaction networks

    PubMed Central

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2015-01-01

    We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms. PMID:25978877

  10. On a theory of stability for nonlinear stochastic chemical reaction networks

    SciTech Connect

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2015-05-14

    We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.

  11. Time-dependent probability density function in cubic stochastic processes.

    PubMed

    Kim, Eun-Jin; Hollerbach, Rainer

    2016-11-01

    We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x,t) in general involves a time integral, and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g., in the short and long time limits). Numerical simulations of the Fokker-Planck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that transient PDFs behave drastically differently from the stationary PDFs in regard to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric with the kurtosis smaller than 3, transient PDFs are skewed with the kurtosis larger than 3; transient PDFs are much broader than stationary PDFs. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in the relaxation process.

  12. Classical analogs of quasifree quantum stochastic processes given by stochastic states of the quantized electromagnetic field

    NASA Astrophysics Data System (ADS)

    Hertfelder, C.; Kümmerer, B.

    2001-03-01

    The mathematical model describing a light beam prepared in an arbitrary quantum optical state is a quasifree quantum stochastic process on the C* algebra of the canonical commutatation relations. For such quantum stochastic processes the concept of stochastic states is introduced. Stochastic quantum states have a classical analog in the following sense: If the light beam is prepared in a stochastic state, one can construct a generalized classical stochastic process, such that the distributions of the quantum observables and the classical random variables coincide. A sufficient algebraic condition for the stochasticity of a quantum state is formulated. The introduced formalism generalizes the Wigner representation from a single field mode to a continuum of modes. For the special case of a single field mode the stochasticity condition provides a new criterion for the positivity of the Wigner function related to the given state. As an example the quantized eletromagnetic field in empty space at temperature T=0 is discussed. It turns out that the corresponding classical stochastic process is not a white noise but a colored noise with a linearly increasing spectrum.

  13. Non-Markovian stochastic processes: colored noise.

    PubMed

    Łuczka, J

    2005-06-01

    We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.

  14. Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

    PubMed

    Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

    2014-07-01

    Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs.

  15. Stochastic growth logistic model with aftereffect for batch fermentation process

    SciTech Connect

    Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

    2014-06-19

    In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

  16. Stochastic growth logistic model with aftereffect for batch fermentation process

    NASA Astrophysics Data System (ADS)

    Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

    2014-06-01

    In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

  17. On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems.

    PubMed

    Zhu, Wei-qiu; Ying, Zu-guang

    2004-11-01

    A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.

  18. Estimation and Analysis of Nonlinear Stochastic Systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Marcus, S. I.

    1975-01-01

    The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

  19. Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation

    NASA Astrophysics Data System (ADS)

    Yang, Yongge; Xu, Wei; Sun, Yahui; Xiao, Yanwen

    2017-01-01

    This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.

  20. Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

    NASA Astrophysics Data System (ADS)

    Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei

    2016-07-01

    This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

  1. Magnetic stochasticity and transport due to nonlinearly excited subdominant microtearing modes

    SciTech Connect

    Hatch, D. R.; Jenko, F.; Doerk, H.; Pueschel, M. J.; Terry, P. W.; Nevins, W. M.

    2013-01-15

    Subdominant, linearly stable microtearing modes are identified as the main mechanism for the development of magnetic stochasticity and transport in gyrokinetic simulations of electromagnetic ion temperature gradient driven plasma microturbulence. The linear eigenmode spectrum is examined in order to identify and characterize modes with tearing parity. Connections are demonstrated between microtearing modes and the nonlinear fluctuations that are responsible for the magnetic stochasticity and electromagnetic transport, and nonlinear coupling with zonal modes is identified as the salient nonlinear excitation mechanism. A simple model is presented, which relates the electromagnetic transport to the electrostatic transport. These results may provide a paradigm for the mechanisms responsible for electromagnetic stochasticity and transport, which can be examined in a broader range of scenarios and parameter regimes.

  2. Power spectra reveal the influence of stochasticity on nonlinear population dynamics

    PubMed Central

    Reuman, Daniel C.; Desharnais, Robert A.; Costantino, Robert F.; Ahmad, Omar S.; Cohen, Joel E.

    2006-01-01

    Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations. PMID:17116860

  3. Iterative splitting method as almost asymptotic symplectic integrator for stochastic nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Geiser, Jürgen

    2017-07-01

    In this paper, we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schrödinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is based on rewriting an iterative splitting approach as a successive approximation method based on a contraction mapping principle and that we have an almost symplectic scheme. We apply a stochastic differential equation, that we can decouple into deterministic and stochastic parts, while each part can be solved analytically. Such decompositions allow accelerating the methods and preserving, under suitable conditions, the symplecticity of the schemes. A numerical analysis and application to the stochastic Schrödunger equation are presented.

  4. Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information

    NASA Astrophysics Data System (ADS)

    Ryashko, Lev

    2015-11-01

    A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

  5. Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination.

    PubMed

    Wang, Lei; Teng, Zhidong; Tang, Tingting; Li, Zhiming

    2017-01-01

    In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.

  6. Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information

    SciTech Connect

    Ryashko, Lev

    2015-11-30

    A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

  7. Reversibility in Quantum Models of Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Gier, David; Crutchfield, James; Mahoney, John; James, Ryan

    Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.

  8. Nonlinear biochemical signal processing via noise propagation

    NASA Astrophysics Data System (ADS)

    Kim, Kyung Hyuk; Qian, Hong; Sauro, Herbert M.

    2013-10-01

    Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance, fluctuations in biochemical activities become significant and such "noise" can propagate through regulatory cascades in terms of biochemical reaction networks. Here we develop an intuitive, yet fully quantitative method for analyzing how noise affects cellular phenotypes based on identifying a system's nonlinearities and noise propagations. We observe that such noise can simultaneously enhance sensitivities in one behavioral region while reducing sensitivities in another. Employing this novel phenomenon we designed three biochemical signal processing modules: (a) A gene regulatory network that acts as a concentration detector with both enhanced amplitude and sensitivity. (b) A non-cooperative positive feedback system, with a graded dose-response in the deterministic case, that serves as a bistable switch due to noise-induced ultra-sensitivity. (c) A noise-induced linear amplifier for gene regulation that requires no feedback. The methods developed in the present work allow one to understand and engineer nonlinear biochemical signal processors based on fluctuation-induced phenotypes.

  9. Minimum Entropy Rate Simplification of Stochastic Processes.

    PubMed

    Henter, Gustav Eje; Kleijn, W Bastiaan

    2016-12-01

    We propose minimum entropy rate simplification (MERS), an information-theoretic, parameterization-independent framework for simplifying generative models of stochastic processes. Applications include improving model quality for sampling tasks by concentrating the probability mass on the most characteristic and accurately described behaviors while de-emphasizing the tails, and obtaining clean models from corrupted data (nonparametric denoising). This is the opposite of the smoothing step commonly applied to classification models. Drawing on rate-distortion theory, MERS seeks the minimum entropy-rate process under a constraint on the dissimilarity between the original and simplified processes. We particularly investigate the Kullback-Leibler divergence rate as a dissimilarity measure, where, compatible with our assumption that the starting model is disturbed or inaccurate, the simplification rather than the starting model is used for the reference distribution of the divergence. This leads to analytic solutions for stationary and ergodic Gaussian processes and Markov chains. The same formulas are also valid for maximum-entropy smoothing under the same divergence constraint. In experiments, MERS successfully simplifies and denoises models from audio, text, speech, and meteorology.

  10. Prediction and control of chaotic processes using nonlinear adaptive networks

    SciTech Connect

    Jones, R.D.; Barnes, C.W.; Flake, G.W.; Lee, K.; Lewis, P.S.; O'Rouke, M.K.; Qian, S.

    1990-01-01

    We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We then present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series, tidal prediction in Venice lagoon, finite differencing, sonar transient detection, control of nonlinear processes, control of a negative ion source, balancing a double inverted pendulum and design advice for free electron lasers and laser fusion targets.

  11. Stochastic Impulse Control of Non-Markovian Processes

    SciTech Connect

    Djehiche, Boualem; Hamadene, Said Hdhiri, Ibtissam

    2010-02-15

    We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.

  12. Nonlinear control of fixed-wing UAVs in presence of stochastic winds

    NASA Astrophysics Data System (ADS)

    Rubio Hervas, Jaime; Reyhanoglu, Mahmut; Tang, Hui; Kayacan, Erdal

    2016-04-01

    This paper studies the control of fixed-wing unmanned aerial vehicles (UAVs) in the presence of stochastic winds. A nonlinear controller is designed based on a full nonlinear mathematical model that includes the stochastic wind effects. The air velocity is controlled exclusively using the position of the throttle, and the rest of the dynamics are controlled with the aileron, elevator, and rudder deflections. The nonlinear control design is based on a smooth approximation of a sliding mode controller. An extended Kalman filter (EKF) is proposed for the state estimation and filtering. A case study is presented: landing control of a UAV on a ship deck in the presence of wind based exclusively on LADAR measurements. The effectiveness of the nonlinear control algorithm is illustrated through a simulation example.

  13. On Stochastic Processes with Constant Valuation

    NASA Astrophysics Data System (ADS)

    Abbas, Ali E.

    2009-12-01

    In the probability literature, a martingale is often referred to as a fair game. A risk neutral decision maker would be indifferent to engaging in a martingale investment for any number of stages or not engaging into it at all if its expected value is equal to his current wealth. But a risk-averse decision maker would not accept a martingale pay-off in exchange for its expected value since his certain equivalent for uncertain deals is less than their mean. Therefore the traditional martingale sequences that are widely studied in probability and finance are not rational investments for risk averse decision makers. A risk seeking decision maker, on the other hand would welcome a martingale investment, since the certain equivalent is larger than the mean. We introduce a class of stochastic processes whose expected utility is constant and equal to the utility of the current wealth. We refer to such processes as risk-adjusted martingales. We show how to construct such processes for any continuous and strictly monotonic utility function.

  14. Nonlinear Processes in Vibroseismic Monitoring

    SciTech Connect

    Khairetdinov, M. S.; Voskoboynikova, G. M.

    2008-06-24

    In this paper, on the basis of numerical calculations and results of processing of the data of field experiments, quantitative estimates of the spectral broadening of the initial sounding seismic oscillations are presented. The estimates were obtained as a result of vibroseismic sounding of fractured dilatancy media typical for seismically and volcanically dangerous zones. The authors' idea about the applicability of the parameters of wave field nonlinearity in the form of possible prognostic characteristics of the earthquake-volcano source development process is justified.

  15. Expectation propagation for continuous time stochastic processes

    NASA Astrophysics Data System (ADS)

    Cseke, Botond; Schnoerr, David; Opper, Manfred; Sanguinetti, Guido

    2016-12-01

    We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.

  16. Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

    NASA Astrophysics Data System (ADS)

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

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

  17. Stochastic processes in the interstellar medium

    NASA Astrophysics Data System (ADS)

    Bron, Emeric

    2014-11-01

    In this thesis, I have tackled two seemingly unrelated problems in the modeling of the neutral interstellar medium (ISM). The first is the description of H2 formation on interstellar dust grains under realistic conditions. The precise determination of the H2 formation rate and abundance is crucial, as it controls most of the subsequent development of the chemical complexity in the ISM, as well as part of its physics. The temperature of small grains (less than 10 nm) fluctuates constantly as those grains are sensitive to the energy of individual UV photons, and the surface mechanisms of H2 formation, which are sensitive to the grain temperature, are kept out of equilibrium by the fluctuations. I have developed an exact resolution formalism for the statistical equilibrium of this system, and implemented its numerical resolution. Among other results, taking the fluctuations into account leads to large differences for the Langmuir-Hinshelwood mechanism, whose efficiency is increased in atomic gas and decreased inside molecular gas. The second problem is related to the ubiquitous presence of molecules such as CH+, whose formation is highly endothermic, in the diffuse ISM where the observed gas temperature (less than 100 K) is insufficient to trigger their formation. It has been proposed that the intermittent dissipation of turbulence could inject the necessary energy, creating hot spots, which could also explain the observed rotational excitation of H2 in such regions. At small scales, the gas is thus perturbed by strong fluctuations of the energy injection rate. I propose a model for the Lagrangian evolution of the local physico-chemical state of the gas based on stochastic processes, and apply it to derive the distribution of the gas temperature in the diffuse atomic medium, and the average excitation of H2 in the diffuse molecular gas. Both problems are thus similar and can be described in a more abstract way as systems whose state is perturbed by strong fluctuations

  18. Nonlinear dirac and diffusion equations in 1+1 dimensions from stochastic considerations

    PubMed

    Maharana

    2000-08-01

    We generalize the method of obtaining fundamental linear partial differential equations such as the diffusion and Schrodinger equation, the Dirac, and the telegrapher's equation from a simple stochastic consideration to arrive at a certain nonlinear form of these equations. A group classification through a one-parameter group of transformations for two of these equations is also carried out.

  19. Stochastic nonlinear wave equation with memory driven by compensated Poisson random measures

    SciTech Connect

    Liang, Fei; Gao, Hongjun

    2014-03-15

    In this paper, we study a class of stochastic nonlinear wave equation with memory driven by Lévy noise. We first show the existence and uniqueness of global mild solutions using a suitable energy function. Second, under some additional assumptions we prove the exponential stability of the solutions.

  20. Asymptotic behaviors of a stochastic delayed SIR epidemic model with nonlinear incidence

    NASA Astrophysics Data System (ADS)

    Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

    2016-11-01

    In this paper, we consider a stochastic delayed SIR epidemic model with nonlinear incidence. We firstly show that the system has a unique global positive solution with any positive initial value, then by constructing some suitable Lyapunov functionals, we investigate the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium, respectively.

  1. Stochastic regimes in the driven oscillator with a step-like nonlinearity

    SciTech Connect

    Bulanov, S. V.; Esirkepov, T. Zh.; Koga, J. K.; Kondo, K.; Kando, M.; Yogo, A.; Bulanov, S. S.

    2015-06-15

    A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the electron energization in the strong electromagnetic wave interaction with thin targets.

  2. Noise bandwidth dependence of soliton phase in simulations of stochastic nonlinear Schrödinger equations.

    PubMed

    Cargill, Daniel S; Moore, Richard O; McKinstrie, C J

    2011-05-01

    We demonstrate that soliton perturbation theory, though widely used, predicts an incorrect phase distribution for solitons of stochastically driven nonlinear Schrödinger equations in physically relevant parameter regimes. We propose a simple variational model that accounts for the effect of radiation on phase evolution and correctly predicts its distribution.

  3. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

    PubMed

    Leszczynski, Henryk; Wrzosek, Monika

    2017-02-01

    We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

  4. On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie

    2017-02-01

    We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.

  5. Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks.

    PubMed

    Smadbeck, Patrick; Kaznessis, Yiannis N

    2014-08-01

    Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized.

  6. Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks

    PubMed Central

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2014-01-01

    Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized. PMID:25215268

  7. The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence

    PubMed Central

    Rifhat, Ramziya; Ge, Qing; Teng, Zhidong

    2016-01-01

    A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value R~0. That is, when R~0<1 and together with an additional condition, the disease is extinct with probability one, and when R~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when R~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems. PMID:27418943

  8. The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence.

    PubMed

    Rifhat, Ramziya; Ge, Qing; Teng, Zhidong

    2016-01-01

    A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value [Formula: see text]. That is, when [Formula: see text] and together with an additional condition, the disease is extinct with probability one, and when [Formula: see text], the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when [Formula: see text], the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.

  9. Stochastic Simulations of Cellular Biological Processes

    DTIC Science & Technology

    2007-06-01

    model kinetics of a system of chemical reactions is to use a stochastic 2. Stochastic Simulation Algorithm approach in terms of the Chemical Master...number of processors and running time) for interactive disk spae ad, herfor, my ceat meory simulations. Therefore, in addition to running in an...management problems for simulations involving a large inteative mode, foNScan as o run in ’n number of long runs or for large reaction networks. interactive

  10. Stochastic resonance during a polymer translocation process

    NASA Astrophysics Data System (ADS)

    Mondal, Debasish; Muthukumar, M.

    2016-04-01

    We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

  11. Stochastic resonance during a polymer translocation process.

    PubMed

    Mondal, Debasish; Muthukumar, M

    2016-04-14

    We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

  12. Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities

    NASA Astrophysics Data System (ADS)

    Gao, Fangzheng; Wu, Yuqiang; Yu, Xin

    2016-12-01

    In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

  13. Soil Erosion as a stochastic process

    NASA Astrophysics Data System (ADS)

    Casper, Markus C.

    2015-04-01

    corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.

  14. Nonlinear transition dynamics in a time-delayed vibration isolator under combined harmonic and stochastic excitations

    NASA Astrophysics Data System (ADS)

    Yang, Tao; Cao, Qingjie

    2017-04-01

    Based on the quasi-zero stiffness vibration isolation (QZS-VI) system, nonlinear transition dynamics have been investigated coupled with both time-delayed displacement and velocity feedbacks. Using a delayed nonlinear Langevin approach, we discuss a new mechanism for the transition of a vibration isolator in which the energy originates from harmonic and noise excitations. For this stochastic process, the effective displacement potential, stationary probability density function and the escape ratio are obtained. We investigate a variety of noise-induced behaviors affecting the transitions between system equilibria states. The results indicate that the phenomena of transition, resonant activation and delay-enhanced stability may emerge in the QZS-VI system. Moreover, we also show that the time delay, delay feedback intensities, and harmonic excitation play significant roles in the resonant activation and delay-enhanced stability phenomena. Finally, a quantitative measure for amplitude response has been carried out to evaluate the isolation performance of the controlled QZS-VI system. The results show that with properly designed feedback parameters, time delay and displacement feedback intensity can play the role of a damping force. This research provides instructive ideas on the application of the time-delayed control in practical engineering.

  15. Further results on output-feedback regulation of stochastic nonlinear systems with SiISS inverse dynamics

    NASA Astrophysics Data System (ADS)

    Yu, Xin; Xie, Xue-Jun; Wu, Yu-Qiang

    2010-10-01

    This article further discusses the problem of output-feedback regulation for more general stochastic nonlinear systems with stochastic integral input-to-state stable inverse dynamics, and focuses on solving the important and unsolved problem proposed in Yu and Xie (Yu, X., and Xie, X.J. (2010), 'Output Feedback Regulation of Stochastic Nonlinear Systems with Stochastic iISS Inverse Dynamics', IEEE Transactions on Automatic Control, 55, 304-320): How to weaken the conditions on nonlinearities in drift and diffusion vector fields? Under the weaker conditions, how to make full use of the known information of stochastic nonlinear systems to design an adaptive output-feedback controller such that all the closed-loop signals are almost surely bounded and the output is driven to zero almost surely?

  16. Stochastic Gompertzian model for breast cancer growth process

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni Binti; Rosli, Norhayati

    2017-05-01

    In this paper, a stochastic Gompertzian model is developed to describe the growth process of a breast cancer by incorporating the noisy behavior into a deterministic Gompertzian model. The prediction quality of the stochastic Gompertzian model is measured by comparing the simulated result with the clinical data of breast cancer growth. The kinetic parameters of the model are estimated via maximum likelihood procedure. 4-stage stochastic Runge-Kutta (SRK4) is used to simulate the sample path of the model. Low values of mean-square error (MSE) of stochastic model indicate good fits. It is shown that the stochastic Gompertzian model is adequate in explaining the breast cancer growth process compared to the deterministic model counterpart.

  17. 100 years after Smoluchowski: stochastic processes in cell biology

    NASA Astrophysics Data System (ADS)

    Holcman, D.; Schuss, Z.

    2017-03-01

    100 years after Smoluchowski introduced his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from a large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here Smoluchowski’s approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation.

  18. Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes

    PubMed Central

    Dobos, László; Király, András; Abonyi, János

    2012-01-01

    Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. PMID:23213298

  19. Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics.

    PubMed

    Li, Yongming; Sui, Shuai; Tong, Shaocheng

    2017-02-01

    This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

  20. Recursive state estimation for discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks

    NASA Astrophysics Data System (ADS)

    Ding, Derui; Shen, Yuxuan; Song, Yan; Wang, Yongxiong

    2016-07-01

    This paper is concerned with the state estimation problem for a class of discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks. The stochastic nonlinearity described by statistical means which covers several classes of well-studied nonlinearities as special cases is taken into discussion. The randomly occurring deception attacks are modelled by a set of random variables obeying Bernoulli distributions with given probabilities. The purpose of the addressed state estimation problem is to design an estimator with hope to minimize the upper bound for estimation error covariance at each sampling instant. Such an upper bound is minimized by properly designing the estimator gain. The proposed estimation scheme in the form of two Riccati-like difference equations is of a recursive form. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed scheme.

  1. Consensus Problem Over High-Order Multiagent Systems With Uncertain Nonlinearities Under Deterministic and Stochastic Topologies.

    PubMed

    Rezaee, Hamed; Abdollahi, Farzaneh

    2016-12-06

    The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.

  2. Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

    SciTech Connect

    Kushner, Harold J.

    2012-08-15

    This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

  3. Idempotent Methods for Continuous Time Nonlinear Stochastic Control

    DTIC Science & Technology

    2012-09-13

    rotates the telescope of the optical pointing and tracking system. At the fine scale, actuation is achieved with a fine track mirror that is...the semi-ring to a ring (and hence a field) is not a possibility. From these basic operations, standard linear algebraic objects can be built...uytsxduxgS          . which are max-plus linear evolution operators. The dynamic programming propagation operator in the stochastic case

  4. Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia

    NASA Astrophysics Data System (ADS)

    Jung, P.; Cornell-Bell, A. H.

    Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.

  5. Identification of stochastic interactions in nonlinear models of structural mechanics

    NASA Astrophysics Data System (ADS)

    Kala, Zdeněk

    2017-07-01

    In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.

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

    PubMed Central

    Venturi, D.; Karniadakis, G. E.

    2014-01-01

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

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

    PubMed

    Venturi, D; Karniadakis, G E

    2014-06-08

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

  8. Fish Processed Production Planning Using Integer Stochastic Programming Model

    NASA Astrophysics Data System (ADS)

    Firmansyah, Mawengkang, Herman

    2011-06-01

    Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.

  9. Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

  10. Stochastic-Convective Transport with Nonlinear Reaction: Biodegradation With Microbial Growth

    NASA Astrophysics Data System (ADS)

    Ginn, T. R.; Simmons, C. S.; Wood, B. D.

    1995-01-01

    The representation of subsurface flow and reactive transport as an ensemble of one-dimensional stream tubes is extended to account for nonlinear biodegradation with coupled microbial growth. The Stochastic-convective reaction (SCR) model is derived for bioreaction of a single solute by a single class of microorganisms coupled with dynamic microbial growth. A new global variable, the integral of the solute degraded per unit length of system traversed, accounts for degradation. Dimensionless scaling and the method of characteristics are used to reduce the model, written for a single convecting reactor (stream tube), to a pair of coupled nonlinear functional equations for solute concentration and microbial biomass. Existence of a solution to the stream tube system is shown, both numerical and approximate analytical approaches to the solution are given, and example computations using both methods are presented. Conditions under which the stream tube solution is "canonical," or scalable to fit any permissible stream tube travel time function, arise from requirements for invariance (over the stream tube ensemble) of effective one-dimensional stream tubes used to represent transport along real stream tubes in three-dimensional space. Averaging of the stream tube solution over travel time and reaction properties representative of physical and chemical heterogeneities is described as a way to separate and upscale the processes of macrodispersion and microbiological reaction. The approach is exercised to simulate Monte Carlo average behavior of bioreactive transport in physically heterogeneous two-dimensional media. Results show that the method captures the ensemble average large-scale effects of the nonlinear reactions more accurately than done in the classical reactive convection-dispersion equation (CDR), even when the appropriate scale dependent dispersion coefficient is afforded to the CDR.

  11. Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory

    NASA Astrophysics Data System (ADS)

    Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua

    2014-04-01

    The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.

  12. An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

    NASA Astrophysics Data System (ADS)

    Erazo, Kalil; Nagarajaiah, Satish

    2017-06-01

    In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

  13. Constructing stochastic models from deterministic process equations by propensity adjustment

    PubMed Central

    2011-01-01

    Background Gillespie's stochastic simulation algorithm (SSA) for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME) in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic model for a biochemical

  14. Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes

    NASA Astrophysics Data System (ADS)

    Dong, Zhao; Xu, Lihu; Zhang, Xicheng

    2014-02-01

    In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1,2). To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by α-stable noises established in (Zhang in Stoch. Process. Appl. 123(4):1213-1228, 2013).

  15. Baldovin-Stella stochastic volatility process and Wiener process mixtures

    NASA Astrophysics Data System (ADS)

    Peirano, P. P.; Challet, D.

    2012-08-01

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

  16. Nonlinear Real-Time Optical Signal Processing.

    DTIC Science & Technology

    1981-06-30

    bandwidth and space-bandwidth products. Real-time homonorphic and loga- rithmic filtering by halftone nonlinear processing has been achieved. A...Page ABSTRACT 1 1. RESEARCH OBJECTIVES AND PROGRESS 3 I-- 1.1 Introduction and Project overview 3 1.2 Halftone Processing 9 1.3 Direct Nonlinear...time homomorphic and logarithmic filtering by halftone nonlinear processing has been achieved. A detailed analysis of degradation due to the finite gamma

  17. Bidirectional Classical Stochastic Processes with Measurements and Feedback

    NASA Technical Reports Server (NTRS)

    Hahne, G. E.

    2005-01-01

    A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

  18. Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination

    PubMed Central

    Wang, Lei; Tang, Tingting

    2017-01-01

    In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed. PMID:28194223

  19. Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Bashkirtseva, Irina; Ryashko, Lev

    2016-04-01

    A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.

  20. Stochastic similarities between hydroclimatic processes for variability characterization

    NASA Astrophysics Data System (ADS)

    Dimitriadis, Panayiotis; Markonis, Yannis; Iliopoulou, Theano; Gournari, Naya; Deligiannis, Ilias; Kastis, Paris; Nasika, Xristina; Lerias, Eleutherios; Moustakis, Yannis; Petsiou, Amalia; Sotiriadou, Alexia; Stefanidis, Eleutherios; Tyrogiannis, Vassilis; Feloni, Elisavet; Koutsoyiannis, Demetris

    2016-04-01

    The most important hydroclimatic processes such as temperature, dew point, wind, precipitation and river discharges are investigated for their stochastic behaviour on annual scale through several historical records. We investigate the stochastic similarities between them in terms of long-term persistence and we comment on their statistical variability giving emphasis on the last period. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

  1. Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent

    USGS Publications Warehouse

    Leirs, H.; Stenseth, N.C.; Nichols, J.D.; Hines, J.E.; Verhagen, R.; Verheyen, W.

    1997-01-01

    Ecology has long been troubled by the controversy over how populations are regulated. Some ecologists focus on the role of environmental effects, whereas others argue that density-dependent feedback mechanisms are central. The relative importance of both processes is still hotly debated, but clear examples of both processes acting in the same population are rare. Keyfactor analysis (regression of population changes on possible causal factors) and time-series analysis are often used to investigate the presence of density dependence, but such approaches may be biased and provide no information on actual demographic rates. Here we report on both density-dependent and density-independent effects in a murid rodent pest species, the multimammate rat Mastomys natalensis (Smith, 1834), using statistical capture-recapture models. Both effects occur simultaneously, but we also demonstrate that they do not affect all demographic rates in the same way. We have incorporated the obtained estimates of demographic rates in a population dynamics model and show that the observed dynamics are affected by stabilizing nonlinear density-dependent components coupled with strong deterministic and stochastic seasonal components.

  2. The effects of nonlinear series resonance on Ohmic and stochastic heating in capacitive discharges

    SciTech Connect

    Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, E.; Mussenbrock, Thomas; Brinkmann, Ralf Peter

    2008-06-15

    The flow of electron and ion conduction currents across a nonlinear capacitive sheath to the electrode surface self-consistently sets the dc bias voltage across the sheath. We incorporate these currents into a model of a homogeneous capacitive sheath in order to determine the enhancement of the Ohmic and stochastic heating due to self-excitation of the nonlinear series resonance in an asymmetric capacitive discharge. At lower pressures, the series resonance can enhance both the Ohmic and stochastic heating by factors of 2-4, with the Ohmic heating tending to zero as the pressure decreases. The model was checked, for a particular set of parameters, by a particle-in-cell (PIC) simulation using the homogeneous sheath approximation, giving good agreement. With a self-consistent Child-law sheath, the PIC simulation showed increased heating, as expected, whether the series resonance is important or not.

  3. A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

    NASA Technical Reports Server (NTRS)

    Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.

    1999-01-01

    In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

  4. Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

    PubMed

    Frank, T D

    2002-07-01

    Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.

  5. 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.

  6. Inferring physical parameters from Lagrangian trajectories using stochastic processes

    NASA Astrophysics Data System (ADS)

    Sykulski, A. M.; Lilly, J. M.; Early, J. J.; Olhede, S. C.

    2016-02-01

    We demonstrate how the theory of stochastic processes can be used to quantify physical features and test hypotheses from observed or modeled Lagrangian trajectories. We propose a simple technique for constructing physically motivated stochastic processes, and then estimating the parameters from observed data. Applications of our approach include new techniques for estimating diffusivity, inertial oscillations, and the decay rate of frequency spectra, amongst others. For example, we demonstrate that a basic four-parameter stochastic process captures the anisotropy of Lagrangian velocities in a quasi-geostrophic forced-dissipative turbulence simulation, and that the estimated anisotropy timescale can be used to infer the Rhines scale of the system. We also highlight how stochastic processes can be used to infer physical features of other datasets, such as trajectories obtained from the Global Drifter Program.The stochastic models we propose are simple, ranging from 3 to 6 parameters depending on the application. This allows for an easy physical interpretation of each parameter, and allows parameters to be estimated from relatively short trajectories. This is useful when data is sparse or when the trajectory is traversing an inhomogeneous environment. Our models handle many of the practicalities of observed data, such as nonstationarity, anisotropy and inhomogeneity, as we demonstrate with examples. The stochastic approach is then combined with statistical theory to construct confidence intervals of the parameter estimates, as well as performing various hypothesis tests, such as testing for anisotropy, or for the presence of frequency-shifted inertial oscillations due to eddies.

  7. Stochastic bifurcations in the nonlinear parallel Ising model.

    PubMed

    Bagnoli, Franco; Rechtman, Raúl

    2016-11-01

    We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

  8. Stochastic bifurcations in the nonlinear parallel Ising model

    NASA Astrophysics Data System (ADS)

    Bagnoli, Franco; Rechtman, Raúl

    2016-11-01

    We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

  9. A discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Lu, F.; Chorin, A. J.

    2015-12-01

    Prediction for a high-dimensional nonlinear dynamic system often encounters difficulties: the system may be too complicated to solve in full, and initial data may be missing because only a small subset of variables is observed. However, only a small subset of the variables may be of interest and need to be predicted. We present a solution by developing a discrete stochastic reduced system for the variables of interest, in which one formulates discrete solvable approximate equations for these variables and uses data and statistical methods to account for the impact of the other variables. The stochastic reduced system can capture the long-time statistical properties of the full system as well as the short-time dynamics, and hence make reliable predictions. A key ingredient in the construction of the stochastic reduced system is a discrete-time stochastic parametrization based on the NARMAX (nonlinear autoregression moving average with exogenous input) model. As an example, this construction is applied to the Lorenz 96 system.

  10. Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

    NASA Astrophysics Data System (ADS)

    Chassaing, J.-C.; Lucor, D.; Trégon, J.

    2012-01-01

    An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.

  11. A System Identification and Change Detection Methodology for Stochastic Nonlinear Dynamic Systems

    SciTech Connect

    Yun, Hae-Bum; Masri, Sami F.; Caffrey, John P.

    2008-07-08

    In this paper a component-level detection methodology for system identification and change detection is discussed. The methodology is based on non-parametric, data-driven, stochastic system identification classifications using statistical pattern recognition techniques. In order to validate the methodology discussed in this paper an experimental study was performed using a complex nonlinear magneto-rheological (MR) damper. The results of this study show that the proposed methodology is very promising to detect interpret changes in critical structural components such as nonlinear springs joints as well as various types of dampers.

  12. Universal fractality of morphological transitions in stochastic growth processes.

    PubMed

    Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V

    2017-06-14

    Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.

  13. Random vibration of nonlinear beams by the new stochastic linearization technique

    NASA Technical Reports Server (NTRS)

    Fang, J.

    1994-01-01

    In this paper, the beam under general time dependent stationary random excitation is investigated, when exact solution is unavailable. Numerical simulations are carried out to compare its results with those yielded by the conventional linearization techniques. It is found that the modified version of the stochastic linearization technique yields considerably more accurate results for the mean square displacement of the beam than the conventional equivalent linearization technique, especially in the case of large nonlinearity.

  14. Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

    NASA Astrophysics Data System (ADS)

    Caraballo, Tomás; Morillas, F.; Valero, J.

    In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

  15. Adaptive mesh refinement for stochastic reaction-diffusion processes

    SciTech Connect

    Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros

    2011-01-01

    We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.

  16. Determining design gust loads for nonlinear aircraft similarity between methods based on matched filter theory and on stochastic simulation

    NASA Technical Reports Server (NTRS)

    Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III

    1992-01-01

    This is a work-in-progress paper. It explores the similarity between the results from two different analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for nonlinear aircraft. To date, numerical studies have been performed using two different nonlinear aircraft configurations. These studies demonstrate that results from the deterministic analysis method are realizable in the stochastic analysis method.

  17. Nonlinear stochastic controllers for power-flow-constrained vibratory energy harvesters

    NASA Astrophysics Data System (ADS)

    Cassidy, Ian L.; Scruggs, Jeffrey T.

    2013-06-01

    This study addresses the formulation of nonlinear feedback controllers for stochastically excited vibratory energy harvesters. Maximizing the average power generated from such systems requires the transducer current to be regulated using a bi-directional power electronic converter. There are many applications where the implementation of these types of converters is infeasible, due to the higher parasitic losses they must sustain. If instead the transducer current is regulated using a converter capable of single-directional power-flow, then these parasitic losses can be reduced significantly. However, the constraint on the power-flow directionality restricts the domain of feasible feedback laws. The only feasible linear feedback law imposes a static relationship between current and voltage, i.e., a static admittance. In stochastic response, the power generation performance can be enhanced significantly beyond that of the optimal static admittance, using nonlinear feedback. In this paper, a general approach to nonlinear control synthesis for power-flow-constrained energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance in stationary stochastic response. Simulation results are presented for a single-degree-of-freedom resonant oscillator with an electromagnetic transducer, as well as for a piezoelectric bimorph cantilever beam.

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

    PubMed Central

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

    2009-01-01

    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. PMID:19862351

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  1. Non-linear stochastic optimal control of acceleration parametrically excited systems

    NASA Astrophysics Data System (ADS)

    Wang, Yong; Jin, Xiaoling; Huang, Zhilong

    2016-02-01

    Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.

  2. Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

    SciTech Connect

    Barbu, Viorel Da Prato, Giuseppe

    2006-03-15

    This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods.The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P{sub t}. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure {nu}. Moreover, we solve the Kolmogorov equation and prove the so-called 'identite du carre du champs'. This will be used to study the Sobolev space W{sup 1,2}(H,{nu}) and to obtain information on the domain of the infinitesimal generator of P{sub t}.

  3. Stochastic diffusion processes on Cartesian meshes

    PubMed Central

    Meinecke, Lina; Lötstedt, Per

    2015-01-01

    Diffusion of molecules is simulated stochastically by letting them jump between voxels in a Cartesian mesh. The jump coefficients are first derived using finite difference, finite element, and finite volume approximations of the Laplacian on the mesh. An alternative is to let the first exit time for a molecule in random walk in a voxel define the jump coefficient. Such coefficients have the advantage of always being non-negative. These four different ways of obtaining the diffusion propensities are compared theoretically and in numerical experiments. A finite difference and a finite volume approximation generate the most accurate coefficients. PMID:26594087

  4. Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.

    PubMed

    Herzallah, Randa

    2015-03-01

    Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

  5. Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

    PubMed

    Gallop, Robert J; Mode, Charles J; Sleeman, Candace K

    2002-01-01

    When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm.

  6. Stochastic Processes in Physics: Deterministic Origins and Control

    NASA Astrophysics Data System (ADS)

    Demers, Jeffery

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

  7. Stochastic filtering for damage identification through nonlinear structural finite element model updating

    NASA Astrophysics Data System (ADS)

    Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.

    2015-03-01

    This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.

  8. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    SciTech Connect

    Keanini, R.G.

    2011-04-15

    Research Highlights: > Systematic approach for physically probing nonlinear and random evolution problems. > Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. > Organization of near-molecular scale vorticity mediated by hydrodynamic modes. > Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion

  9. Stochastic and Deterministic Assembly Processes in Subsurface Microbial Communities

    SciTech Connect

    Stegen, James C.; Lin, Xueju; Konopka, Allan; Fredrickson, Jim K.

    2012-03-29

    A major goal of microbial community ecology is to understand the forces that structure community composition. Deterministic selection by specific environmental factors is sometimes important, but in other cases stochastic or ecologically neutral processes dominate. Lacking is a unified conceptual framework aiming to understand why deterministic processes dominate in some contexts but not others. Here we work towards such a framework. By testing predictions derived from general ecological theory we aim to uncover factors that govern the relative influences of deterministic and stochastic processes. We couple spatiotemporal data on subsurface microbial communities and environmental parameters with metrics and null models of within and between community phylogenetic composition. Testing for phylogenetic signal in organismal niches showed that more closely related taxa have more similar habitat associations. Community phylogenetic analyses further showed that ecologically similar taxa coexist to a greater degree than expected by chance. Environmental filtering thus deterministically governs subsurface microbial community composition. More importantly, the influence of deterministic environmental filtering relative to stochastic factors was maximized at both ends of an environmental variation gradient. A stronger role of stochastic factors was, however, supported through analyses of phylogenetic temporal turnover. While phylogenetic turnover was on average faster than expected, most pairwise comparisons were not themselves significantly non-random. The relative influence of deterministic environmental filtering over community dynamics was elevated, however, in the most temporally and spatially variable environments. Our results point to general rules governing the relative influences of stochastic and deterministic processes across micro- and macro-organisms.

  10. Adaptive fuzzy decentralised control for stochastic nonlinear large-scale systems in pure-feedback form

    NASA Astrophysics Data System (ADS)

    Tong, Shaocheng; Xu, Yinyin; Li, Yongming

    2015-06-01

    This paper is concerned with the problem of adaptive fuzzy decentralised output-feedback control for a class of uncertain stochastic nonlinear pure-feedback large-scale systems with completely unknown functions, the mismatched interconnections and without requiring the states being available for controller design. With the help of fuzzy logic systems approximating the unknown nonlinear functions, a fuzzy state observer is designed estimating the unmeasured states. Therefore, the nonlinear filtered signals are incorporated into the backstepping recursive design, and an adaptive fuzzy decentralised output-feedback control scheme is developed. It is proved that the filter system converges to a small neighbourhood of the origin based on appropriate choice of the design parameters. Simulation studies are included illustrating the effectiveness of the proposed approach.

  11. Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints.

    PubMed

    Wang, Huanqing; Chen, Bing; Liu, Xiaoping; Liu, Kefu; Lin, Chong

    2013-12-01

    This paper is concerned with the problem of adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with input saturation. To overcome the design difficulty from nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is first introduced to approximate the saturation function; then, an adaptive fuzzy tracking controller based on the mean-value theorem is constructed by using backstepping technique. The proposed adaptive fuzzy controller guarantees that all signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighborhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.

  12. Thermodynamic and stochastic theory of hydrodynamic and power-producing processes

    SciTech Connect

    Ross, J.

    1992-09-16

    Thermodynamics of the transport processes of diffusion, thermal conduction, and viscous flow at a macroscopic level are developed for the simplest cases of one-dimensional transport in fluids for individual linear and nonlinear processes approaching a stationary non-equilibrium state. Formulation has started of thermodynamic and stochastic theory of combinations of transport processes. Global thermodynamic and stochastic theory of open chemical systems frar from equilibrium is continued with analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states with assumed local equilibrium. Stationary solutions are obtained of the master equation for single and multi-intermediate autocatalytic chemical systems. A kinetic potential is identified that governs the deterministic time evolution of coupled tank reactors. A second-order response theory was developed to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor.

  13. Stochastic Stability of Nonlinear 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

    This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works 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. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

  14. Stochastic dynamics of electric dipole in external electric fields: A perturbed nonlinear pendulum approach

    NASA Astrophysics Data System (ADS)

    Kapranov, Sergey V.; Kouzaev, Guennadi A.

    2013-06-01

    The motion of a dipole in external electric fields is considered in the framework of nonlinear pendulum dynamics. A stochastic layer is formed near the separatrix of the dipole pendulum in a restoring static electric field under the periodic perturbation by plane-polarized electric fields. The width of the stochastic layer depends on the direction of the forcing field variation, and this width can be evaluated as a function of perturbation frequency, amplitude, and duration. A numerical simulation of the approximate stochastic layer width of a perturbed pendulum yields a multi-peak frequency spectrum. It is described well enough at high perturbation amplitudes by an analytical estimation based on the separatrix map with an introduced expression of the most effective perturbation phase. The difference in the fractal dimensions of the phase spaces calculated geometrically and using the time-delay reconstruction is attributed to the predominant development of periodic and chaotic orbits, respectively. The correlation of the stochastic layer width with the phase space fractal dimensions is discussed.

  15. Transient behavior of a stochastic process for screening progressive diseases.

    PubMed

    Houshyar, A; al-Khayyal, F A

    1991-01-01

    This paper extends a mathematical model developed by the authors for describing the stochastic process underlying the etiology of non-contagious progressive diseases. For a population with no prior history of scheduled screening, the number of undetected and detected diseased individuals in the population under an established screening policy is used to calculate the expected total screening cost at any given time during the transient period of the associated stochastic process. A graphical representation of our model shows the status of different subgroups of a particular age group at any time T, and provides a clear summary of the expected number of individuals whose disease remains undetected.

  16. Extreme Values of Queues, Point Processes and Stochastic Networks.

    DTIC Science & Technology

    2014-09-26

    AD-A158 619 EXTREMIE YALUES OF QUEUES POINT PROCESSES AND STOCHASTIC i/i NETUORKS(U) GEORGIA INST OF TECH ATLANTA R F SERFOZO 25 JUN 85 SFOSR-TR-85...O If "Extreme Values of Queues, Point Processes VW- and Stochastic Networks" 1 Grant No. AFOSR 84-0367 by Professor Richard F. Serfozo Industrial and...NOS. Bldg. 410 PROGRAM PROJECT TASK WORK UNIT Boiling AFB, D.C. 20332-6448 ELEMENT NO. NO. NO. NO. 61102F 2304 A5 11. TITLE (Include Security

  17. A unified nonlinear stochastic time series analysis for climate science.

    PubMed

    Moon, Woosok; Wettlaufer, John S

    2017-03-13

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

  18. A unified nonlinear stochastic time series analysis for climate science

    PubMed Central

    Moon, Woosok; Wettlaufer, John S.

    2017-01-01

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

  19. A unified nonlinear stochastic time series analysis for climate science

    NASA Astrophysics Data System (ADS)

    Moon, Woosok; Wettlaufer, John S.

    2017-03-01

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

  20. A unified nonlinear stochastic time series analysis for climate science

    NASA Astrophysics Data System (ADS)

    Moon, Woosok; Wettlaufer, John

    2017-04-01

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

  1. Nonlinear Phase Distortion in a Ti:Sapphire Optical Amplifier for Optical Stochastic Cooling

    SciTech Connect

    Andorf, Matthew; Lebedev, Valeri; Piot, Philippe; Ruan, Jinhao

    2016-06-01

    Optical Stochastic Cooling (OSC) has been considered for future high-luminosity colliders as it offers much faster cooling time in comparison to the micro-wave stochastic cooling. The OSC technique relies on collecting and amplifying a broadband optical signal from a pickup undulator and feeding the amplified signal back to the beam. It creates a corrective kick in a kicker undulator. Owing to its superb gain qualities and broadband amplification features, Titanium:Sapphire medium has been considered as a gain medium for the optical amplifier (OA) needed in the OSC*. A limiting factor for any OA used in OSC is the possibility of nonlinear phase distortions. In this paper we experimentally measure phase distortions by inserting a single-pass OA into one leg of a Mach-Zehnder interferometer. The measurement results are used to estimate the reduction of the corrective kick a particle would receive due to these phase distortions in the kicker undulator.

  2. Semi-analytical expression of stochastic closed curve attractors in nonlinear dynamical systems under weak noise

    NASA Astrophysics Data System (ADS)

    Guo, Kongming; Jiang, Jun; Xu, Yalan

    2016-09-01

    In this paper, a simple but accurate semi-analytical method to approximate probability density function of stochastic closed curve attractors is proposed. The expression of distribution applies to systems with strong nonlinearities, while only weak noise condition is needed. With the understanding that additive noise does not change the longitudinal distribution of the attractors, the high-dimensional probability density distribution is decomposed into two low-dimensional distributions: the longitudinal and the transverse probability density distributions. The longitudinal distribution can be calculated from the deterministic systems, while the probability density in the transverse direction of the curve can be approximated by the stochastic sensitivity function method. The effectiveness of this approach is verified by comparing the expression of distribution with the results of Monte Carlo numerical simulations in several planar systems.

  3. Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

    NASA Technical Reports Server (NTRS)

    Naguib, A.; Hudy, L.; Humphreys, W. M., Jr.

    2002-01-01

    Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

  4. Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements

    NASA Astrophysics Data System (ADS)

    Song, Jun; Niu, Yugang; Jia, Tinggang

    2016-09-01

    This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.

  5. Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion

    NASA Astrophysics Data System (ADS)

    Chotorlishvili, L.; Toklikishvili, Z.; Berakdar, J.

    2009-09-01

    We study a chain of nonlinear interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semiclassical dynamics is chaotic. This is achievable by tuning the external field parameters according to the method described in this paper. We show analytically for a finite spin chain that Arnold diffusion is the underlying mechanism for the present stochastic control. Quantum mechanically we consider the regime where the classical dynamics is regular or chaotic. For the latter we utilize the random matrix theory. The efficiency and the stability of the non-equilibrium quantum spin states are quantified by the time dependence of the Bargmann angle related to the geometric phases of the states.

  6. Anomalous scaling of stochastic processes and the Moses effect.

    PubMed

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

    2017-04-01

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

  7. Anomalous scaling of stochastic processes and the Moses effect

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

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

  8. Extending Newtonian Dynamics to Include Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2009-01-01

    A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.

  9. Fuzzy Adaptive Quantized Control for a Class of Stochastic Nonlinear Uncertain Systems.

    PubMed

    Liu, Zhi; Wang, Fang; Zhang, Yun; Chen, C L Philip

    2016-02-01

    In this paper, a fuzzy adaptive approach for stochastic strict-feedback nonlinear systems with quantized input signal is developed. Compared with the existing research on quantized input problem, the existing works focus on quantized stabilization, while this paper considers the quantized tracking problem, which recovers stabilization as a special case. In addition, uncertain nonlinearity and the unknown stochastic disturbances are simultaneously considered in the quantized feedback control systems. By putting forward a new nonlinear decomposition of the quantized input, the relationship between the control signal and the quantized signal is established, as a result, the major technique difficulty arising from the piece-wise quantized input is overcome. Based on fuzzy logic systems' universal approximation capability, a novel fuzzy adaptive tracking controller is constructed via backstepping technique. The proposed controller guarantees that the tracking error converges to a neighborhood of the origin in the sense of probability and all the signals in the closed-loop system remain bounded in probability. Finally, an example illustrates the effectiveness of the proposed control approach.

  10. Condition assessment of nonlinear processes

    DOEpatents

    Hively, Lee M.; Gailey, Paul C.; Protopopescu, Vladimir A.

    2002-01-01

    There is presented a reliable technique for measuring condition change in nonlinear data such as brain waves. The nonlinear data is filtered and discretized into windowed data sets. The system dynamics within each data set is represented by a sequence of connected phase-space points, and for each data set a distribution function is derived. New metrics are introduced that evaluate the distance between distribution functions. The metrics are properly renormalized to provide robust and sensitive relative measures of condition change. As an example, these measures can be used on EEG data, to provide timely discrimination between normal, preseizure, seizure, and post-seizure states in epileptic patients. Apparatus utilizing hardware or software to perform the method and provide an indicative output is also disclosed.

  11. Study of Nonlinear Mesoscale Processes: Applications to Lagrangian Data Analysis and Subgrid Scale Parameterization

    DTIC Science & Technology

    1997-09-30

    regions, and assimilation methods . In general, the accuracy of both short-term and long-term predictions improves signif- icantly with the assimilation of...Foundation (TAO Project). Assimilation methods for nonlinear Lagrangian processes and parameterization of turbu- lent phenomena using stochastic models are

  12. Stochastic processes in light-assisted nanoparticle formation

    NASA Astrophysics Data System (ADS)

    Naruse, Makoto; Liu, Yang; Nomura, Wataru; Yatsui, Takashi; Aida, Masaki; Kish, Laszlo B.; Ohtsu, Motoichi

    2012-05-01

    Recently, light-assisted nanofabrication have been introduced, such as the synthesis of quantum dots using photo-induced desorption that yields reduced size fluctuations or metal sputtering under light illumination resulting in self-organized, nanoparticle chains. The physical mechanisms have originally been attributed to material desorption or plasmon resonance effects. However, significant stochastic phenomena are also present that have not been explained yet. We introduce stochastic models taking account of the light-assisted processes that reproduce phenomenological characteristics consistent with the experimental observations.

  13. Refractory pulse counting processes in stochastic neural computers.

    PubMed

    McNeill, Dean K; Card, Howard C

    2005-03-01

    This letter quantitiatively investigates the effect of a temporary refractory period or dead time in the ability of a stochastic Bernoulli processor to record subsequent pulse events, following the arrival of a pulse. These effects can arise in either the input detectors of a stochastic neural network or in subsequent processing. A transient period is observed, which increases with both the dead time and the Bernoulli probability of the dead-time free system, during which the system reaches equilibrium. Unless the Bernoulli probability is small compared to the inverse of the dead time, the mean and variance of the pulse count distributions are both appreciably reduced.

  14. A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity

    NASA Astrophysics Data System (ADS)

    Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang

    2017-09-01

    A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 < 1, the disease eventually becomes extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.

  15. Tsallis distributions and 1/f noise from nonlinear stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Ruseckas, J.; Kaulakys, B.

    2011-11-01

    Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/fβ behavior of the power spectral density. The superstatistical framework to get 1/fβ noise with q-exponential and q-Gaussian distributions of the signal intensity is proposed, as well.

  16. 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

  17. Gene regulation and noise reduction by coupling of stochastic processes

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  18. Gene regulation and noise reduction by coupling of stochastic processes

    PubMed Central

    Hornos, José Eduardo M.; Reinitz, John

    2015-01-01

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

  19. Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Abrams, D.; Williams, C.

    1999-01-01

    We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.

  20. Gene regulation and noise reduction by coupling of stochastic processes.

    PubMed

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

    2015-02-01

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

  1. Concurrent processing in nonlinear structural stability

    NASA Technical Reports Server (NTRS)

    Darbhamulla, S. P.; Razzaq, Z.; Storaasli, O. O.

    1986-01-01

    A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the 'Finite Element Machine', developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.

  2. Concurrent processing in nonlinear structural stability

    NASA Technical Reports Server (NTRS)

    Darbhamulla, S. P.; Razzaq, Z.; Storaasli, O. O.

    1986-01-01

    A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the 'Finite Element Machine', developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.

  3. Multiresolution stochastic simulations of reaction-diffusion processes.

    PubMed

    Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros

    2008-10-21

    Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle models of physical processes.

  4. Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models.

    PubMed

    Huang, Guanghui; Wan, Jianping; Chen, Hui

    2013-02-01

    Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.

  5. An integrated optimal control algorithm for discrete-time nonlinear stochastic system

    NASA Astrophysics Data System (ADS)

    Kek, Sie Long; Lay Teo, Kok; Mohd Ismail, A. A.

    2010-12-01

    Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.

  6. Leader-Following Consensus for High-Order Nonlinear Stochastic Multiagent Systems.

    PubMed

    Hua, Changchun; Li, Yafeng; Guan, Xinping

    2017-01-24

    This paper considers the distributed consensus tracking problem for a class of high-order stochastic multiagent systems with uncertain nonlinear functions under a fixed undirected graph. Through the recursive method, the novel nonlinear distributed controllers are designed. By constructing a kind of special form for the virtual controller in the first step of recursive design, we realize that the state variables of every agent are separated except the outputs of the adjacency agents. The designed controller of each agent only depends on its own state variables and the outputs of the adjacent multiagents. With the proposed method, it is not required any more that the orders of the agents are same. This makes the designed controller be easier to be implemented and the proposed method be applicable for a wider class of multiagent systems. The efficiency of the design approach is illustrated by a simulation example.

  7. Analysis of degree of nonlinearity and stochastic nature of HRV signal during meditation using delay vector variance method.

    PubMed

    Reddy, L Ram Gopal; Kuntamalla, Srinivas

    2011-01-01

    Heart rate variability analysis is fast gaining acceptance as a potential non-invasive means of autonomic nervous system assessment in research as well as clinical domains. In this study, a new nonlinear analysis method is used to detect the degree of nonlinearity and stochastic nature of heart rate variability signals during two forms of meditation (Chi and Kundalini). The data obtained from an online and widely used public database (i.e., MIT/BIH physionet database), is used in this study. The method used is the delay vector variance (DVV) method, which is a unified method for detecting the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. From the results it is clear that there is a significant change in the nonlinearity and stochastic nature of the signal before and during the meditation (p value > 0.01). During Chi meditation there is a increase in stochastic nature and decrease in nonlinear nature of the signal. There is a significant decrease in the degree of nonlinearity and stochastic nature during Kundalini meditation.

  8. Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

    PubMed

    Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F

    2017-01-01

    A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

  9. Cox process representation and inference for stochastic reaction-diffusion processes.

    PubMed

    Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

    2016-05-25

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

  10. Cox process representation and inference for stochastic reaction-diffusion processes

    NASA Astrophysics Data System (ADS)

    Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

    2016-05-01

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

  11. Stochastic Optimal Regulation of Nonlinear Networked Control Systems by Using Event-Driven Adaptive Dynamic Programming.

    PubMed

    Sahoo, Avimanyu; Jagannathan, Sarangapani

    2017-02-01

    In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.

  12. A stochastic diffusion process for Lochner's generalized Dirichlet distribution

    DOE PAGES

    Bakosi, J.; Ristorcelli, J. R.

    2013-10-01

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

  13. A stochastic diffusion process for Lochner's generalized Dirichlet distribution

    SciTech Connect

    Bakosi, J.; Ristorcelli, J. R.

    2013-10-01

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

  14. Survival-time statistics for sample space reducing stochastic processes

    NASA Astrophysics Data System (ADS)

    Yadav, Avinash Chand

    2016-04-01

    Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic process that results in a random sequence of strictly decreasing integers {x (t )},0 ≤t ≤τ , with boundary conditions x (0 )=N and x (τ ) = 1. This model is shown to be exactly solvable: PN(τ ) , the probability that the process survives for time τ is analytically evaluated. In the limit of large N , the asymptotic form of this probability distribution is Gaussian, with mean and variance both varying logarithmically with system size: <τ >˜lnN and στ2˜lnN . Correspondence can be made between survival-time statistics in the SSR process and record statistics of independent and identically distributed random variables.

  15. Survival-time statistics for sample space reducing stochastic processes.

    PubMed

    Yadav, Avinash Chand

    2016-04-01

    Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic process that results in a random sequence of strictly decreasing integers {x(t)},0≤t≤τ, with boundary conditions x(0)=N and x(τ) = 1. This model is shown to be exactly solvable: P_{N}(τ), the probability that the process survives for time τ is analytically evaluated. In the limit of large N, the asymptotic form of this probability distribution is Gaussian, with mean and variance both varying logarithmically with system size: 〈τ〉∼lnN and σ_{τ}^{2}∼lnN. Correspondence can be made between survival-time statistics in the SSR process and record statistics of independent and identically distributed random variables.

  16. Stochastic modeling of transient stream aquifer interaction with the nonlinear Boussinesq equation

    NASA Astrophysics Data System (ADS)

    Srivastava, Kirti; Serrano, Sergio E.; Workman, S. R.

    2006-09-01

    SummaryIn this article the effect of highly fluctuating stream stage on the adjacent alluvial valley aquifer is studied with a new analytical solution to the nonlinear transient groundwater flow equation subject to stochastic conductivity and time varying boundary conditions. A random conductivity field with known correlation structure represents uncertain heterogeneity. The resulting nonlinear stochastic Boussinesq equation is solved with the decomposition method. New expressions for the mean of the hydraulic head and its variance distribution are given. The procedure allows for the calculation of the mean head and error bounds in real situations when a limited sample allows the estimation of the conductivity mean and correlation structure only. Under these circumstances, the usual assumptions of a specific conductivity probability distribution, logarithmic transformation, small perturbation, discretization, or Monte Carlo simulations are not possible. The solution is verified via an application to the Scioto River aquifer in Ohio, which suffers from periodic large fluctuations in river stage from seasonal flooding. Predicted head statistics are compared with observed heads at different monitoring wells across the aquifer. Results show that the observed transient water table elevation in the observation well lies in the predicted mean plus or minus one standard deviation bounds. The magnitude of uncertainty in predicted head depends on the statistical properties of the conductivity field, as described by its coefficient of variability and its correlation length scale.

  17. Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

    PubMed

    Sulis, William H

    2017-10-01

    Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

  18. Nonlinear Real-Time Optical Signal Processing

    DTIC Science & Technology

    1990-09-01

    pattern recognition. Additional work concerns the relationship of parallel computation paradigms to optical computing and halftone screen techniques...paradigms to optical computing and halftone screen techniques for implementing general nonlinear functions. 3\\ 2 Research Progress This section...Vol. 23, No. 8, pp. 34-57, 1986. 2.4 Nonlinear Optical Processing with Halftones : Degradation and Compen- sation Models This paper is concerned with

  19. Stochastic Analysis of Reaction–Diffusion Processes

    PubMed Central

    Hu, Jifeng; Kang, Hye-Won

    2013-01-01

    Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

  20. An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

    NASA Astrophysics Data System (ADS)

    Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

    2016-04-01

    Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction

  1. Stochastic MPC with applications to process control

    NASA Astrophysics Data System (ADS)

    Jurado, I.; Millán, P.; Quevedo, D.; Rubio, F. R.

    2015-04-01

    This paper presents a model predictive control formulation for Networked Control Systems subject to independent and identically distributed delays and packet dropouts. The design takes into account the presence of a communication network in the control loop, resorting to a buffer at the actuator side to store and consistently apply delayed control sequences when fresh control inputs are not available. The proposed approach uses a statistical description of transmissions to optimise the expected future control performance conditioned upon the current system state, previously calculated control packets and transmission acknowledgements. Experimental studies using a quadruple tank process illustrate the applicability of the method to process control.

  2. Litchi freshness rapid non-destructive evaluating method using electronic nose and non-linear dynamics stochastic resonance model.

    PubMed

    Ying, Xiaoguo; Liu, Wei; Hui, Guohua

    2015-01-01

    In this paper, litchi freshness rapid non-destructive evaluating method using electronic nose (e-nose) and non-linear stochastic resonance (SR) was proposed. EN responses to litchi samples were continuously detected for 6 d Principal component analysis (PCA) and non-linear stochastic resonance (SR) methods were utilized to analyze EN detection data. PCA method could not totally discriminate litchi samples, while SR signal-to-noise ratio (SNR) eigen spectrum successfully discriminated all litchi samples. Litchi freshness predictive model developed using SNR eigen values shows high predictive accuracy with regression coefficients R(2) = 0 .99396.

  3. Finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

    NASA Astrophysics Data System (ADS)

    Qi, Wenhai; Gao, Xianwen

    2016-01-01

    This paper focuses on the problem of finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. By employing an appropriate Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is designed to ensure H∞ finite-time boundedness of the resulting closed-loop system that contains time-varying delay, admissible external disturbance, It ?-type stochastic disturbance and nonlinearity. All the proposed conditions are established in the form of linear matrix inequalities. Finally, an example is given to demonstrate the validity of the main results.

  4. Deterministic geologic processes and stochastic modeling

    SciTech Connect

    Rautman, C.A.; Flint, A.L.

    1991-12-31

    Recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. Consideration of the spatial distribution of measured values and geostatistical measures of spatial variability indicates that there are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. These deterministic features have their origin in the complex, yet logical, interplay of a number of deterministic geologic processes, including magmatic evolution; volcanic eruption, transport, and emplacement; post-emplacement cooling and alteration; and late-stage (diagenetic) alteration. Because of geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly, using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling. It is unlikely that any single representation of physical properties at the site will be suitable for all modeling purposes. Instead, the same underlying physical reality will need to be described many times, each in a manner conducive to assessing specific performance issues.

  5. Stochastic processes dominate during boreal bryophyte community assembly.

    PubMed

    Fenton, Nicole J; Bergeron, Yves

    2013-09-01

    Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of

  6. Non-linear Post Processing Image Enhancement

    NASA Technical Reports Server (NTRS)

    Hunt, Shawn; Lopez, Alex; Torres, Angel

    1997-01-01

    A non-linear filter for image post processing based on the feedforward Neural Network topology is presented. This study was undertaken to investigate the usefulness of "smart" filters in image post processing. The filter has shown to be useful in recovering high frequencies, such as those lost during the JPEG compression-decompression process. The filtered images have a higher signal to noise ratio, and a higher perceived image quality. Simulation studies comparing the proposed filter with the optimum mean square non-linear filter, showing examples of the high frequency recovery, and the statistical properties of the filter are given,

  7. A Generalized Stochastic Lanchester Attrition Process

    DTIC Science & Technology

    1975-09-01

    superior side is able to make full use of its superiority (square law) or not (linear law). This is one interpretation of the dis- tinction as we...surviving Red force y (recall the nota - tion introduced in Assumption (1), above) the probability that the surviving target force has the composition z...the a- algebra of all its subsets. The sample space for our attrition process is the family ft of functions from R+ to E, which are right

  8. Prediction Theory of Periodically Correlated Stochastic Processes

    DTIC Science & Technology

    2015-05-12

    in order to do a reliable forecasting of periodically correlated sequences with large period (or continuous time processes) the standard method of...aimed at sequences with large periods. It has been known already for years that in order to do a reliable forecasting of periodically correlated...we showed that this technique is very efficient. We successfully used it to study structure, regularity, autoregressive representation, innovation

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

    SciTech Connect

    Sarıkaya, Mehmet Zeki; Kiriş, Mehmet Eyüp; Çelik, Nuri

    2016-04-18

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

  10. Localization of nonlinear damage using state-space-based predictions under stochastic excitation

    NASA Astrophysics Data System (ADS)

    Liu, Gang; Mao, Zhu; Todd, Michael; Huang, Zongming

    2014-02-01

    This paper presents a study on localizing damage under stochastic excitation by state-space-based methods, where the damaged response contains some nonlinearity. Two state-space-based modeling algorithms, namely auto- and cross-predictions, are employed in this paper, and the greatest prediction error will be achieved at the sensor pair closest to the actual damage, in terms of localization. To quantify the distinction of prediction error distributions obtained at different sensor locations, the Bhattacharyya distance is adopted as the quantification metric. There are two lab-scale test-beds adopted as validation platforms, including a two-story plane steel frame with bolt loosening damage and a three-story benchmark aluminum frame with a simulated tunable crack. Band-limited Gaussian noise is applied through an electrodynamic shaker to the systems. Testing results indicate that the damage detection capability of the state-space-based method depends on the nonlinearity-induced high frequency responses. Since those high frequency components attenuate quickly in time and space, the results show great capability for damage localization, i.e., the highest deviation of Bhattacharyya distance is coincident with the sensors close to the physical damage location. This work extends the state-space-based damage detection method for localizing damage to a stochastically excited scenario, which provides the advantage of compatibility with ambient excitations. Moreover, results from both experiments indicate that the state-space-based method is only sensitive to nonlinearity-induced damage, thus it can be utilized in parallel with linear classifiers or normalization strategies to insulate the operational and environmental variability, which often affects the system response in a linear fashion.

  11. Stochastic optimal controller design for uncertain nonlinear networked control system via neuro dynamic programming.

    PubMed

    Xu, Hao; Jagannathan, Sarangapani

    2013-03-01

    The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.

  12. Stochastic Integrals and Processes with Independent Increments.

    DTIC Science & Technology

    1985-03-01

    bounded variation over every finite La interval. This will be case iff it is the case for all a > 0. The process 4(t), t > 0, will be assumed to be...the sample paths of are of bounded variation over [O,t] with probability one, and so, as Kallenberg noted, one may simple use the Lebesgue-Stieltjes...over (O,t]. Assume further that f IdM(xs) < -, i.e. that almost every path of aJx[0, ti is of bounded variation over [O,t]. Let dlI denote the total

  13. Multitime correlation functions in nonclassical stochastic processes

    NASA Astrophysics Data System (ADS)

    Krumm, F.; Sperling, J.; Vogel, W.

    2016-06-01

    A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.

  14. Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

    PubMed

    Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

    2017-09-01

    The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

  15. Contextuality Scenarios Arising from Networks of Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Iglesias, Rodrigo; Tohmé, Fernando; Auday, Marcelo

    2016-10-01

    An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class 𝒳 of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations are coherent, in the sense that the distribution on a face of a simplex coincides with the marginal of the distribution over the entire simplex. An empirical model is called contextual if its distributions cannot be obtained by marginalizing a joint distribution over 𝒳. Contextual empirical models arise naturally in quantum theory, giving rise to some of its counter -intuitive statistical consequences. In this paper, we present a different and classical source of contextual empirical models: the interaction among many stochastic processes. We attach an empirical model to the ensuing network in which each node represents an open stochastic process with input and output random variables. The statistical behaviour of the network in the long run makes the empirical model generically contextual and even strongly contextual.

  16. System Design Support by Optimization Method Using Stochastic Process

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

    We proposed the new optimization method based on stochastic process. The characteristics of this method are to obtain the approximate solution of the optimum solution as an expected value. In numerical calculation, a kind of Monte Carlo method is used to obtain the solution because of stochastic process. Then, it can obtain the probability distribution of the design variable because it is generated in the probability that design variables were in proportion to the evaluation function value. This probability distribution shows the influence of design variables on the evaluation function value. This probability distribution is the information which is very useful for the system design. In this paper, it is shown the proposed method is useful for not only the optimization but also the system design. The flight trajectory optimization problem for the hang-glider is shown as an example of the numerical calculation.

  17. A stochastic model for ecological systems with strong nonlinear response to environmental drivers: application to two water-borne diseases.

    PubMed

    Codeço, Claudia Torres; Lele, Subhash; Pascual, Mercedes; Bouma, Menno; Ko, Albert I

    2008-02-06

    Ecological systems with threshold behaviour show drastic shifts in population abundance or species diversity in response to small variation in critical parameters. Examples of threshold behaviour arise in resource competition theory, epidemiological theory and environmentally driven population dynamics, to name a few. Although expected from theory, thresholds may be difficult to detect in real datasets due to stochasticity, finite population size and confounding effects that soften the observed shifts and introduce variability in the data. Here, we propose a modelling framework for threshold responses to environmental drivers that allows for a flexible treatment of the transition between regimes, including variation in the sharpness of the transition and the variance of the response. The model assumes two underlying stochastic processes whose mixture determines the system's response. For environmentally driven systems, the mixture is a function of an environmental covariate and the response may exhibit strong nonlinearity. When applied to two datasets for water-borne diseases, the model was able to capture the effect of rainfall on the mean number of cases as well as the variance. A quantitative description of this kind of threshold behaviour is of more general application to predict the response of ecosystems and human health to climate change.

  18. Novel mapping in non-equilibrium stochastic processes

    NASA Astrophysics Data System (ADS)

    Heseltine, James; Kim, Eun-jin

    2016-04-01

    We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a non-equilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length { L } and the associated action { J }, where { L } represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function’s mean position (μ) is decreased from the final equilibrium value {μ }* (the carrying capacity), { L } and { J } increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from {μ }*,{ L } and { J } increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.

  19. Quantum stochastic processes for maps on Hilbert C*-modules

    SciTech Connect

    Heo, Jaeseong; Ji, Un Cig

    2011-05-15

    We discuss pairs ({phi}, {Phi}) of maps, where {phi} is a map between C*-algebras and {Phi} is a {phi}-module map between Hilbert C*-modules, which are generalization of representations of Hilbert C*-modules. A covariant version of Stinespring's theorem for such a pair ({phi}, {Phi}) is established, and quantum stochastic processes constructed from pairs ({l_brace}{phi}{sub t{r_brace}}, {l_brace}{Phi}{sub t{r_brace}}) of families of such maps are studied. We prove that the quantum stochastic process J={l_brace}J{sub t{r_brace}} constructed from a {phi}-quantum dynamical semigroup {Phi}={l_brace}{Phi}{sub t{r_brace}} is a j-map for the quantum stochastic process j={l_brace}j{sub t{r_brace}} constructed from the given quantum dynamical semigroup {phi}={l_brace}{phi}{sub t{r_brace}}, and that J is covariant if the {phi}-quantum dynamical semigroup {Phi} is covariant.

  20. Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm.

    PubMed

    Overgaard, Rune V; Jonsson, Niclas; Tornøe, Christoffer W; Madsen, Henrik

    2005-02-01

    Pharmacokinetic/pharmacodynamic modelling is most often performed using non-linear mixed-effects models based on ordinary differential equations with uncorrelated intra-individual residuals. More sophisticated residual error models as e.g. stochastic differential equations (SDEs) with measurement noise can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. This general approach enables a decomposition of the intra-individual residual variation epsilon into system noise w and measurement noise e. The present work describes implementation of SDEs in a non-linear mixed-effects model, where parameter estimation was performed by a novel approximation of the likelihood function. This approximation is constructed by combining the First-Order Conditional Estimation (FOCE) method used in non-linear mixed-effects modelling with the Extended Kalman Filter used in models with SDEs. Fundamental issues concerning the proposed model and estimation algorithm are addressed by simulation studies, concluding that system noise can successfully be separated from measurement noise and inter-individual variability.

  1. Stochastic system identification of skin properties: linear and wiener static nonlinear methods.

    PubMed

    Chen, Yi; Hunter, Ian W

    2012-10-01

    Wiener static nonlinear system identification was used to study the linear dynamics and static nonlinearities in the response of skin and underlying tissue under indentation in vivo. A device capable of measuring the dynamic mechanical properties of bulk skin tissue was developed and it incorporates a custom-built Lorentz force actuator that measures the dynamic compliance between the input force (<12 N) and the output displacement (<20 mm). A simple linear stochastic system identification technique produced a variance accounted for (VAF) of 75-81% and Wiener static nonlinear techniques increased the VAF by 5%. Localized linear techniques increased the VAF to 85-95% with longer tests. Indentation experiments were conducted on 16 test subjects to determine device sensitivity and repeatability. Using the device, the coefficient of variation of test metrics was found to be as low as 2% for a single test location. The measured tissue stiffness was 300 N/m near the surface and 4.5 kN/m for high compression. The damping ranged from 5 to 23 N s/m. The bulk skin properties were also shown to vary significantly with gender and body mass index. The device and techniques used in this research can be applied to consumer product analysis, medical diagnosis and tissue research.

  2. Random migration processes between two stochastic epidemic centers.

    PubMed

    Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B

    2016-04-01

    We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. Copyright © 2016 Elsevier Inc. All rights reserved.

  3. Nonlinear Real-Time Optical Signal Processing.

    DTIC Science & Technology

    1984-10-01

    DTIC ELECTE I B IIMAGE PROCESSING INSTITUTE 84 11 26 107 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Dota Entered), REPORT DOCUMENTATION...30, 1984 N NONLINEAR REAL-TIME OPTICAL SIGNAL PROCESSING i E~ A.A. Sawchuk, Principal Investigator T.C. Strand and A.R. Tanguay. Jr. October 1, 1984...RDepartment of Electrical Engineering Image Processing institute University of Southern California University Park-MC 0272 Los Angeles, California

  4. Nonlinear and Nonstationary Signal Processing

    NASA Astrophysics Data System (ADS)

    Wunsch, Carl

    Stationary linear systems driven by Gaussian processes are the basic representations of time series used in the Earth sciences. A large body of literature has developed around these misleadingly simple models, which straddle statistics, optimization, control, probability theory, and related fields. That fundamental errors of inference are still made in the refereed literature is perhaps a testimony to the subtleties and confusion that arise when statistics meets the real geophysical world. A major journal devoted to modern climate studies recently felt compelled to publish a tutorial explaining the importance of avoiding aliasing errors when sampling meteorological variables; this subject was clearly understood 100 years ago.

  5. Sparse stochastic processes and discretization of linear inverse problems.

    PubMed

    Bostan, Emrah; Kamilov, Ulugbek S; Nilchian, Masih; Unser, Michael

    2013-07-01

    We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies continuous-domain signals as solutions of linear stochastic differential equations. Accordingly, we show that the class of admissible priors for the discretized version of the signal is confined to the family of infinitely divisible distributions. Our estimators not only cover the well-studied methods of Tikhonov and l1-type regularizations as particular cases, but also open the door to a broader class of sparsity-promoting regularization schemes that are typically nonconvex. We provide an algorithm that handles the corresponding nonconvex problems and illustrate the use of our formalism by applying it to deconvolution, magnetic resonance imaging, and X-ray tomographic reconstruction problems. Finally, we compare the performance of estimators associated with models of increasing sparsity.

  6. Analysis of trajectory entropy for continuous stochastic processes at equilibrium.

    PubMed

    Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

    2014-07-17

    The analytical expression for the trajectory entropy of the overdamped Langevin equation is derived via two approaches. The first route goes through the Fokker-Planck equation that governs the propagation of the conditional probability density, while the second method goes through the path integral of the Onsager-Machlup action. The agreement of these two approaches in the continuum limit underscores the equivalence between the partial differential equation and the path integral formulations for stochastic processes in the context of trajectory entropy. The values obtained using the analytical expression are also compared with those calculated with numerical solutions for arbitrary time resolutions of the trajectory. Quantitative agreement is clearly observed consistently across different models as the time interval between snapshots in the trajectories decreases. Furthermore, analysis of different scenarios illustrates how the deterministic and stochastic forces in the Langevin equation contribute to the variation in dynamics measured by the trajectory entropy.

  7. Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

    Treesearch

    Patrick C. Tobin; Ottar N. Bjornstad

    2005-01-01

    Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

  8. Laboratory investigation of nonlinear whistler wave processes

    NASA Astrophysics Data System (ADS)

    Amatucci, B.; Tejero, E. M.; Crabtree, C. E.; Blackwell, D. D.; Mithaiwala, M.; Rudakov, L.; Ganguli, G.

    2014-12-01

    Nonlinear interactions involving whistler wave turbulence can result from wave-particle interactions and instabilities in sharp boundary layers. Given sufficient whistler energy density, nonlinear scattering off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift (see Crabtree, Phys. Plasmas 19, 032903 (2012)). In the magnetosphere, boundary layers containing highly sheared plasma flows drive lower hybrid waves, leading to the formation of quasi-static structures in the nonlinearly saturated state. Such processes are being investigated in the NRL Space Physics Simulation Chamber (SPSC) in conditions scaled to match the respective environments. The specific nonlinear process being examined is the scattering of a transversely propagating, primarily electrostatic, lower hybrid wave into a more parallel propagating electromagnetic whistler mode. Sufficiently large amplitude lower hybrid waves have been observed to scatter into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic antennas. The experiments have demonstrated large changes in wave propagation angle and small frequency downshifts consistent with nonlinear Landau damping when pump wave amplitudes exceed the small threshold value (dB/B0 ~ 4×10-7). *This work supported by the NRL Base Program.

  9. Stationary distribution and periodic solution for stochastic predator-prey systems with nonlinear predator harvesting

    NASA Astrophysics Data System (ADS)

    Zuo, Wenjie; Jiang, Daqing

    2016-07-01

    In this paper, we investigate the dynamics of the stochastic autonomous and non-autonomous predator-prey systems with nonlinear predator harvesting respectively. For the autonomous system, we first give the existence of the global positive solution. Then, in the case of persistence, we prove that there exists a unique stationary distribution and it has ergodicity by constructing a suitable Lyapunov function. The result shows that, the relatively weaker white noise will strengthen the stability of the system, but the stronger white noise will result in the extinction of one or two species. Particularly, for the non-autonomous periodic system, we show that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, numerical simulations illustrate our theoretical results.

  10. Nonlinear functional response parameter estimation in a stochastic predator-prey model.

    PubMed

    Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio

    2012-01-01

    Parameter estimation for the functional response of predator-prey systems is a critical methodological problem in population ecology. In this paper we consider a stochastic predator-prey system with non-linear Ivlev functional response and propose a method for model parameter estimation based on time series of field data. We tackle the problem of parameter estimation using a Bayesian approach relying on a Markov Chain Monte Carlo algorithm. The efficiency of the method is tested on a set of simulated data. Then, the method is applied to a predator-prey system of importance for Integrated Pest Management and biological control, the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis. The model is estimated on a dataset obtained from a field survey. Finally, the estimated model is used to forecast predator-prey dynamics in similar fields, with slightly different initial conditions.

  11. Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Mahdi Alavi, S. M.; Saif, Mehrdad

    2013-12-01

    This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

  12. Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems

    NASA Astrophysics Data System (ADS)

    Hua, Changchun; Liu, Guopin; Bai, Zhenhua; Guan, Xinping

    2016-12-01

    In this paper, we focus on the problem of adaptive stabilisation for a class of interconnected uncertain switched stochastic nonlinear systems. Classical adaptive and backstepping technique are employed for control synthesis. Instead of estimating the switching parameters directly, we design the adaptive controller based on the estimations of bounds on switching time-varying parameters. A smooth function is introduced to deal with the difficulties caused by unknown interactions and tuning function approach is used to circumvent the overparameter problem. It is shown that under the action of the proposed controller all the signals of the overall closed-loop systems are globally uniformly bounded in probability under arbitrary switching. Simulation results are presented to illustrate the effectiveness of the proposed approach.

  13. Adaptive Consensus Control of Nonlinear Multiagent Systems With Unknown Control Directions Under Stochastic Topologies.

    PubMed

    Rezaee, Hamed; Abdollahi, Farzaneh

    2017-08-15

    The consensus problem over high-order nonlinear multiagent systems with the Brunovsky-type model is studied. The model parameters and control directions of agents are supposed to be unknown. Hence, based on Nussbaum-type functions, an adaptive protocol is proposed, which guarantees achieving consensus in the network when the parameters and control directions of the agents are unknown and unidentical. The main contribution of this paper (compared with the existing similar results in the literature) is to guarantee achieving consensus in networks of agents when the communication topology is not connected constantly, and communication links stochastically switch over time. It is shown that if the probability of the network connectivity is not zero, under some conditions, almost sure consensus can be achieved. Illustrative examples verify the accuracy of the proposed consensus protocol.

  14. Neural network-based finite horizon stochastic optimal control design for nonlinear networked control systems.

    PubMed

    Xu, Hao; Jagannathan, Sarangapani

    2015-03-01

    The stochastic optimal control of nonlinear networked control systems (NNCSs) using neuro-dynamic programming (NDP) over a finite time horizon is a challenging problem due to terminal constraints, system uncertainties, and unknown network imperfections, such as network-induced delays and packet losses. Since the traditional iteration or time-based infinite horizon NDP schemes are unsuitable for NNCS with terminal constraints, a novel time-based NDP scheme is developed to solve finite horizon optimal control of NNCS by mitigating the above-mentioned challenges. First, an online neural network (NN) identifier is introduced to approximate the control coefficient matrix that is subsequently utilized in conjunction with the critic and actor NNs to determine a time-based stochastic optimal control input over finite horizon in a forward-in-time and online manner. Eventually, Lyapunov theory is used to show that all closed-loop signals and NN weights are uniformly ultimately bounded with ultimate bounds being a function of initial conditions and final time. Moreover, the approximated control input converges close to optimal value within finite time. The simulation results are included to show the effectiveness of the proposed scheme.

  15. An efficient distribution method for nonlinear transport problems in stochastic porous media

    NASA Astrophysics Data System (ADS)

    Ibrahima, F.; Tchelepi, H.; Meyer, D. W.

    2015-12-01

    Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.

  16. Non-linear Feature Extraction by Redundancy Reduction in an Unsupervised Stochastic Neural Network.

    PubMed

    Parra, L; Deco, G

    1997-06-01

    Unsupervised feature extraction by a stochastic neural network can be defined as a minimization of the redundancy between the elements of the output layer, given complete information transfer from input to output. Redundancy minimization can be achieved by minimization of the mutual information between the units of the output layer. Complete information transfer is enforced by maximizing the mutual information of the input and output. With these two conditions we define a novel learning algorithm for stochastic recurrent networks. The minimum of redundancy corresponds to the extraction of statistically independent features, leading to a factorial representation of the environment. The resulting learning rule includes Hebbian and anti-Hebbian learning terms. These two terms are weighted by the amount of information transmitted in the learning synapse minus the grade of redundant information in the corresponding output neuron, giving thus, an information-theoretic interpretation of the proportionality constant of Hebb's biological rule. Simulations demonstrate the performance of this method. When a retina is simulated, the learning algorithm forms decorrelated receptive fields. This represents the first experiment that extends the results of the linear principle component analysis to the nonlinear case by a direct implementation of Barlow's principle of redundancy reduction for unsupervised features extraction by receptive fields formation in a retina model. Copyright 1997 Elsevier Science Ltd.

  17. Real-Time Nonlinear Optical Information Processing.

    DTIC Science & Technology

    1979-06-01

    operations aree presented. One approach realizes the halftone method of nonlinear optical processing in real time by replacing the conventional...photographic recording medium with a real-time image transducer. In the second approach halftoning is eliminated and the real-time device is used directly

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

    ERIC Educational Resources Information Center

    Ahmet, Kara

    2015-01-01

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

  19. Multiple-scale stochastic processes: Decimation, averaging and beyond

    NASA Astrophysics Data System (ADS)

    Bo, Stefano; Celani, Antonio

    2017-02-01

    The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.

  20. Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems.

    PubMed

    Li, Yongming; Tong, Shaocheng

    2016-08-25

    In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

  1. Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

    NASA Astrophysics Data System (ADS)

    Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

    2013-06-01

    We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem.

  2. Nonequilibrium dynamics of stochastic point processes with refractoriness

    SciTech Connect

    Deger, Moritz; Cardanobile, Stefano; Rotter, Stefan; Helias, Moritz; Atay, Fatihcan M.

    2010-08-15

    Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.

  3. Synchronization, stickiness effects and intermittent oscillations in coupled nonlinear stochastic networks

    NASA Astrophysics Data System (ADS)

    Kouvaris, N.; Provata, A.

    2009-08-01

    Long distance reactive and diffusive coupling is introduced in a spatially extended nonlinear stochastic network of interacting particles. The network serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. If the network includes only local nearest neighbour interactions, the system organizes into a number of local asynchronous oscillators. It is shown that (a) Introduction of all-to-all coupling in the network leads the system into global, center-type, conservative oscillations as dictated by the mean-field dynamics. (b) Introduction of reactive coupling to the network leads the system to intermittent oscillations where the trajectories stick for short times in bounded regions of space, with subsequent jumps between different bounded regions. (c) Introduction of diffusive coupling to the system does not alter the dynamics for small values of the diffusive coupling pdiff, while after a critical value pdiff c the system synchronizes into a limit cycle with specific frequency, deviating non-trivially from the mean-field center-type behaviour. The frequency of the limit cycle oscillations depends on the reaction rates and on the diffusion coupling. The amplitude σ of the limit cycle depends on the control parameter pdiff.

  4. Population density equations for stochastic processes with memory kernels

    NASA Astrophysics Data System (ADS)

    Lai, Yi Ming; de Kamps, Marc

    2017-06-01

    We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

  5. Simulation of Stochastic Processes by Coupled ODE-PDE

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2008-01-01

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

  6. Fingerprints of determinism in an apparently stochastic corrosion process.

    PubMed

    Rivera, M; Uruchurtu-Chavarín, J; Parmananda, P

    2003-05-02

    We detect hints of determinism in an apparently stochastic corrosion problem. This experimental system has industrial relevance as it mimics the corrosion processes of pipelines transporting water, hydrocarbons, or other fuels to remote destinations. We subject this autonomous system to external periodic perturbations. Keeping the amplitude of the superimposed perturbations constant and varying the frequency, the system's response is analyzed. It reveals the presence of an optimal forcing frequency for which maximal response is achieved. These results are consistent with those for a deterministic system and indicate a classical resonance between the forcing signal and the autonomous dynamics. Numerical studies using a generic corrosion model are carried out to complement the experimental findings.

  7. Posterior Probability and Fluctuation Theorem in Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Ohkubo, Jun

    2009-12-01

    A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.

  8. A Fractional Order Recovery SIR Model from a Stochastic Process.

    PubMed

    Angstmann, C N; Henry, B I; McGann, A V

    2016-03-01

    Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.

  9. A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term.

    PubMed

    Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W

    2014-01-01

    A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.

  10. Computing the trajectory mutual information between a point process and an analog stochastic process.

    PubMed

    Pasha, Syed Ahmed; Solo, Victor

    2012-01-01

    In a number of application areas such as neural coding there is interest in computing, from real data, the information flows between stochastic processes one of which is a point process. Of particular interest is the calculation of the trajectory (as opposed to marginal) mutual information between an observed point process which is influenced by an underlying but unobserved analog stochastic process i.e. a state. Using particle filtering we develop a model based trajectory mutual information calculation for apparently the first time.

  11. Stochastic weather inputs for improved urban water demand forecasting: application of nonlinear input variable selection and machine learning methods

    NASA Astrophysics Data System (ADS)

    Quilty, J.; Adamowski, J. F.

    2015-12-01

    Urban water supply systems are often stressed during seasonal outdoor water use as water demands related to the climate are variable in nature making it difficult to optimize the operation of the water supply system. Urban water demand forecasts (UWD) failing to include meteorological conditions as inputs to the forecast model may produce poor forecasts as they cannot account for the increase/decrease in demand related to meteorological conditions. Meteorological records stochastically simulated into the future can be used as inputs to data-driven UWD forecasts generally resulting in improved forecast accuracy. This study aims to produce data-driven UWD forecasts for two different Canadian water utilities (Montreal and Victoria) using machine learning methods by first selecting historical UWD and meteorological records derived from a stochastic weather generator using nonlinear input variable selection. The nonlinear input variable selection methods considered in this work are derived from the concept of conditional mutual information, a nonlinear dependency measure based on (multivariate) probability density functions and accounts for relevancy, conditional relevancy, and redundancy from a potential set of input variables. The results of our study indicate that stochastic weather inputs can improve UWD forecast accuracy for the two sites considered in this work. Nonlinear input variable selection is suggested as a means to identify which meteorological conditions should be utilized in the forecast.

  12. Nonlinear stochastic exclusion financial dynamics modeling and time-dependent intrinsic detrended cross-correlation

    NASA Astrophysics Data System (ADS)

    Zhang, Wei; Wang, Jun

    2017-09-01

    In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.

  13. Time Series, Stochastic Processes and Completeness of Quantum Theory

    NASA Astrophysics Data System (ADS)

    Kupczynski, Marian

    2011-03-01

    Most of physical experiments are usually described as repeated measurements of some random variables. Experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that it provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in the standard descriptive statistical analysis, were found in time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR (2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of the experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.

  14. Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

    The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

  15. Stochastic investigation of temperature process for climatic variability identification

    NASA Astrophysics Data System (ADS)

    Lerias, Eleutherios; Kalamioti, Anna; Dimitriadis, Panayiotis; Markonis, Yannis; Iliopoulou, Theano; Koutsoyiannis, Demetris

    2016-04-01

    The temperature process is considered as the most characteristic hydrometeorological process and has been thoroughly examined in the climate-change framework. We use a dataset comprising hourly temperature and dew point records to identify statistical variability with emphasis on the last period. Specifically, we investigate the occurrence of mean, maximum and minimum values and we estimate statistical properties such as marginal probability distribution function and the type of decay of the climacogram (i.e., mean process variance vs. scale) for various time periods. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

  16. Stochastic investigation of wind process for climatic variability identification

    NASA Astrophysics Data System (ADS)

    Deligiannis, Ilias; Tyrogiannis, Vassilis; Daskalou, Olympia; Dimitriadis, Panayiotis; Markonis, Yannis; Iliopoulou, Theano; Koutsoyiannis, Demetris

    2016-04-01

    The wind process is considered one of the hydrometeorological processes that generates and drives the climate dynamics. We use a dataset comprising hourly wind records to identify statistical variability with emphasis on the last period. Specifically, we investigate the occurrence of mean, maximum and minimum values and we estimate statistical properties such as marginal probability distribution function and the type of decay of the climacogram (i.e., mean process variance vs. scale) for various time periods. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

  17. Synaptic Size Dynamics as an Effectively Stochastic Process

    PubMed Central

    Statman, Adiel; Kaufman, Maya; Minerbi, Amir; Ziv, Noam E.; Brenner, Naama

    2014-01-01

    Long-term, repeated measurements of individual synaptic properties have revealed that synapses can undergo significant directed and spontaneous changes over time scales of minutes to weeks. These changes are presumably driven by a large number of activity-dependent and independent molecular processes, yet how these processes integrate to determine the totality of synaptic size remains unknown. Here we propose, as an alternative to detailed, mechanistic descriptions, a statistical approach to synaptic size dynamics. The basic premise of this approach is that the integrated outcome of the myriad of processes that drive synaptic size dynamics are effectively described as a combination of multiplicative and additive processes, both of which are stochastic and taken from distributions parametrically affected by physiological signals. We show that this seemingly simple model, known in probability theory as the Kesten process, can generate rich dynamics which are qualitatively similar to the dynamics of individual glutamatergic synapses recorded in long-term time-lapse experiments in ex-vivo cortical networks. Moreover, we show that this stochastic model, which is insensitive to many of its underlying details, quantitatively captures the distributions of synaptic sizes measured in these experiments, the long-term stability of such distributions and their scaling in response to pharmacological manipulations. Finally, we show that the average kinetics of new postsynaptic density formation measured in such experiments is also faithfully captured by the same model. The model thus provides a useful framework for characterizing synapse size dynamics at steady state, during initial formation of such steady states, and during their convergence to new steady states following perturbations. These findings show the strength of a simple low dimensional statistical model to quantitatively describe synapse size dynamics as the integrated result of many underlying complex processes

  18. Synaptic size dynamics as an effectively stochastic process.

    PubMed

    Statman, Adiel; Kaufman, Maya; Minerbi, Amir; Ziv, Noam E; Brenner, Naama

    2014-10-01

    Long-term, repeated measurements of individual synaptic properties have revealed that synapses can undergo significant directed and spontaneous changes over time scales of minutes to weeks. These changes are presumably driven by a large number of activity-dependent and independent molecular processes, yet how these processes integrate to determine the totality of synaptic size remains unknown. Here we propose, as an alternative to detailed, mechanistic descriptions, a statistical approach to synaptic size dynamics. The basic premise of this approach is that the integrated outcome of the myriad of processes that drive synaptic size dynamics are effectively described as a combination of multiplicative and additive processes, both of which are stochastic and taken from distributions parametrically affected by physiological signals. We show that this seemingly simple model, known in probability theory as the Kesten process, can generate rich dynamics which are qualitatively similar to the dynamics of individual glutamatergic synapses recorded in long-term time-lapse experiments in ex-vivo cortical networks. Moreover, we show that this stochastic model, which is insensitive to many of its underlying details, quantitatively captures the distributions of synaptic sizes measured in these experiments, the long-term stability of such distributions and their scaling in response to pharmacological manipulations. Finally, we show that the average kinetics of new postsynaptic density formation measured in such experiments is also faithfully captured by the same model. The model thus provides a useful framework for characterizing synapse size dynamics at steady state, during initial formation of such steady states, and during their convergence to new steady states following perturbations. These findings show the strength of a simple low dimensional statistical model to quantitatively describe synapse size dynamics as the integrated result of many underlying complex processes.

  19. Cox process representation and inference for stochastic reaction–diffusion processes

    PubMed Central

    Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

    2016-01-01

    Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction–diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction–diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction–diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling. PMID:27222432

  20. Evolution and mass extinctions as lognormal stochastic processes

    NASA Astrophysics Data System (ADS)

    Maccone, Claudio

    2014-10-01

    In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra

  1. Finite dimensional Markov process approximation for stochastic time-delayed dynamical systems

    NASA Astrophysics Data System (ADS)

    Sun, Jian-Qiao

    2009-05-01

    This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. A simple one-dimensional stochastic system is used to demonstrate the method and the theory. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.

  2. Reduced-order wavelet-Galerkin solution for the coupled, nonlinear stochastic response of slender buildings in transient winds

    NASA Astrophysics Data System (ADS)

    Le, Thai-Hoa; Caracoglia, Luca

    2015-05-01

    A tall building is prone to wind-induced stochastic vibration, originating from complex fluid-structure interaction, dynamic coupling and nonlinear aerodynamic phenomena. The loading induced by extreme wind events, such as "downburst storms", hurricanes and tornadoes is naturally transient and nonstationary in comparison with the hypothesis of stationary wind loads, used in both structural engineering research and practice. Time-domain integration methods, widely applied for solving nonlinear differential equations, are hardly applicable to the analysis of coupled, nonlinear and stochastic response of tall buildings under transient winds. Therefore, the investigation of alternative and computationally-efficient simulation methods is important. This study employs the wavelet-Galerkin (WG) method to achieve this objective, by examining the stochastic dynamic response of two tall building models subject to stationary and transient wind loads. These are (1) a single-degree-of-freedom equivalent model of a tall structure and (2) a multi-degree-of-freedom reduced-order full building model. Compactly supported Daubechies wavelets are used as orthonormal basis functions in conjunction with the Galerkin projection scheme to decompose and transform the coupled, nonlinear differential equations of the two models into random algebraic equations in the wavelet domain. Methodology, feasibility and applicability of the WG method are investigated in some special cases of stiffness nonlinearity (Duffing type) and damping nonlinearity (Van-der-Pol type) for the single-degree-of-freedom model. For the reduced-order tall building model the WG method is used to solve for dynamic coupling, aerodynamics and transient wind load effects. Computation of "connection coefficients", effects of boundary conditions, wavelet resolution and wavelet order are examined in order to adequately replicate the dynamic response. Realizations of multivariate stationary and transient wind loads for the

  3. Estimation of Critical Conditions for Noise-Induced Bifurcation in Nonautonomous Nonlinear Systems by Stochastic Sensitivity Function

    NASA Astrophysics Data System (ADS)

    Sun, Yahui; Hong, Ling; Jiang, Jun; Li, Zigang

    This paper proposes an efficient but simple method to determine the approximate stationary probability distribution around periodic attractors of nonautonomous nonlinear systems under multiple time-dependent parametric noises and estimate the critical noise intensity for noise-induced explosive bifurcations under a given confidence probability. After adopting a stroboscopic map constructed by a method with higher accuracy and efficiency, nonautonomous dynamical systems around periodic attractors are transformed into mapping ones. Then the mean-square analysis method of discrete systems is used to derive the stochastic sensitivity function. Based on the confidence ellipses of stochastic attractors and the global structure of deterministic nonlinear systems, the critical noise intensity of noise-induced explosive bifurcations under a given confidence probability is estimated. A Mathieu-Duffing oscillator under both multiplicative and additive noises is studied to show the validity of the proposed method.

  4. Stochastic investigation of precipitation process for climatic variability identification

    NASA Astrophysics Data System (ADS)

    Sotiriadou, Alexia; Petsiou, Amalia; Feloni, Elisavet; Kastis, Paris; Iliopoulou, Theano; Markonis, Yannis; Tyralis, Hristos; Dimitriadis, Panayiotis; Koutsoyiannis, Demetris

    2016-04-01

    The precipitation process is important not only to hydrometeorology but also to renewable energy resources management. We use a dataset consisting of daily and hourly records around the globe to identify statistical variability with emphasis on the last period. Specifically, we investigate the occurrence of mean, maximum and minimum values and we estimate statistical properties such as marginal probability distribution function and the type of decay of the climacogram (i.e., mean process variance vs. scale). Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

  5. Thermodynamic and stochastic theory of hydrodynamic and power-producing processes. [Annual report], September 1991--September 1992

    SciTech Connect

    Ross, J.

    1992-09-16

    Thermodynamics of the transport processes of diffusion, thermal conduction, and viscous flow at a macroscopic level are developed for the simplest cases of one-dimensional transport in fluids for individual linear and nonlinear processes approaching a stationary non-equilibrium state. Formulation has started of thermodynamic and stochastic theory of combinations of transport processes. Global thermodynamic and stochastic theory of open chemical systems frar from equilibrium is continued with analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states with assumed local equilibrium. Stationary solutions are obtained of the master equation for single and multi-intermediate autocatalytic chemical systems. A kinetic potential is identified that governs the deterministic time evolution of coupled tank reactors. A second-order response theory was developed to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor.

  6. Stem Cell Differentiation as a Non-Markov Stochastic Process.

    PubMed

    Stumpf, Patrick S; Smith, Rosanna C G; Lenz, Michael; Schuppert, Andreas; Müller, Franz-Josef; Babtie, Ann; Chan, Thalia E; Stumpf, Michael P H; Please, Colin P; Howison, Sam D; Arai, Fumio; MacArthur, Ben D

    2017-09-27

    Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage. We observe that cells pass from the pluripotent state to the neuronal state via an intermediate epiblast-like state. However, analysis of the rate at which cells enter and exit these observed cell states using a hidden Markov model indicates the presence of a chain of unobserved molecular states that each cell transits through stochastically in sequence. This chain of hidden states allows individual cells to record their position on the differentiation trajectory, thereby encoding a simple form of cellular memory. We suggest a statistical mechanics interpretation of these results that distinguishes between functionally distinct cellular "macrostates" and functionally similar molecular "microstates" and propose a model of stem cell differentiation as a non-Markov stochastic process. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

  7. Suprathreshold stochastic resonance in neural processing tuned by correlation.

    PubMed

    Durrant, Simon; Kang, Yanmei; Stocks, Nigel; Feng, Jianfeng

    2011-07-01

    Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.

  8. Analysis of electrochemical noise by the stochastic process detector method

    SciTech Connect

    Roberge, P.R. . Dept. of Chemistry and Chemical Engineering)

    1994-07-01

    Electrochemical noise (EN) generated during the corrosion of metal specimens can be analyzed for its stochastic nature. Voltage fluctuations observed during the exposure of commercial aluminum (Al) sheet material were analyzed using a new technique based on randomness of these fluctuations. The stochastic process detector (SPD) technique was found to be very sensitive to the presence of deterministic features that are sometimes present in noise records. Results obtained with three orthogonal faces of Aluminum Association (AA) 7075-T6 Al alloy (UNS A97075) exposed to a saline solution were compared to electrochemical impedance spectroscopy (EIS) measurements and micrographs of exposed specimens. Some fundamental characteristics of voltage fluctuations revealed by SPD appeared to be related directly to the degree of localized corrosion in progress on the metal surfaces. The noise fluctuations' voltage rise times (RT) seemed to be related directly to the propensity of the AA 7075-T6 alloy tested to suffer from localized forms of corrosion visible under optical microscopy (OM). These findings agreed with variations observed in the constant-phase element (CPE) exponents, as calculated from EIS measurements, which also have been related to the degree of localized attack on corroding specimens.

  9. Separation of Stochastic and Deterministic Information from Seismological Time Series with Nonlinear Dynamics and Maximum Entropy Methods

    SciTech Connect

    Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias

    2007-11-13

    We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information.

  10. Local mean consistency on numerical solutions of stochastic wave equation with cubic nonlinearities on 2D rectangles

    NASA Astrophysics Data System (ADS)

    Hazaimeh, Haziem M.

    2017-06-01

    In this article we study that the linear-implicit Euler method of the solution of nonlinear stochastic wave equation in 2 dimensions has the non-exploding explicit representation and is mean consistent. In [15], we proved that the strong Fourier solution of the semi-linear wave equations exists and is unique on an appropriate Hilbert space. A linear-implicit Euler method is used to discretize the related Fourier coefficients and mean consistency is discussed.

  11. Laboratory investigation of nonlinear whistler wave processes

    NASA Astrophysics Data System (ADS)

    Amatucci, Bill; Tejero, Erik; Crabtree, Chris; Enloe, Lon; Blackwell, Dave; Ganguli, Guru

    2015-11-01

    Nonlinear interactions involving whistler wave turbulence result from processes such as wave-particle interactions in the radiation belts and instability generation in sharp magnetospheric boundary layers. Nonlinear scattering of large amplitude waves off thermal electrons substantially changes the wave vector direction and energy flux, while inducing a small frequency shift [Crabtree, Phys. Plasmas 19, 032903 (2012)]. This nonlinear scattering of primarily electrostatic lower hybrid waves into electromagnetic whistler modes is being investigated in the NRL Space Chamber under conditions scaled to match the respective environments. Lower hybrid waves are generated directly by antennas or self-consistently from sheared cross-magnetic field flows with scale length less than an ion gyroradius via the Electron-Ion Hybrid Instability [Ganguli, Phys. Fluids 31, 2753 (1988)), Amatucci, Phys. Plasmas 10, 1963 (2003)]. Sufficiently large amplitude lower hybrid waves have been observed to convert into whistler modes by scattering from thermal electrons. The plasma response as a function of transmitted lower hybrid wave amplitude is monitored with magnetic loop antennas. Details of the observed wave spectra and mode characteristics will be presented. This work supported by the NRL Base Program.

  12. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics.

    PubMed

    Drogoul, Audric; Veltz, Romain

    2017-02-01

    In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

  13. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics

    NASA Astrophysics Data System (ADS)

    Drogoul, Audric; Veltz, Romain

    2017-02-01

    In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

  14. Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling.

    PubMed

    He, Wangli; Zhang, Biao; Han, Qing-Long; Qian, Feng; Kurths, Jurgen; Cao, Jinde

    2017-02-01

    This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

  15. Relaxation process of quantum system: Stochastic Liouville equation and initial correlation

    SciTech Connect

    Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

    2010-08-15

    Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.

  16. Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.

    PubMed

    Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J

    2016-12-22

    Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.

  17. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schrödinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    NASA Astrophysics Data System (ADS)

    Keanini, R. G.

    2011-04-01

    A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schrödinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion and spread of single, multiple, and continuous sets of Burger's vortex sheets, evolving within deterministic and random strain rate fields, under both viscous and inviscid conditions, are obtained. In order to promote application to other nonlinear problems, a tutorial development of the framework is presented. Likewise, time-incremental solution approaches and

  18. 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

  19. Interacting Stochastic Processes: From Viciousness to Caging to Force Chains

    NASA Astrophysics Data System (ADS)

    Xu, Shiliyang

    This thesis documents a quest to develop and study several novel interacting stochastic processes. As for the first example, we generalize a system of vicious random walkers in which the only interaction between any two random walkers is that when they intersect, both walkers are annihilated. We define a system of N vicious accelerating walkers with each walker undergoing random acceleration and compute the survival probability distribution for this system. We also define and study a system of N vicious Levy flights in which any two Levy flights crossing one another annihilate each other. The average mean-squared displacement of a Levy flight is not proportional to time, but scales with what is known as the Levy index divided by two. In both cases, vicious accelerating walkers and vicious Levy flights, we are motivated by ultimately generalizing our understanding of Gaussian random matrices via non-Markovian and non-Gaussian extensions respectively. Moreover, inspired by recent experiments on periodically sheared colloids at low densities, we define and investigate several new contact processes, or interacting stochastic processes, with conserved particle number and three-or-more-body interactions. We do so to characterize the periodically sheared colloidal system at higher densities. We find two new dynamical phase transitions between an active phase, where some fraction of the colloids are always being displaced from their position at the beginning and end of each shear cycle, and an inactive phase in which all colloids return to their initial positions at the end of each shear cycle. One of the transitions is discontinuous, while the second, which is due to a caging, or crowding, effect at high densities, appears to be continuous and in a new universality from what is known as conserved directed percolation. The latter transition may have implications for the onset of glassiness in dense, particulate systems. In addition, this thesis also includes analysis of

  20. Optical Computing and Nonlinear Optical Signal Processing

    NASA Astrophysics Data System (ADS)

    Peyghambarian, N.

    1987-01-01

    Employment of optical techniques in signal processing and communication and computing systems has become a major research and development effort at many industrial, government, and university laboratories across the nation and in Europe and Japan. implementation of optical computing concepts and the use of bistable etalons and non-linear logic devices in computing have gained a lot of support and enthusiasm from the optics community in recent years. The significance Iof this field and its potential importance in future technologies is evidenced by the large number of conferences, workshops, and special issues on the subject.

  1. Complementary relations in non-equilibrium stochastic processes

    NASA Astrophysics Data System (ADS)

    Kim, Eun-jin; Nicholson, S. B.

    2015-08-01

    We present novel complementary relations in non-equilibrium stochastic processes. Specifically, by utilising path integral formulation, we derive statistical measures (entropy, information, and work) and investigate their dependence on variables (x, v), reference frames, and time. In particular, we show that the equilibrium state maximises the simultaneous information quantified by the product of the Fisher information based on x and v while minimising the simultaneous disorder/uncertainty quantified by the sum of the entropy based on x and v as well as by the product of the variances of the PDFs of x and v. We also elucidate the difference between Eulerian and Lagrangian entropy. Our theory naturally leads to Hamilton-Jacobi relation for forced-dissipative systems.

  2. Counting statistics of non-Markovian quantum stochastic processes.

    PubMed

    Flindt, Christian; Novotný, Tomás; Braggio, Alessandro; Sassetti, Maura; Jauho, Antti-Pekka

    2008-04-18

    We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.

  3. Closed-form expressions of some stochastic adapting equations for nonlinear adaptive activation function neurons.

    PubMed

    Fiori, Simone

    2003-12-01

    In recent work, we introduced nonlinear adaptive activation function (FAN) artificial neuron models, which learn their activation functions in an unsupervised way by information-theoretic adapting rules. We also applied networks of these neurons to some blind signal processing problems, such as independent component analysis and blind deconvolution. The aim of this letter is to study some fundamental aspects of FAN units' learning by investigating the properties of the associated learning differential equation systems.

  4. Stochastic simulation of spatially correlated geo-processes

    USGS Publications Warehouse

    Christakos, G.

    1987-01-01

    In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

  5. Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

    PubMed Central

    Zimmer, Christoph

    2016-01-01

    Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802

  6. Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

    PubMed

    Zimmer, Christoph

    2016-01-01

    Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

  7. Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

    NASA Technical Reports Server (NTRS)

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

    1998-01-01

    Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for

  8. CFD Data Generation Process for Nonlinear Loads

    NASA Technical Reports Server (NTRS)

    Arslan, Alan; Magee, Todd; Unger, Eric; Hartwich, Peter; Agrawal, Shreekant; Giesing, Joseph; Bharadvaj, Bala; Chaderjian, Neal; Murman, Scott

    1999-01-01

    This paper discusses the development of a process to generate a CFD database for the non-linear loads process capability for critical loads evaluation at Boeing Long Beach. The CFD simulations were performed for wing/body configurations at high angles of attack and Reynolds numbers with transonic and elastic deflection effects. Convergence criteria had to be tailored for loads applications rather than the usual drag performance. The time-accurate approach was subsequently adopted in order to improve convergence and model possible unsteadiness in the flowfield. In addition, uncertainty issues relating to the turbulence model and grid resolution in areas of high vortical flows were addressed and investigated for one of the cases.

  9. Stochastic P systems and the simulation of biochemical processes with dynamic compartments.

    PubMed

    Spicher, Antoine; Michel, Olivier; Cieslak, Mikolaj; Giavitto, Jean-Louis; Prusinkiewicz, Przemyslaw

    2008-03-01

    We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.

  10. Data-Driven Reduction and Climate Prediction by Nonlinear Stochastic Energy-Conserving Models

    NASA Astrophysics Data System (ADS)

    Kondrashov, D. A.

    2013-05-01

    Comprehensive dynamical climate models aim at simulating past, present and future climate and, more recently, at predicting it. These models, commonly known as general circulation models or global climate models (GCMs) represent a broad range of time and space scales and use a state vector that has many millions of degrees of freedom. Considerable work, both theoretical and data-based, has shown that much of the observed climate variability can be represented with a substantially smaller number of degrees of freedom. While detailed weather prediction out to a few days requires high numerical resolution, it is fairly clear that the dimension of the phase space in which a major fraction of climate variance can be predicted is likely to be much smaller. Low-dimensional models (LDMs) can simulate and predict that variability provided they are able to account for (i) linear and nonlinear interactions between the resolved high-variance climate components; and (ii) the interactions between the resolved components and the huge number of unresolved ones. Here we will present applications of a particular data-driven LDM approach, namely energy-conserving formulation of empirical model reduction (EMR). As an operational methodology, EMR attempts to construct a low-order nonlinear system of multi-level prognostic equations driven by stochastic forcing, and to estimate both the dynamical operator and the properties of the driving noise directly from observations or from a high-order model's simulation. The multi-level EMR structure for modeling the noise allows one to capture feedback between high- and low-frequency components of the variability, thus parameterizing the "fast" scales — often referred to as the "noise" — in terms of the memory of the "slow" scales, the "signal." EMR already proved to be highly competitive for real-time ENSO prediction among state-of-the art dynamical and statistical models. New opportunities for EMR prediction will be illustrated in the

  11. Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models

    USGS Publications Warehouse

    Geist, Eric L.

    2016-01-01

    Non-linear resonant coupling of edge waves can occur with tsunamis generated by large-magnitude subduction zone earthquakes. Earthquake rupture zones that straddle beneath the coastline of continental margins are particularly efficient at generating tsunami edge waves. Using a stochastic model for earthquake slip, it is shown that a wide range of edge-wave modes and wavenumbers can be excited, depending on the variability of slip. If two modes are present that satisfy resonance conditions, then a third mode can gradually increase in amplitude over time, even if the earthquake did not originally excite that edge-wave mode. These three edge waves form a resonant triad that can cause unexpected variations in tsunami amplitude long after the first arrival. An M ∼ 9, 1100 km-long continental subduction zone earthquake is considered as a test case. For the least-variable slip examined involving a Gaussian random variable, the dominant resonant triad includes a high-amplitude fundamental mode wave with wavenumber associated with the along-strike dimension of rupture. The two other waves that make up this triad include subharmonic waves, one of fundamental mode and the other of mode 2 or 3. For the most variable slip examined involving a Cauchy-distributed random variable, the dominant triads involve higher wavenumbers and modes because subevents, rather than the overall rupture dimension, control the excitation of edge waves. Calculation of the resonant period for energy transfer determines which cases resonant coupling may be instrumentally observed. For low-mode triads, the maximum transfer of energy occurs approximately 20–30 wave periods after the first arrival and thus may be observed prior to the tsunami coda being completely attenuated. Therefore, under certain circumstances the necessary ingredients for resonant coupling of tsunami edge waves exist, indicating that resonant triads may be observable and implicated in late, large-amplitude tsunami arrivals.

  12. Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models

    NASA Astrophysics Data System (ADS)

    Geist, Eric L.

    2016-02-01

    Non-linear resonant coupling of edge waves can occur with tsunamis generated by large-magnitude subduction zone earthquakes. Earthquake rupture zones that straddle beneath the coastline of continental margins are particularly efficient at generating tsunami edge waves. Using a stochastic model for earthquake slip, it is shown that a wide range of edge-wave modes and wavenumbers can be excited, depending on the variability of slip. If two modes are present that satisfy resonance conditions, then a third mode can gradually increase in amplitude over time, even if the earthquake did not originally excite that edge-wave mode. These three edge waves form a resonant triad that can cause unexpected variations in tsunami amplitude long after the first arrival. An M ˜ 9, 1100 km-long continental subduction zone earthquake is considered as a test case. For the least-variable slip examined involving a Gaussian random variable, the dominant resonant triad includes a high-amplitude fundamental mode wave with wavenumber associated with the along-strike dimension of rupture. The two other waves that make up this triad include subharmonic waves, one of fundamental mode and the other of mode 2 or 3. For the most variable slip examined involving a Cauchy-distributed random variable, the dominant triads involve higher wavenumbers and modes because subevents, rather than the overall rupture dimension, control the excitation of edge waves. Calculation of the resonant period for energy transfer determines which cases resonant coupling may be instrumentally observed. For low-mode triads, the maximum transfer of energy occurs approximately 20-30 wave periods after the first arrival and thus may be observed prior to the tsunami coda being completely attenuated. Therefore, under certain circumstances the necessary ingredients for resonant coupling of tsunami edge waves exist, indicating that resonant triads may be observable and implicated in late, large-amplitude tsunami arrivals.

  13. Perfusion quantification by model-free arterial spin labeling using nonlinear stochastic regularization deconvolution.

    PubMed

    Ahlgren, André; Wirestam, Ronnie; Petersen, Esben Thade; Ståhlberg, Freddy; Knutsson, Linda

    2013-11-01

    Quantification of cerebral blood flow can be accomplished by model-free arterial spin labeling using the quantitative STAR labeling of arterial regions (QUASAR) sequence. The required deconvolution is normally based on block-circulant singular value decomposition (cSVD)/oscillation SVD (oSVD), an algorithm associated with nonphysiological residue functions and potential effects of arterial dispersion. The aim of this work was to amend this by implementing nonlinear stochastic regularization (NSR) deconvolution, previously used to retrieve realistic residue functions in dynamic susceptibility contrast MRI. To characterize the residue function in model-free arterial spin labeling, and possibly to improve absolute cerebral blood flow quantification, NSR was applied to deconvolution of QUASAR data. For comparison, SVD-based deconvolution was also employed. Residue function characteristics and cerebral blood flow values from 10 volunteers were obtained. Simulations were performed to support the in vivo results. NSR was able to resolve realistic residue functions in contrast to the SVD-based methods. Mean cerebral blood flow estimates in gray matter were 36.6 ± 2.6, 28.6 ± 3.3, 40.9 ± 3.6, and 42.9 ± 3.9 mL/100 g/min for cSVD, oSVD, NSR, and NSR with correction for arterial dispersion, respectively. In simulations, the NSR-based perfusion estimates showed better accuracy than the SVD-based approaches. Perfusion quantification by model-free arterial spin labeling is evidently dependent on the selected deconvolution method, and NSR is a feasible alternative to SVD-based methods. Copyright © 2012 Wiley Periodicals, Inc.

  14. Nonlinear neural networks. II. Information processing

    NASA Astrophysics Data System (ADS)

    van Hemmen, J. L.; Grensing, D.; Huber, A.; Kühn, R.

    1988-01-01

    Information processing in nonlinear neural networks with a finite number q of stored patterns is studied. Each network is characterized completely by its synaptic kernel Q. At low temperatures, the nonlinearity typically results in 2q-2- q metastable, pure states in addition to the q retrieval states that are associated with the q stored patterns. These spurious states start appearing at a temperaturetilde T_q , which depends on q. We give sufficient conditions to guarantee that the retrieval states bifurcate first at a critical temperature T c and thattilde T_q / T c → 0 as q→∞. Hence, there is a large temperature range where only the retrieval states and certain symmetric mixtures thereof exist. The latter are unstable, as they appear at T c . For clipped synapses, the bifurcation and stability structure is analyzed in detail and shown to approach that of the (linear) Hopfield model as q→∞. We also investigate memories that forget and indicate how forgetfulness can be explained in terms of the eigenvalue spectrum of the synaptic kernel Q.

  15. Nonlinear oscillatory processes in wheeled vehicles

    NASA Astrophysics Data System (ADS)

    Mikhlin, Yu. V.; Mitrokhin, S. G.

    2011-04-01

    The free damped vibrations of a wheeled vehicle with independent suspension are analyzed with allowance for the nonlinear characteristics of the suspension springs and shock absorbers. The vibrations of a wheeled vehicle with a suspension with smooth nonlinear characteristics are studied for a model with seven degrees of freedoms. The skeleton curves and nonlinear normal modes are obtained. For a model with two degrees of freedoms (quarter-car) that corresponds to axisymmetric vibrations, the nonlinear normal modes are found in the case of a shock absorber with nonsmooth nonlinear characteristic

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

    PubMed

    Lei, Youming; Zheng, Fan

    2016-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Lei, Youming; Zheng, Fan

    2016-12-01

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

  18. Nonlinear Optical Image Processing with Bacteriorhodopsin Films

    NASA Technical Reports Server (NTRS)

    Downie, John D.; Deiss, Ron (Technical Monitor)

    1994-01-01

    The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

  19. Nonlinear Optical Image Processing with Bacteriorhodopsin Films

    NASA Technical Reports Server (NTRS)

    Downie, John D.; Deiss, Ron (Technical Monitor)

    1994-01-01

    The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

  20. Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Sun, Jian-Qiao

    This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.

  1. A stochastic process approach of the drake equation parameters

    NASA Astrophysics Data System (ADS)

    Glade, Nicolas; Ballet, Pascal; Bastien, Olivier

    2012-04-01

    The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.

  2. Biologically variable respiration as a stochastic process in ventilation - a stochastic model study.

    PubMed

    Min, Kyongyob; Hosoi, Keita; Degami, Masayuki; Kinoshita, Yoshinori

    2010-01-01

    Based on the fractal bronchial tree, we introduced a function of "asynchronous phasic contractions of lobular bronchiole", which would generate fluctuations in tidal volumes. Stochastic control theory was able to describe a genesis of biological variability in spontaneous respirations using a Schroedinger wave function.

  3. Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models.

    PubMed

    Champagnat, Nicolas; Ferrière, Régis; Méléard, Sylvie

    2006-05-01

    A distinctive signature of living systems is Darwinian evolution, that is, a propensity to generate as well as self-select individual diversity. To capture this essential feature of life while describing the dynamics of populations, mathematical models must be rooted in the microscopic, stochastic description of discrete individuals characterized by one or several adaptive traits and interacting with each other. The simplest models assume asexual reproduction and haploid genetics: an offspring usually inherits the trait values of her progenitor, except when a mutation causes the offspring to take a mutation step to new trait values; selection follows from ecological interactions among individuals. Here we present a rigorous construction of the microscopic population process that captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by the trait values of each individual, and interactions between individuals. A by-product of this formal construction is a general algorithm for efficient numerical simulation of the individual-level model. Once the microscopic process is in place, we derive different macroscopic models of adaptive evolution. These models differ in the renormalization they assume, i.e. in the limits taken, in specific orders, on population size, mutation rate, mutation step, while rescaling time accordingly. The macroscopic models also differ in their mathematical nature: deterministic, in the form of ordinary, integro-, or partial differential equations, or probabilistic, like stochastic partial differential equations or superprocesses. These models include extensions of Kimura's equation (and of its approximation for small mutation effects) to frequency- and density-dependent selection. A novel class of macroscopic models obtains when assuming that individual birth and death occur on a short timescale compared with the timescale of typical population growth. On a timescale of very rare mutations, we

  4. Sliding mode control for a class of nonlinear discrete-time networked systems with multiple stochastic communication delays

    NASA Astrophysics Data System (ADS)

    Ma, Lifeng; Wang, Zidong; Niu, Yugang; Bo, Yumimg; Guo, Zhi

    2011-04-01

    In this article, a sliding mode control problem is studied for a class of uncertain nonlinear networked systems with multiple communication delays. A sequence of stochastic variables obeying Bernoulli distribution is applied in the system model to describe the randomly occurring communication delays. The discrete-time system considered is also subject to parameter uncertainties and state-dependent stochastic disturbances. A novel discrete switching function is proposed to facilitate the sliding mode controller design. The sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is robustly exponentially stable in the mean square if two LMIs with an equality constraint are feasible. A discrete-time SMC controller is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.

  5. 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.

  6. Visibility graph analysis for re-sampled time series from auto-regressive stochastic processes

    NASA Astrophysics Data System (ADS)

    Zhang, Rong; Zou, Yong; Zhou, Jie; Gao, Zhong-Ke; Guan, Shuguang

    2017-01-01

    Visibility graph (VG) and horizontal visibility graph (HVG) play a crucial role in modern complex network approaches to nonlinear time series analysis. However, depending on the underlying dynamic processes, it remains to characterize the exponents of presumably exponential degree distributions. It has been recently conjectured that there is a critical value of exponent λc = ln 3 / 2 , which separates chaotic from correlated stochastic processes. Here, we systematically apply (H)VG analysis to time series from autoregressive (AR) models, which confirms the hypothesis that an increased correlation length results in larger values of λ > λc. On the other hand, we numerically find a regime of negatively correlated process increments where λ < λc, which is in contrast to this hypothesis. Furthermore, by constructing graphs based on re-sampled time series, we find that network measures show non-trivial dependencies on the autocorrelation functions of the processes. We propose to choose the decorrelation time as the maximal re-sampling delay for the algorithm. Our results are detailed for time series from AR(1) and AR(2) processes.

  7. Stochastic simulations of cargo transport by processive molecular motors.

    PubMed

    Korn, Christian B; Klumpp, Stefan; Lipowsky, Reinhard; Schwarz, Ulrich S

    2009-12-28

    We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

  8. Stochastic simulations of cargo transport by processive molecular motors

    NASA Astrophysics Data System (ADS)

    Korn, Christian B.; Klumpp, Stefan; Lipowsky, Reinhard; Schwarz, Ulrich S.

    2009-12-01

    We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

  9. Quantifying time-inhomogeneous stochastic introgression processes with hazard rates.

    PubMed

    Ghosh, Atiyo; Serra, Maria Conceição; Haccou, Patsy

    2012-06-01

    Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It is currently of particular concern as a possible mechanism for the spread of modified crop genes to wild populations. The hazard rate is the probability per time unit that such an escape takes place, given that it has not happened before. It is a quantitative measure of introgression risk that takes the stochastic elements inherent in introgression processes into account. We present a methodology to calculate the hazard rate for situations with time-varying gene flow from a crop to a large recipient wild population. As an illustration, several types of time-inhomogeneity are examined, including deterministic periodicity as well as random variation. Furthermore, we examine the effects of an extended fitness bottleneck of hybrids and backcrosses in combination with time-varying gene flow. It is found that bottlenecks decrease the hazard rate, but also slow down and delay its changes in reaction to changes in gene flow. Furthermore, we find that random variation in gene flow generates a lower hazard rate than analogous deterministic variation. We discuss the implications of our findings for crop management and introgression risk assessment. Copyright © 2012 A. Ghosh. Published by Elsevier Inc. All rights reserved.

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

    SciTech Connect

    Granita; Bahar, A.

    2015-03-09

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

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

    NASA Astrophysics Data System (ADS)

    Granita, Bahar, A.

    2015-03-01

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

  12. Environmental changes affect the assembly of soil bacterial community primarily by mediating stochastic processes.

    PubMed

    Zhang, Ximei; Johnston, Eric R; Liu, Wei; Li, Linghao; Han, Xingguo

    2016-01-01

    Both 'species fitness difference'-based deterministic processes, such as competitive exclusion and environmental filtering, and 'species fitness difference'-independent stochastic processes, such as birth/death and dispersal/colonization, can influence the assembly of soil microbial communities. However, how both types of processes are mediated by anthropogenic environmental changes has rarely been explored. Here we report a novel and general pattern that almost all anthropogenic environmental changes that took place in a grassland ecosystem affected soil bacterial community assembly primarily through promoting or restraining stochastic processes. We performed four experiments mimicking 16 types of environmental changes and separated the compositional variation of soil bacterial communities caused by each environmental change into deterministic and stochastic components, with a recently developed method. Briefly, because the difference between control and treatment communities is primarily caused by deterministic processes, the deterministic change was quantified as (mean compositional variation between treatment and control) - (mean compositional variation within control). The difference among replicate treatment communities is primarily caused by stochastic processes, so the stochastic change was estimated as (mean compositional variation within treatment) - (mean compositional variation within control). The absolute of the stochastic change was greater than that of the deterministic change across almost all environmental changes, which was robust for both taxonomic and functional-based criterion. Although the deterministic change may become more important as environmental changes last longer, our findings showed that changes usually occurred through mediating stochastic processes over 5 years, challenging the traditional determinism-dominated view.

  13. PLASMA EMISSION BY NONLINEAR ELECTROMAGNETIC PROCESSES

    SciTech Connect

    Ziebell, L. F.; Petruzzellis, L. T.; Gaelzer, R.; Yoon, P. H.; Pavan, J. E-mail: laripetruzzellis@yahoo.com.br E-mail: yoonp@umd.edu

    2015-06-20

    The plasma emission, or electromagnetic (EM) radiation at the plasma frequency and/or its harmonic(s), is generally accepted as the radiation mechanism responsible for solar type II and III radio bursts. Identification and characterization of these solar radio burst phenomena were done in the 1950s. Despite many decades of theoretical research since then, a rigorous demonstration of the plasma emission process based upon first principles was not available until recently, when, in a recent Letter, Ziebell et al. reported the first complete numerical solution of EM weak turbulence equations; thus, quantitatively analyzing the plasma emission process starting from the initial electron beam and the associated beam-plasma (or Langmuir wave) instability, as well as the subsequent nonlinear conversion of electrostatic Langmuir turbulence into EM radiation. In the present paper, the same problem is revisited in order to elucidate the detailed physical mechanisms that could not be reported in the brief Letter format. Findings from the present paper may be useful for interpreting observations and full-particle numerical simulations.

  14. Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis.

    PubMed

    Wang, Huanqing; Chen, Bing; Liu, Kefu; Liu, Xiaoping; Lin, Chong

    2014-05-01

    This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

  15. The stochastic modelling of kleptoparasitism using a Markov process.

    PubMed

    Broom, Mark; Crowe, Mary L; Fitzgerald, Meghan R; Rychtár, Jan

    2010-05-21

    Kleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480-489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449-458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134-142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

  16. Information theory, model error, and predictive skill of stochastic models for complex nonlinear systems

    NASA Astrophysics Data System (ADS)

    Giannakis, Dimitrios; Majda, Andrew J.; Horenko, Illia

    2012-10-01

    Many problems in complex dynamical systems involve metastable regimes despite nearly Gaussian statistics with underlying dynamics that is very different from the more familiar flows of molecular dynamics. There is significant theoretical and applied interest in developing systematic coarse-grained descriptions of the dynamics, as well as assessing their skill for both short- and long-range prediction. Clustering algorithms, combined with finite-state processes for the regime transitions, are a natural way to build such models objectively from data generated by either the true model or an imperfect model. The main theme of this paper is the development of new practical criteria to assess the predictability of regimes and the predictive skill of such coarse-grained approximations through empirical information theory in stationary and periodically-forced environments. These criteria are tested on instructive idealized stochastic models utilizing K-means clustering in conjunction with running-average smoothing of the training and initial data for forecasts. A perspective on these clustering algorithms is explored here with independent interest, where improvement in the information content of finite-state partitions of phase space is a natural outcome of low-pass filtering through running averages. In applications with time-periodic equilibrium statistics, recently developed finite-element, bounded-variation algorithms for nonstationary autoregressive models are shown to substantially improve predictive skill beyond standard autoregressive models.

  17. Second order parametric processes in nonlinear silica microspheres.

    PubMed

    Xu, Yong; Han, Ming; Wang, Anbo; Liu, Zhiwen; Heflin, James R

    2008-04-25

    We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-Q nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally generate quantum entangled photon pairs. Practical issues regarding implementation of the nonlinear microsphere are also discussed.

  18. Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia.

    PubMed

    Ben Amar, Martine; Bianca, Carlo

    2016-09-27

    We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

  19. Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

    PubMed Central

    Ben Amar, Martine; Bianca, Carlo

    2016-01-01

    We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold. PMID:27669998

  20. Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

    NASA Astrophysics Data System (ADS)

    Ben Amar, Martine; Bianca, Carlo

    2016-09-01

    We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

  1. A hybrid continuous-discrete method for stochastic reaction–diffusion processes

    PubMed Central

    Zheng, Likun; Nie, Qing

    2016-01-01

    Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

  2. Foundations of quantum mechanics: Connection with stochastic processes

    NASA Astrophysics Data System (ADS)

    Olavo, L. S.

    2000-05-01

    In this paper we explore the mathematical and epistemological connections between the stochastic derivation of the Schrödinger equation and the one proposed by ourselves in previous papers. It will be shown that these connections are accomplished by means of the fluctuation-dissipation theorem, to which we may unambiguously relate the symbols and physical references of both approaches. As a by-product of our investigation, it will be possible to interpret the time-energy dispersion relation on sounder grounds. It will also be possible to discuss the superposition principle and to interpret it on a quite simple basis. The origin of the stochasticity and its relation to stability will be also addressed and the bridge to an axiomatic formulation of stochastic electrodynamics will be constructed.

  3. Stochastic model updating utilizing Bayesian approach and Gaussian process model

    NASA Astrophysics Data System (ADS)

    Wan, Hua-Ping; Ren, Wei-Xin

    2016-03-01

    Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.

  4. Stochastic Vorticity and Associated Filtering Theory

    SciTech Connect

    Amirdjanova, A.; Kallianpur, G.

    2002-12-19

    The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki-Kallianpur-Kunita stochastic differential equation for the optimal filter is derived.

  5. Non-linear interactions in a boundary layer developing over an array of cubes using stochastic estimation

    NASA Astrophysics Data System (ADS)

    Blackman, Karin; Perret, Laurent

    2016-09-01

    In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density, λp = 25%, is studied within a wind tunnel using combined particle image velocimetry and hot-wire anemometry to investigate the non-linear interactions between large-scale momentum regions and small-scale structures induced by the presence of the roughness. Due to the highly turbulent nature of the roughness sub-layer and measurement equipment limitations, temporally resolved flow measurements are not feasible, making the conventional filtering methods used for triple decomposition unsuitable for the present work. Thus, multi-time delay linear stochastic estimation is used to decompose the flow into large-scales and small-scales. Analysis of the scale-decomposed skewness of the turbulent velocity (u') shows a significant contribution of the non-linear term uL ' uS ' 2 ¯ , which represents the influence of the large-scales ( uL ' ) onto the small-scales ( uS ' ). It is shown that this non-linear influence of the large-scale momentum regions occurs with all three components of velocity in a similar manner. Finally, through two-point spatio-temporal correlation analysis, it is shown quantitatively that large-scale momentum regions influence small-scale structures throughout the boundary layer through a non-linear top-down mechanism.

  6. On Wiener-Masani's algorithm for finding the generating function of multivariate stochastic processes

    NASA Technical Reports Server (NTRS)

    Miamee, A. G.

    1988-01-01

    It is shown that the algorithms for determining the generating function and prediction error matrix of multivariate stationary stochastic processes developed by Wiener and Masani (1957), and later by Masani (1960) will work in some more general setting.

  7. Nonlinear dynamics of cable stays. Part 2: stochastic cable support excitation

    NASA Astrophysics Data System (ADS)

    Georgakis, C. T.; Taylor, C. A.

    2005-03-01

    In this paper, an extensive behavioural study of cable vibrations, induced by in-plane stochastic cable-stayed structural vibrations, is made. Finite element modelling (FEM) and analysis (FEA) is used to determine in-plane and out-of-plane cable displacements induced by stochastic cable end displacements. The effects of stochastic cable support displacements, with abrupt and gradual transients, are studied. Regions of large-amplitude cable vibrations, induced by stochastic cable end displacements, are compared with those found from sinusoidal cable end displacements. The results show that, together with important similarities in cable response, there are also important differences in cable response between sinusoidal and stochastic cable support excitation. Differences in cable response amplitudes are found and discussed. It is also found that "cable-stiffening" occurs, for specific cable excitation parameters, as it does for sinusoidal cable support excitation, but to a lesser extent. Throughout the analyses, maximum cable stresses are calculated and, in some cases, are found to be near that required for cable material yielding.

  8. Learning Process of a Stochastic Feed-Forward Neural Network

    NASA Astrophysics Data System (ADS)

    Fujiki, Sumiyoshi; Fujiki, Nahomi

    1995-03-01

    A positive reinforcement type learning algorithm is formulated for a stochastic feed-forward neural network by minimizing a relative entropic measure, and a learning equation similar to that of the Boltzmann machine is obtained. The learning of the network actually shows a similar result to that of the Boltzmann machine in the classification problems of AND and XOR, by numerical experiments.

  9. Stochastic Process Analysis of Interactive Discourse in Early Counseling Interviews.

    ERIC Educational Resources Information Center

    Friedlander, Myrna L.; Phillips, Susan D.

    1984-01-01

    Examined patterns of interactive discourse to suggest how client and counselor establish a working alliance in their early interviews. Based on classification of 312 conversational turns from 14 dyads, a stochastic analysis was conducted. Results showed the sequences of talk were highly stable and predictable. (JAC)

  10. Survey of Bayesian Models for Modelling of Stochastic Temporal Processes

    SciTech Connect

    Ng, B

    2006-10-12

    This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.

  11. Stochastic Dynamics and Bifurcation Behavior of Nonlinear Nonconservative Systems in the Presence of Noise

    DTIC Science & Technology

    1990-08-31

    diagonalizable matrix A satisfy 5 Xi i k for j = 1,2,...,n, Ik ki = >k 2 (2) 1 where k is an integer vector k = (k1 , ,..., kn) with k1 > 0. Furthermore...stochastic systems and secondly, to demonstrate the relationship between stochastic averaging and normal form theory for non- nilpotent systems. To this...for large k. Furthermore, since the matrix A is diagonal, the image of LA, Im(LA), and its null space, ker (LA), span the whole space. Consequently, in

  12. Advanced Computer Simulations Of Nanomaterials And Stochastic Biological Processes

    NASA Astrophysics Data System (ADS)

    Minakova, Maria S.

    This dissertation consists of several parts. The first two chapters are devoted to of study of dynamic processes in cellular organelles called filopodia. A stochastic kinetics approach is used to describe non-equilibrium evolution of the filopodial system from nano- to micro scales. Dynamic coupling between chemistry and mechanics is also taken into account in order to investigate the influence of focal adhesions on cell motility. The second chapter explores the possibilities and effects of motor enhanced delivery of actin monomers to the polymerizing tips of filopodia, and how the steady-state filopodial length can exceed the limit set by pure diffusion. Finally, we also challenge the currently existing view of active transport and propose a new theoretical model that accurately describes the motor dynamics and concentration profiles seen in experiments in a physically meaningful way. The third chapter is a result of collaboration between three laboratories, as a part of Energy Frontier Research Center at the University of North Carolina at Chapel Hill. The work presented here unified the fields of synthetic chemistry, photochemistry, and computational physical chemistry in order to investigate a novel bio-synthetic compound and its energy transfer capabilities. This particular peptide-based design has never been studied via Molecular Dynamics with high precision, and it is the first attempt known to us to simulate the whole chromophore-peptide complex in solution in order to gain detailed information about its structural and dynamic features. The fourth chapter deals with the non-equilibrium relaxation induced transport of water molecules in a microemulsion. This problem required a different set of methodologies and a more detailed, all-atomistic treatment of the system. We found interesting water clustering effects and elucidated the most probable mechanism of water transfer through oil under the condition of saturated Langmuir monolayers. Together these

  13. A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution.

    PubMed

    Rice, Sean H

    2008-09-25

    Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general prospective evolution equation compliments the Price equation

  14. Changing the dynamical behavior of nonlinear reaction diffusion systems by stochastic electric fields

    SciTech Connect

    Enderlein, J.; Kuhnert, L.

    1996-12-12

    The idea of changing the diffusivities of charged ions in a solution by the application of an external stochastic electric field is proposed. The effect of such a change of the diffusion coefficients on the dynamical behavior of the Belouzov-Zhabotinsky reaction is theoretically studied and discussed. 35 refs., 3 figs.

  15. The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence

    NASA Astrophysics Data System (ADS)

    Zhao, Dianli; Zhang, Tiansi; Yuan, Sanling

    2016-02-01

    A stochastic version of the SIS epidemic model with vaccination (SIVS) is studied. When the noise is small, the threshold parameter is identified, which determines the extinction and persistence of the epidemic. Besides, the results show that large noise will suppress the epidemic from prevailing regardless of the saturated incidence. The results are illustrated by computer simulations.

  16. Nonlinear vector eigen-solver and parallel reassembly processing for structural nonlinear vibration

    NASA Astrophysics Data System (ADS)

    Xue, D. Y.; Mei, Chuh

    1993-12-01

    In the frequency domain solution of large amplitude nonlinear vibration, two operations are computationally costly. They are: (1) the iterative eigen-solution and (2) the iterative nonlinear matrix reassembly. This study introduces a nonlinear eigen-solver which greatly speeds up the solution procedure by using a combination of vector iteration and nonlinear matrix updating. A feature of this new method is that it avoids repeatedly using a costly eigen-solver or equation solver. This solution procedure has also been engaged in parallel processing to further speed up the computation. Parallel nonlinear matrix reassembly is the main interest in this parallel processing. Force Macro is used in the parallel program on a CRAY-2S supercomputer.

  17. Spectral theory for the failure of linear control in a nonlinear stochastic system.

    PubMed

    Grigoriev, Roman O; Handel, Andreas

    2002-12-01

    We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly non-normal evolution operators. In spatially extended systems the non-normality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the non-normality and the type of nonlinearity are all crucially important to understand and describe the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong non-normality is due to the presence of mean flow rather than the action of control.

  18. Real-Time Implementation of Nonlinear Processing Functions.

    DTIC Science & Technology

    1981-08-01

    crystal devices and then to use them in a coherent optical data- processing apparatus using halftone masks custom designed at the University oi Southern...California. With the halftone mask technique, we have demonstrated logarithmic nonlinear transformation, allowing us to separate multiplicative images...improved.,_ This device allowed nonlinear functions to be implemented directly wit - out the need for specially made halftone masks. Besides

  19. On the nature of heart rate variability in a breathing normal subject: a stochastic process analysis.

    PubMed

    Buchner, Teodor; Petelczyc, Monika; Zebrowski, Jan J; Prejbisz, Aleksander; Kabat, Marek; Januszewicz, Andrzej; Piotrowska, Anna Justyna; Szelenberger, Waldemar

    2009-06-01

    Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology.

  20. Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

    NASA Astrophysics Data System (ADS)

    Ata, Metin; Kitaura, Francisco-Shu; Müller, Volker

    2015-02-01

    We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi N-body simulation at redshift z = 0, inferring the underlying dark matter density field from subsamples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-σ) from the posterior distribution up to scales of about k ˜ 1 h Mpc-1 in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood including a scale-dependent non-linear deterministic bias can yield reconstructions with power spectra deviating more than 10 per cent at k = 0.2 h Mpc-1. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.

  1. Analytical results for stochastically growing networks: Connection to the zero-range process

    NASA Astrophysics Data System (ADS)

    Mohanty, P. K.; Jalan, Sarika

    2008-04-01

    We introduce a stochastic model of growing networks where both the number of new nodes which join the network and the number of connections vary stochastically. We provide an exact mapping between this model and the zero-range process, and calculate analytically the degree distribution for any given evolution rule. We argue that this mapping can be used to infer a possible evolution rule for any given network. This is being demonstrated for a protein-protein interaction network of Saccharomyces cerevisiae.

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

    NASA Technical Reports Server (NTRS)

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

    1973-01-01

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

  3. Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed

    NASA Astrophysics Data System (ADS)

    Menzel, Andreas M.

    2015-11-01

    Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

  4. Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed.

    PubMed

    Menzel, Andreas M

    2015-11-01

    Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

  5. Bubble nonlinear dynamics and stimulated scattering process

    NASA Astrophysics Data System (ADS)

    Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu

    2016-02-01

    A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

  6. Observer-Based Fuzzy Adaptive Output-Feedback Control of Stochastic Nonlinear Multiple Time-Delay Systems.

    PubMed

    Wang, Huanqing; Liu, Peter Xiaoping; Shi, Peng

    2017-09-01

    This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems' universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.

  7. Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

    NASA Astrophysics Data System (ADS)

    Yu, Zhaoxu; Li, Shugang; Li, Fangfei

    2016-01-01

    The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.

  8. Coherent response of a stochastic nonlinear oscillator to a driving force: analytical characterization of the spectral signatures

    NASA Astrophysics Data System (ADS)

    Plata, J.

    2016-01-01

    We study the dynamics of a classical nonlinear oscillator subject to noise and driven by a sinusoidal force. In particular, we give an analytical identification of the mechanisms responsible for the supernarrow peaks observed recently in the spectrum of a mechanical realization of the system. Our approach, based on the application of averaging techniques, simulates standard detection schemes used in practice. The spectral peaks, detected in a range of parameters corresponding to the existence of two attractors in the deterministic system, are traced to characteristics already present in the linearized stochastic equations. It is found that, for specific variations of the parameters, the characteristic frequencies near the attractors converge on the driving frequency and, as a consequence, the widths of the peaks in the spectrum are significantly reduced. The implications of the study to the control of the observed coherent response of the system are discussed.

  9. Multi-faults detection and estimation for nonlinear stochastic system based on particle filter and hypothesis test

    NASA Astrophysics Data System (ADS)

    Ding, Bo; Fang, Huajing

    2016-12-01

    This paper is concerned with the fault detection and estimation for nonlinear stochastic system with additive multi-faults. The states of system are estimated by the improved particle filter which composed of basic particle filter and preliminary fault estimation. Since the preliminary fault estimation contains noise, the faults are detected by the method of hypothesis testing, while the amplitude of each fault is estimated by the average of the sample of preliminary fault estimation. Meanwhile, the relationship of the sample size, the significance level of two types of error, the amplitude of fault and the variance of the error of preliminary fault estimation are also given. The effectiveness of the proposed method is verified by the simulation of three-vessel water tank system.

  10. Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation

    NASA Astrophysics Data System (ADS)

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

    Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

  11. Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

    PubMed

    Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

    2016-04-01

    Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

  12. EFFECTS OF ROTATION ON STOCHASTICITY OF GRAVITATIONAL WAVES IN THE NONLINEAR PHASE OF CORE-COLLAPSE SUPERNOVAE

    SciTech Connect

    Kotake, Kei; Iwakami-Nakano, Wakana; Ohnishi, Naofumi

    2011-08-01

    By performing three-dimensional (3D) simulations that demonstrate the neutrino-driven core-collapse supernovae aided by the standing accretion shock instability (SASI), we study how the spiral modes of the SASI can impact the properties of the gravitational-wave (GW) emission. To see the effects of rotation in the nonlinear postbounce phase, we give a uniform rotation on the flow advecting from the outer boundary of the iron core, the specific angular momentum of which is assumed to agree with recent stellar evolution models. We compute fifteen 3D models in which the initial angular momentum and the input neutrino luminosities from the protoneutron star are changed in a systematic manner. By performing a ray-tracing analysis, we accurately estimate the GW amplitudes generated by anisotropic neutrino emission. Our results show that the gravitational waveforms from neutrinos in models that include rotation exhibit a common feature; otherwise, they vary much more stochastically in the absence of rotation. The breaking of the stochasticity stems from the excess of the neutrino emission parallel to the spin axis. This is because the compression of matter is more enhanced in the vicinity of the equatorial plane due to the growth of the spiral SASI modes, leading to the formation of the spiral flows circulating around the spin axis with higher temperatures. We point out that recently proposed future space interferometers like Fabry-Perot-type DECIGO would permit the detection of these signals for a Galactic supernova.

  13. Mechanistic Basis for Nonlinear Dose-Response Relationships for Low-Dose Radiation-Induced Stochastic Effects

    PubMed Central

    Scott, Bobby R.; Walker, Dale M.; Tesfaigzi, Yohannes; Schöllnberger, Helmut; Walker, Vernon

    2003-01-01

    The linear nonthreshold (LNT) model plays a central role in low-dose radiation risk assessment for humans. With the LNT model, any radiation exposure is assumed to increase one’s risk of cancer. Based on the LNT model, others have predicted tens of thousands of deaths related to environmental exposure to radioactive material from nuclear accidents (e.g., Chernobyl) and fallout from nuclear weapons testing. Here, we introduce a mechanism-based model for low-dose, radiation-induced, stochastic effects (genomic instability, apoptosis, mutations, neoplastic transformation) that leads to a LNT relationship between the risk for neoplastic transformation and dose only in special cases. It is shown that nonlinear dose-response relationships for risk of stochastic effects (problematic nonlethal mutations, neoplastic transformation) should be expected based on known biological mechanisms. Further, for low-dose, low-dose rate, low-LET radiation, large thresholds may exist for cancer induction. We summarize previously published data demonstrating large thresholds for cancer induction. We also provide evidence for low-dose-radiation-induced, protection (assumed via apoptosis) from neoplastic transformation. We speculate based on work of others (Chung 2002) that such protection may also be induced to operate on existing cancer cells and may be amplified by apoptosis-inducing agents such as dietary isothiocyanates. PMID:19330114

  14. Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

    NASA Astrophysics Data System (ADS)

    Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

    2016-09-01

    The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

  15. Categorical Analysis of Human T Cell Heterogeneity with One-Dimensional Soli-Expression by Nonlinear Stochastic Embedding.

    PubMed

    Cheng, Yang; Wong, Michael T; van der Maaten, Laurens; Newell, Evan W

    2016-01-15

    Rapid progress in single-cell analysis methods allow for exploration of cellular diversity at unprecedented depth and throughput. Visualizing and understanding these large, high-dimensional datasets poses a major analytical challenge. Mass cytometry allows for simultaneous measurement of >40 different proteins, permitting in-depth analysis of multiple aspects of cellular diversity. In this article, we present one-dimensional soli-expression by nonlinear stochastic embedding (One-SENSE), a dimensionality reduction method based on the t-distributed stochastic neighbor embedding (t-SNE) algorithm, for categorical analysis of mass cytometry data. With One-SENSE, measured parameters are grouped into predefined categories, and cells are projected onto a space composed of one dimension for each category. In contrast with higher-dimensional t-SNE, each dimension (plot axis) in One-SENSE has biological meaning that can be easily annotated with binned heat plots. We applied One-SENSE to probe relationships between categories of human T cell phenotypes and observed previously unappreciated cellular populations within an orchestrated view of immune cell diversity. The presentation of high-dimensional cytometric data using One-SENSE showed a significant improvement in distinguished T cell diversity compared with the original t-SNE algorithm and could be useful for any high-dimensional dataset.

  16. Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility.

    PubMed

    Myrskylä, Mikko; Goldstein, Joshua R

    2013-02-01

    In this article, we show how stochastic diffusion models can be used to forecast demographic cohort processes using the Hernes, Gompertz, and logistic models. Such models have been used deterministically in the past, but both behavioral theory and forecast utility are improved by introducing randomness and uncertainty into the standard differential equations governing population processes. Our approach is to add time-series stochasticity to linearized versions of each process. We derive both Monte Carlo and analytic methods for estimating forecast uncertainty. We apply our methods to several examples of marriage and fertility, extending them to simultaneous forecasting of multiple cohorts and to processes restricted by factors such as declining fecundity.

  17. BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS1

    PubMed Central

    Gary Chan, Kwun Chuen; Wang, Mei-Cheng

    2011-01-01

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

  18. Unifying Three Perspectives on Information Processing in Stochastic Thermodynamics

    NASA Astrophysics Data System (ADS)

    Barato, A. C.; Seifert, U.

    2014-03-01

    So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system, or (iii) by identifying an implicit Maxwell demon in steady-state transport. We derive the corresponding second laws from one master fluctuation theorem and discuss their relationship. In particular, we show that both the entropy production involving mutual information between system and controller and the one involving a Shannon entropy difference of an information reservoir like a tape carry an extra term different from the usual current times affinity. We, thus, generalize stochastic thermodynamics to the presence of an information reservoir.

  19. Trajectory Entropy of Continuous Stochastic Processes at Equilibrium.

    PubMed

    Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

    2014-03-20

    We propose to quantify the trajectory entropy of a dynamic system as the information content in excess of a free-diffusion reference model. The space-time trajectory is now the dynamic variable, and its path probability is given by the Onsager-Machlup action. For the time propagation of the overdamped Langevin equation, we solved the action path integral in the continuum limit and arrived at an exact analytical expression that emerged as a simple functional of the deterministic mean force and the stochastic diffusion. This work may have direct implications in chemical and phase equilibria, bond isomerization, and conformational changes in biological macromolecules as well transport problems in general.

  20. Disentangling the importance of ecological niches from stochastic processes across scales

    PubMed Central

    Chase, Jonathan M.; Myers, Jonathan A.

    2011-01-01

    Deterministic theories in community ecology suggest that local, niche-based processes, such as environmental filtering, biotic interactions and interspecific trade-offs largely determine patterns of species diversity and composition. In contrast, more stochastic theories emphasize the importance of chance colonization, random extinction and ecological drift. The schisms between deterministic and stochastic perspectives, which date back to the earliest days of ecology, continue to fuel contemporary debates (e.g. niches versus neutrality). As illustrated by the pioneering studies of Robert H. MacArthur and co-workers, resolution to these debates requires consideration of how the importance of local processes changes across scales. Here, we develop a framework for disentangling the relative importance of deterministic and stochastic processes in generating site-to-site variation in species composition (β-diversity) along ecological gradients (disturbance, productivity and biotic interactions) and among biogeographic regions that differ in the size of the regional species pool. We illustrate how to discern the importance of deterministic processes using null-model approaches that explicitly account for local and regional factors that inherently create stochastic turnover. By embracing processes across scales, we can build a more synthetic framework for understanding how niches structure patterns of biodiversity in the face of stochastic processes that emerge from local and biogeographic factors. PMID:21768151

  1. Effect of coupling on stochastic resonance and stochastic antiresonance processes in a unidirectionally N-coupled systems in periodic sinusoidal potential

    NASA Astrophysics Data System (ADS)

    Wadop Ngouongo, Y. J.; Djuidjé Kenmoé, G.; Kofané, T. C.

    2017-04-01

    This work presents the characterization of stochastic resonance (SR) and stochastic antiresonance (SAR) in terms of hysteresis loop area (HLA). In connection with SR and SAR phenomena, we study the dynamics of a chain of particles coupled by nonlinear springs in a periodic sinusoidal potential. The dependence of the coupling parameter as well as the system size on SR and SAR is analysed. We consider the role played by the nonlinear coupling on the SR. We show that there is a range of coupling parameter where only SAR is observed, after this range the SR can occur, however, there also exists a range where neither SAR nor SR appear. It is noted that the maximum and the minimum of the average input energy increases with the coupling parameter. Also demonstrate that there exists an optimal value of the number of particles N for which the average input energy of the first particle reaches the saturation.

  2. Characterizing Nonlinear Heartbeat Dynamics within a Point Process Framework

    PubMed Central

    Brown, Emery N.; Barbieri, Riccardo

    2010-01-01

    Human heartbeat intervals are known to have nonlinear and nonstationary dynamics. In this paper, we propose a model of R–R interval dynamics based on a nonlinear Volterra–Wiener expansion within a point process framework. Inclusion of second-order nonlinearities into the heartbeat model allows us to estimate instantaneous heart rate (HR) and heart rate variability (HRV) indexes, as well as the dynamic bispectrum characterizing higher order statistics of the nonstationary non-Gaussian time series. The proposed point process probability heartbeat interval model was tested with synthetic simulations and two experimental heartbeat interval datasets. Results show that our model is useful in characterizing and tracking the inherent nonlinearity of heartbeat dynamics. As a feature, the fine temporal resolution allows us to compute instantaneous nonlinearity indexes, thus sidestepping the uneven spacing problem. In comparison to other nonlinear modeling approaches, the point process probability model is useful in revealing nonlinear heartbeat dynamics at a fine timescale and with only short duration recordings. PMID:20172783

  3. Single Cell Analysis Reveals the Stochastic Phase of Reprogramming to Pluripotency Is an Ordered Probabilistic Process

    PubMed Central

    Burger, Steven; Russell, Alexander C.; Nelson, Craig E.

    2014-01-01

    Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs). Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to provide a precise

  4. Single cell analysis reveals the stochastic phase of reprogramming to pluripotency is an ordered probabilistic process.

    PubMed

    Chung, Kyung-Min; Kolling, Frederick W; Gajdosik, Matthew D; Burger, Steven; Russell, Alexander C; Nelson, Craig E

    2014-01-01

    Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs). Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to provide a precise

  5. NONLINEAR OPTICS: Nonlinear optical processes in planar waveguides and excitation of surface polaritons

    NASA Astrophysics Data System (ADS)

    Yashkir, O. V.; Yashkir, Yu N.

    1987-11-01

    An investigation is made of nonlinear optical interaction of light propagating in a planar waveguide with surface polaritons. Reduced wave equations for the amplitudes of the waveguide modes and surface polaritons are used to study the characteristics of generation of surface polaritons of difference frequency, parametric frequency up-conversion of the polaritons, and stimulated Raman scattering by the polaritons. An analysis is made of the characteristic properties of the investigated nonlinear optical processes.

  6. Si-rich Silicon Nitride for Nonlinear Signal Processing Applications.

    PubMed

    Lacava, Cosimo; Stankovic, Stevan; Khokhar, Ali Z; Bucio, T Dominguez; Gardes, F Y; Reed, Graham T; Richardson, David J; Petropoulos, Periklis

    2017-12-01

    Nonlinear silicon photonic devices have attracted considerable attention thanks to their ability to show large third-order nonlinear effects at moderate power levels allowing for all-optical signal processing functionalities in miniaturized components. Although significant efforts have been made and many nonlinear optical functions have already been demonstrated in this platform, the performance of nonlinear silicon photonic devices remains fundamentally limited at the telecom wavelength region due to the two photon absorption (TPA) and related effects. In this work, we propose an alternative CMOS-compatible platform, based on silicon-rich silicon nitride that can overcome this limitation. By carefully selecting the material deposition parameters, we show that both of the device linear and nonlinear properties can be tuned in order to exhibit the desired behaviour at the selected wavelength region. A rigorous and systematic fabrication and characterization campaign of different material compositions is presented, enabling us to demonstrate TPA-free CMOS-compatible waveguides with low linear loss (~1.5 dB/cm) and enhanced Kerr nonlinear response (Re{γ} = 16 Wm(-1)). Thanks to these properties, our nonlinear waveguides are able to produce a π nonlinear phase shift, paving the way for the development of practical devices for future optical communication applications.

  7. Cells, cancer, and rare events: homeostatic metastability in stochastic nonlinear dynamical models of skin cell proliferation.

    PubMed

    Warren, Patrick B

    2009-09-01

    A recently proposed model for skin cell proliferation [E. Clayton, Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.

  8. Cells, cancer, and rare events: Homeostatic metastability in stochastic nonlinear dynamical models of skin cell proliferation

    NASA Astrophysics Data System (ADS)

    Warren, Patrick B.

    2009-09-01

    A recently proposed model for skin cell proliferation [E. Clayton , Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.

  9. Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems.

    PubMed

    Shaocheng Tong; Yue Li; Yongming Li; Yanjun Liu

    2011-12-01

    In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.

  10. Distinguishing between discreteness effects in stochastic reaction processes.

    PubMed

    Haruna, Taichi

    2015-05-01

    The effect of discreteness on stochastic dynamics of chemically reacting systems is studied analytically. We apply the scheme bridging the chemical master equation and the chemical Fokker-Planck equation by a parameter representing the degree of discreteness previously proposed by the author for two concrete systems. One is an autocatalytic reaction system, and the other is a branching-annihilation reaction system. It is revealed that the change in characteristic time scales when discreteness is decreased is yielded between the two systems for different reasons. In the former system, it originates from the boundaries where one of the chemical species is zero, whereas in the latter system, it is due to modification of the most probable extinction path caused by discreteness loss.

  11. Sampling Representations and Approximations for Certain Functions and Stochastic Processes.

    DTIC Science & Technology

    1980-01-01

    Journal of Mathematical Analysis and Applications , 18, 75-84. Butzer, P.L. and Splettst5sser, W...communications) Iad. Red. Upr. Svyaui R IIA (.oVscow). Kramer, H.P. (1973). The digital form of operators on band-limited functions, Journal of mathematical Analysis and Applications , 44...and certain nonlinear transformations, Journal of Mathematical Analysis and Applications , 53, No. 1,

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

    PubMed

    Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

    2016-01-01

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

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

    PubMed Central

    Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

    2016-01-01

    Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169

  14. Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.

    2010-01-01

    Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

  15. A new nonlocal nonlinear diffusion of image processing

    NASA Astrophysics Data System (ADS)

    Guidotti, Patrick

    A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of Perona-Malik.

  16. Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

    NASA Astrophysics Data System (ADS)

    Kanjilal, Oindrila; Manohar, C. S.

    2017-07-01

    The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

  17. Nonlinear Flow Process: A New Package to Compute Nonlinear Flow in MODFLOW.

    PubMed

    Mayaud, Cyril; Walker, Patrica; Hergarten, Stefan; Birk, Steffen

    2015-01-01

    A new MODFLOW package (Nonlinear Flow Process; NLFP) simulating nonlinear flow following the Forchheimer equation was developed and implemented in MODLFOW-2005. The method is based on an iterative modification of the conductance calculated and used by MODFLOW to obtain an effective Forchheimer conductance. The package is compatible with the different layer types, boundary conditions, and solvers as well as the wetting capability of MODFLOW. The correct implementation is demonstrated using four different benchmark scenarios for which analytical solutions are available. A scenario considering transient flow in a more realistic setting and a larger model domain with a higher number of cells demonstrates that NLFP performs well under more complex conditions, although it converges moderately slower than the standard MODFLOW depending on the nonlinearity of flow. Thus, this new tool opens a field of opportunities to groundwater flow simulation with MODFLOW, especially for core sample simulation or vuggy karstified aquifers as well as for nonlinear flow in the vicinity of pumping wells.

  18. Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

    SciTech Connect

    Buividovich, P. V.

    2011-02-15

    We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.

  19. Characterization of Periodically Poled Nonlinear Materials Using Digital Image Processing

    DTIC Science & Technology

    2008-04-01

    Interactions Due to the nonlinear nature of the response, a nonlinear polarization at new frequencies is generated which can radiate at frequencies not...present in the incident radiation field. This coupling allows energy to be transferred between different wavelengths and forms the basis of the...physical mechanism behind these processes. An isolated atom would radiate in the typical dipole radiation pattern, but in a material, a large number of

  20. Stochastic process of pragmatic information for 2D spiral wave turbulence in globally and locally coupled Alief-Panfilov oscillators

    NASA Astrophysics Data System (ADS)

    Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi

    2017-09-01

    Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.

  1. Nonlinear fiber applications for ultrafast all-optical signal processing

    NASA Astrophysics Data System (ADS)

    Kravtsov, Konstantin

    In the present dissertation different aspects of all-optical signal processing, enabled by the use of nonlinear fibers, are studied. In particular, we focus on applications of a novel heavily GeO2-doped (HD) nonlinear fiber, that appears to be superior to many other types of nonlinear fibers because of its high nonlinearity and suitability for the use in nonlinear optical loop mirrors (NOLMs). Different functions, such as all-optical switching, thresholding, and wavelength conversion, are demonstrated with the HD fibers in the NOLM configuration. These basic functions are later used for realization of ultrafast time-domain demultiplexers, clock recovery, detectors of short pulses in stealth communications, and primitive elements for analog computations. Another important technology that benefits from the use of nonlinear fiber-based signal processing is optical code-division multiple access (CDMA). It is shown in both theory and experiment that all-optical thresholding is a unique way of improving existing detection methods for optical CDMA. Also, it is the way of implementation of true asynchronous optical spread-spectrum networks, which allows full realization of optical CDMA potential. Some aspects of quantum signal processing and manipulation of quantum states are also studied in this work. It is shown that propagation and collisions of Thirring solitons lead to a substantial squeezing of quantum states, which may find applications for generation of squeezed light.

  2. Effects of injection timing on nonlinear dynamics of the combustion process in the lean-burn premixed natural gas engine

    NASA Astrophysics Data System (ADS)

    Ding, Shun-Liang; Song, En-Zhe; Yang, Li-Ping; Yao, Chong; Ma, Xiu-Zhen

    2017-02-01

    The nonlinear dynamics of the combustion process in the lean-burn premixed natural gas engine are studied in this paper. Based on nonlinear dynamic theory, the complexity of the combustion process is analyzed under different injection timing conditions. The phase spaces are reconstructed for the experimentally obtained in-cylinder pressure real-time series and the return maps are plotted for the IMEP time series. The results of phase space reconstruction manifest that the attractors are limited to the finite range in the reconstructed phase space. The attractors have a folded and twist geometry structure. The attractors under medium injection timing conditions are looser and more complex. The return maps indicate the coexistence of the stochastic and deterministic components in the patterns combustion process. With the injection timing increasing, there are both a transition from stochastic to deterministic and a transition from deterministic to stochastic, forming the region of deterministic behavior. The largest Lyapunov exponents (LLE) for in-cylinder pressure time series are calculated and the coefficients of variations (COV) of IMEP are also analyzed. The results express that the LLE values are positive. There are a "steep increase" and a "steep decrease" for the LLE and COV values as the injection timing increasing.

  3. Predators temper the relative importance of stochastic processes in the assembly of prey metacommunities.

    PubMed

    Chase, Jonathan M; Biro, Elizabeth G; Ryberg, Wade A; Smith, Kevin G

    2009-11-01

    Communities assemble through a combination of stochastic processes, which can make environmentally similar communities divergent (high beta-diversity), and deterministic processes, which can make environmentally similar communities convergent (low beta-diversity). Top predators can influence both stochasticity (e.g. colonization and extinction events) and determinism (e.g. size of the realized species pool), in community assembly, and thus their net effect is unknown. We investigated how predatory fish influenced the scaling of prey diversity in ponds at local and regional spatial scales. While fish reduced both local and regional richness, their effects were markedly more intense at the regional scale. Underlying this result was that the presence of fish made localities within metacommunities more similar in their community composition (lower beta-diversity), suggesting that fish enhance the deterministic, relative to the stochastic, components of community assembly. Thus, the presence of predators can alter fundamental mechanisms of community assembly and the scaling of diversity within metacommunities.

  4. Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes.

    PubMed

    Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco

    2013-05-13

    Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.

  5. Nonlinear real-time optical signal processing

    NASA Astrophysics Data System (ADS)

    Sawchuk, A. A.; Jenkins, B. J.

    1986-07-01

    During the period 1 July 1984 - 30 June 1985, the research under Grant AFOSR-84-0181 has concentrated on four major areas. First, work has continued on an experimental sequential optical binary parallel architecture that is constructed from an array of binary optical switching elements (NOR gates) with interconnections done by a computer-generated hologram. We are examining new binary array SLM's, high efficiency, high space-bandwidth product (SBWP) interconnection holograms, and compact reflection versions of the general architecture with the intent of building a larger demonstration system with great capabilities. Next, we have studied improved methods of providing the interconnections in these systems by the use of hybrid digital/analog (facet) holograms. We have examined analytical techniques for mapping circuit diagrams into gate locations and hologram arrays, and optimization procedures to determine the minimum set of necessary space-invariant basis functions and minimum set of space-variant indexing holograms. Another area of study has been the evaluation of devices and materials for high speed optical switching and bistability. Switching energies of 1 to 10 pJ and response times of 10 ns have been experimentally demonstrated at the University of Arizona for devices consisting of an array of Fabry-Perot cavities filled with a nonlinear material. We have begun to use the specifications of these devices and other high speed switching technologies in order to determine better designs and fundamental limits of the binary optical computing architectures under consideration.

  6. NONLINEAR LANGEVIN MODEL WITH PRODUCT STOCHASTICITY FOR BIOLOGICAL NETWORKS: THE CASE OF THE SCHNAKENBERG MODEL

    PubMed Central

    Cao, Youfang; Liang, Jie

    2016-01-01

    Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.

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

    NASA Astrophysics Data System (ADS)

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

    2013-07-01

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

  8. Stochastic processes in climate modeling: from Lorenz to the El-Niño recharge oscillator and beyond

    NASA Astrophysics Data System (ADS)

    Ghil, M.; Chekroun, M. D.; Simonnet, E.

    2009-04-01

    In the past few years, much of the climate community's work has gone toward building highly detailed, IPCC-class general circulation models (GCMs) capable of simulating climate change. In this context, subgrid-scale physics has increasingly been modeled using stochastic processes, but the broader consequences of this approach have not yet been sufficiently explored. Stochastic subgrid-scale parametrizations have substantial non-local effects on the low-frequency dynamics itself. Moreover, due to the random forcing present in these parametrizations, traditional dynamical systems concepts — e.g., strange attractors and deterministic bifurcations — are no longer appropriate. In this talk, we present and apply mathematical concepts and tools developed by L. Arnold and his Bremen school during the last two decades. These tools have not been widely exploited so far in climate research, although they offer powerful theoretical and numerical ways of investigating stochastic models. More specifically, we use random dynamical systems (RDS) theory to analyze the stochastic dynamics of climate models. To illustrate our approach, we consider at first simple conceptual models. The first example is the well-known 3-variable Lorenz (1963) model, to which we add multiplicative noise. We show how to obtain a full description of the resulting stochastic dynamics by computing this model's random attractor and its associated invariant measure. The second example is Timmermann and Jin's (GRL, 2002) nonlinear recharge-discharge model of the El Niño/Southern Oscillation (ENSO), a model that captures several essential features of ENSO physics. A multiplicative noise term is added to this TJ model to represent wind bursts. Numerical simulations of the modified TJ model's random attractor show that Smale horseshoes are excited by the multiplicative noise, even for a parameter regime in which a Hopf bifurcation occurs in the deterministic system; such intricate structures only arise in

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

    PubMed

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

    2014-04-01

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

  10. Stochasticity and determinism: how density-independent and density-dependent processes affect population variability.

    PubMed

    Ohlberger, Jan; Rogers, Lauren A; Stenseth, Nils Chr

    2014-01-01

    A persistent debate in population ecology concerns the relative importance of environmental stochasticity and density dependence in determining variability in adult year-class strength, which contributes to future reproduction as well as potential yield in exploited populations. Apart from the strength of the processes, the timing of density regulation may affect how stochastic variation, for instance through climate, translates into changes in adult abundance. In this study, we develop a life-cycle model for the population dynamics of a large marine fish population, Northeast Arctic cod, to disentangle the effects of density-independent and density-dependent processes on early life-stages, and to quantify the strength of compensatory density dependence in the population. The model incorporates information from scientific surveys and commercial harvest, and dynamically links multiple effects of intrinsic and extrinsic factors on all life-stages, from eggs to spawners. Using a state-space approach we account for observation error and stochasticity in the population dynamics. Our findings highlight the importance of density-dependent survival in juveniles, indicating that this period of the life cycle largely determines the compensatory capacity of the population. Density regulation at the juvenile life-stage dampens the impact of stochastic processes operating earlier in life such as environmental impacts on the production of eggs and climate-dependent survival of larvae. The timing of stochastic versus regulatory processes thus plays a crucial role in determining variability in adult abundance. Quantifying the contribution of environmental stochasticity and compensatory mechanisms in determining population abundance is essential for assessing population responses to climate change and exploitation by humans.

  11. Sensitivity of membranes to their environment. Role of stochastic processes.

    PubMed Central

    Offner, F F

    1984-01-01

    Ionic flow through biomembranes often exhibits a sensitivity to the environment, which is difficult to explain by classical theory, that usually assumes that the free energy available to change the membrane permeability results from the environmental change acting directly on the permeability control mechanism. This implies, for example, that a change delta V in the trans-membrane potential can produce a maximum free energy change, delta V X q, on a gate (control mechanism) carrying a charge q. The analysis presented here shows that when stochastic fluctuations are considered, under suitable conditions (gate cycle times rapid compared with the field relaxation time within a channel), the change in free energy is limited, not by the magnitude of the stimulus, but by the electrochemical potential difference across the membrane, which may be very much greater. Conformational channel gates probably relax more slowly than the field within the channel; this would preclude appreciable direct amplification of the stimulus. It is shown, however, that the effect of impermeable cations such as Ca++ is to restore the amplification of the stimulus through its interaction with the electric field. The analysis predicts that the effect of Ca++ should be primarily to affect the number of channels that are open, while only slightly affecting the conductivity of an open channel. PMID:6093903

  12. Quantum manifestations of classical stochasticity. I. Energetics of some nonlinear systems

    NASA Astrophysics Data System (ADS)

    Weissman, Yitzhak; Jortner, Joshua

    1982-08-01

    In this paper we present the results of a semiclassical investigation and a quantum mechanical study of the bound energy spectrum of the Henon-Heiles Hamiltonian (HHH) and of the Barbanis Hamiltonian (BH). We have derived a simple semiclassical formula for the energy levels E, and for their sensitivity dE/dɛ with respect to the strength ɛ of the nonlinear coupling for the HHH, and established general relations between E and its derivatives dnE/dɛn (n⩾1). Numerical quantum mechanical computations of the energy levels were conducted for the HHH and for the BH. The nonlinear coupling constant was adjusted so that for the HHH there will be ˜150 states up to the classical critical energy Ec and ˜300 states up to the dissociation energy ED. The E values were obtained by direct diagonalization using a basis containing 760 states, while the values of dE/dɛ were computed utilizing the Hellmann-Feynman theorem. Good agreement between the semiclassical and the quantum mechanical spectra was observerd well above Ec. These results raise the distict possibility that the semiclassical approxmation for these nonlinear systems does not break down in the vicinity of Ec and that the bound level structure does not provide a manifestation of the classical transition from quasiperiodic to chaotic motion.

  13. Sliding mode control: an approach to regulate nonlinear chemical processes

    PubMed

    Camacho; Smith

    2000-01-01

    A new approach for the design of sliding mode controllers based on a first-order-plus-deadtime model of the process, is developed. This approach results in a fixed structure controller with a set of tuning equations as a function of the characteristic parameters of the model. The controller performance is judged by simulations on two nonlinear chemical processes.

  14. Approximations of Stochastic Equations Driven by Predictable Processes,

    DTIC Science & Technology

    1987-12-01

    a process of bounded variation , the first two terms are approximated by smoother processes, but the bounded variation processes are left fixed. Thus...equations with differentials of possibly discontinuous semimartingales. Lebesgue-Stieltjes integrals are used in [2] when differentials of bounded variation processes

  15. Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs.

    PubMed

    Schmidt, Deena R; Thomas, Peter J

    2014-04-17

    Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin-Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.

  16. Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

    NASA Astrophysics Data System (ADS)

    Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin

    2016-11-01

    In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 < 1, the disease may die out, and when R¯0 > 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.

  17. An Identification Technique for Non-Linear Dynamical Systems Under Stochastic Excitations

    NASA Astrophysics Data System (ADS)

    Kulisiewicz, M.; Iwankiewicz, R.; Piesiak, S.

    1997-02-01

    An identification technique is devised for SDOF dynamical mechanical systems under random excitations. The system is assumed to be governed by a non-linear equation of motion in general form, in which the restoring force and the dissipative terms are given by arbitrary power functions. Algebraic equations are obtained for the expectations of some suitable excitation and response quantities. It is shown that these equations are valid for any stationary random excitations if the system attains the steady state. Based on these equations, an identification technique has been devised and verified experimentally for white noise and coloured (pink) noise random excitations.

  18. All-optical processing in coherent nonlinear spectroscopy

    SciTech Connect

    Oron, Dan; Dudovich, Nirit; Silberberg, Yaron

    2004-08-01

    In spectroscopy, the fingerprint of a substance is usually comprised of a sequence of spectral lines with characteristic frequencies and strengths. Identification of substances often involves postprocessing, where the measured spectrum is compared with tabulated fingerprint spectra. Here we suggest a scheme for nonlinear spectroscopy, where, through coherent control of the nonlinear process, the information from the entire spectrum can be practically collected into a single coherent entity. We apply this for all-optical analysis of coherent Raman spectra and demonstrate enhanced detection and effective background suppression using coherent processing.

  19. Kinetic theory of age-structured stochastic birth-death processes

    NASA Astrophysics Data System (ADS)

    Greenman, Chris D.; Chou, Tom

    2016-01-01

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

  20. Kinetic theory of age-structured stochastic birth-death processes.

    PubMed

    Greenman, Chris D; Chou, Tom

    2016-01-01

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

  1. A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

    NASA Astrophysics Data System (ADS)

    Taverniers, Søren; Tartakovsky, Daniel M.

    2017-02-01

    Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton-Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

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

    NASA Astrophysics Data System (ADS)

    Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

    2017-08-01

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

  3. Nonlinear Cochlear Signal Processing and Phoneme Perception

    NASA Astrophysics Data System (ADS)

    Allen, Jont B.; Régnier, Marion; Phatak, Sandeep; Li, Feipeng

    2009-02-01

    The most important communication signal is human speech. It is helpful to think of speech communication in terms of Claude Shannon's information theory channel model. When thus viewed, it immediately becomes clear that the most complex part of speech communication channel is in auditory system (the receiver). In my opinion, even after years of work, relatively little is know about how the human auditory system decodes speech. Given cochlear damaged, speech scores are greatly reduced, even with tiny amounts of noise. The exact reasons for this SNR-loss presently remain unclear, but I speculate that the source of this must be cochlear outer hair cell temporal processing, not central processing. Specifically, "temporal edge enhancement" of the speech signal and forward masking could easily be modified in such ears, leading to SNR-Loss. What ever the reason, SNR-Loss is the key problem that needs to be fully researched.

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

    PubMed

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

    2017-01-01

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

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

    PubMed Central

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

    2017-01-01

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

  6. Investigation of Nonlinear Whistler Wave Processes in the Laboratory

    NASA Astrophysics Data System (ADS)

    Tejero, E. M.; Blackwell, D. D.; Amatucci, B.; Crabtree, C. E.; Ganguli, G.; Rudakov, L.

    2015-12-01

    Nonlinear interactions involving whistler wave turbulence can strongly effect the dynamics of the radiation belts. The building blocks of whistler wave turbulence are currently being studied in the NRL Space Physics Simulation Chamber (SPSC) under scaled magnetospheric conditions. These processes include parametric three-wave decay and a nonlinear wave-particle scattering off of thermal electrons that can substantially change the wave vector direction and energy flux. In the laboratory experiments, both of these processes have been observed and characterized. The results are consistent with theoretical predictions. Results from continuing laboratory experiments demonstrating triggered emissions and chorus-like emissions via nonlinear whistler wave-energetic particle interactions will be discussed. These chirped whistler waves are also observed to exhibit three-wave decay/coalescence and wave-particle scattering.

  7. A nonlinear filtering process diagnostic system for the Space Station

    NASA Technical Reports Server (NTRS)

    Yoel, Raymond R.; Buchner, M.; Loparo, K.; Cubukcu, Arif

    1988-01-01

    A nonlinear filtering process diagnostic system, terrestrial simulation and real time implementation studies is presented. Possible applications to Space Station subsystem elements are discussed. A process diagnostic system using model based nonlinear filtering for systems with random structure was shown to provide improvements in stability, robustness, and overall performance in comparison to linear filter based systems. A suboptimal version of the nonlinear filter (zero order approximation filter, or ZOA filter) was used in simulation studies, initially, with a pressurized water reactor model and then with water/steam heat exchanger models. Finally, a real time implementation for leak detection in a water/steam heat exchanger was conducted using the ZOA filter and heat exchanger models.

  8. River water quality management considering agricultural return flows: application of a nonlinear two-stage stochastic fuzzy programming.

    PubMed

    Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam

    2015-04-01

    In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.

  9. Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

    PubMed

    Barber, Jared; Tanase, Roxana; Yotov, Ivan

    2016-06-01

    Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.

  10. Stochastic Process Underlying Emergent Recognition of Visual Objects Hidden in Degraded Images

    PubMed Central

    Murata, Tsutomu; Hamada, Takashi; Shimokawa, Tetsuya; Tanifuji, Manabu; Yanagida, Toshio

    2014-01-01

    When a degraded two-tone image such as a “Mooney” image is seen for the first time, it is unrecognizable in the initial seconds. The recognition of such an image is facilitated by giving prior information on the object, which is known as top-down facilitation and has been intensively studied. Even in the absence of any prior information, however, we experience sudden perception of the emergence of a salient object after continued observation of the image, whose processes remain poorly understood. This emergent recognition is characterized by a comparatively long reaction time ranging from seconds to tens of seconds. In this study, to explore this time-consuming process of emergent recognition, we investigated the properties of the reaction times for recognition of degraded images of various objects. The results show that the time-consuming component of the reaction times follows a specific exponential function related to levels of image degradation and subject's capability. Because generally an exponential time is required for multiple stochastic events to co-occur, we constructed a descriptive mathematical model inspired by the neurophysiological idea of combination coding of visual objects. Our model assumed that the coincidence of stochastic events complement the information loss of a degraded image leading to the recognition of its hidden object, which could successfully explain the experimental results. Furthermore, to see whether the present results are specific to the task of emergent recognition, we also conducted a comparison experiment with the task of perceptual decision making of degraded images, which is well known to be modeled by the stochastic diffusion process. The results indicate that the exponential dependence on the level of image degradation is specific to emergent recognition. The present study suggests that emergent recognition is caused by the underlying stochastic process which is based on the coincidence of multiple stochastic events

  11. Stochastic process underlying emergent recognition of visual objects hidden in degraded images.

    PubMed

    Murata, Tsutomu; Hamada, Takashi; Shimokawa, Tetsuya; Tanifuji, Manabu; Yanagida, Toshio

    2014-01-01

    When a degraded two-tone image such as a "Mooney" image is seen for the first time, it is unrecognizable in the initial seconds. The recognition of such an image is facilitated by giving prior information on the object, which is known as top-down facilitation and has been intensively studied. Even in the absence of any prior information, however, we experience sudden perception of the emergence of a salient object after continued observation of the image, whose processes remain poorly understood. This emergent recognition is characterized by a comparatively long reaction time ranging from seconds to tens of seconds. In this study, to explore this time-consuming process of emergent recognition, we investigated the properties of the reaction times for recognition of degraded images of various objects. The results show that the time-consuming component of the reaction times follows a specific exponential function related to levels of image degradation and subject's capability. Because generally an exponential time is required for multiple stochastic events to co-occur, we constructed a descriptive mathematical model inspired by the neurophysiological idea of combination coding of visual objects. Our model assumed that the coincidence of stochastic events complement the information loss of a degraded image leading to the recognition of its hidden object, which could successfully explain the experimental results. Furthermore, to see whether the present results are specific to the task of emergent recognition, we also conducted a comparison experiment with the task of perceptual decision making of degraded images, which is well known to be modeled by the stochastic diffusion process. The results indicate that the exponential dependence on the level of image degradation is specific to emergent recognition. The present study suggests that emergent recognition is caused by the underlying stochastic process which is based on the coincidence of multiple stochastic events.

  12. Time parameters and Lorentz transformations of relativistic stochastic processes.

    PubMed

    Dunkel, Jörn; Hänggi, Peter; Weber, Stefan

    2009-01-01

    Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time-parametrized process approaches the relativistic Jüttner-Maxwell distribution, the associated proper-time-parametrized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.

  13. Predictive Aspects of a Stochastic Model for Citation Processes.

    ERIC Educational Resources Information Center

    Glanzel, W.; Schubert, A.

    1995-01-01

    A statistical model for citation processes is presented as a particular version of a nonhomogenous birth process. The mean value function and special transition probabilities, which can readily be calculated on the basis of known and estimated parameters, give essential information on the change of citation impact in time. (10 references) (KRN)

  14. First-passage and first-exit times of a Bessel-like stochastic process

    NASA Astrophysics Data System (ADS)

    Martin, Edgar; Behn, Ulrich; Germano, Guido

    2011-05-01

    We study a stochastic process Xt which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is dXt=(nD/Xt)dt+2DdWt, where Wt is the Wiener process. The drift term can arise from a logarithmic potential or from taking Xt as the norm of a multidimensional random walk. Due to the singularity of the drift term for Xt=0, different natures of boundary at the origin arise depending on the real parameter n: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary.

  15. First-passage and first-exit times of a Bessel-like stochastic process.

    PubMed

    Martin, Edgar; Behn, Ulrich; Germano, Guido

    2011-05-01

    We study a stochastic process X(t) which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is dX(t)=(nD/X(t))dt+√(2D)dW(t), where W(t) is the Wiener process. The drift term can arise from a logarithmic potential or from taking X(t) as the norm of a multidimensional random walk. Due to the singularity of the drift term for X(t)=0, different natures of boundary at the origin arise depending on the real parameter n: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary.

  16. Mapping Rule-Based And Stochastic Constraints To Connection Architectures: Implication For Hierarchical Image Processing

    NASA Astrophysics Data System (ADS)

    Miller, Michael I.; Roysam, Badrinath; Smith, Kurt R.

    1988-10-01

    Essential to the solution of ill posed problems in vision and image processing is the need to use object constraints in the reconstruction. While Bayesian methods have shown the greatest promise, a fundamental difficulty has persisted in that many of the available constraints are in the form of deterministic rules rather than as probability distributions and are thus not readily incorporated as Bayesian priors. In this paper, we propose a general method for mapping a large class of rule-based constraints to their equivalent stochastic Gibbs' distribution representation. This mapping allows us to solve stochastic estimation problems over rule-generated constraint spaces within a Bayesian framework. As part of this approach we derive a method based on Langevin's stochastic differential equation and a regularization technique based on the classical autologistic transfer function that allows us to update every site simultaneously regardless of the neighbourhood structure. This allows us to implement a completely parallel method for generating the constraint sets corresponding to the regular grammar languages on massively parallel networks. We illustrate these ideas by formulating the image reconstruction problem based on a hierarchy of rule-based and stochastic constraints, and derive a fully parallelestimator structure. We also present results computed on the AMT DAP500 massively parallel digital computer, a mesh-connected 32x32 array of processing elements which are configured in a Single-Instruction, Multiple Data stream architecture.

  17. Dynamic response of mechanical systems to impulse process stochastic excitations: Markov approach

    NASA Astrophysics Data System (ADS)

    Iwankiewicz, R.

    2016-05-01

    Methods for determination of the response of mechanical dynamic systems to Poisson and non-Poisson impulse process stochastic excitations are presented. Stochastic differential and integro-differential equations of motion are introduced. For systems driven by Poisson impulse process the tools of the theory of non-diffusive Markov processes are used. These are: the generalized Itô’s differential rule which allows to derive the differential equations for response moments and the forward integro-differential Chapman-Kolmogorov equation from which the equation governing the probability density of the response is obtained. The relation of Poisson impulse process problems to the theory of diffusive Markov processes is given. For systems driven by a class of non-Poisson (Erlang renewal) impulse processes an exact conversion of the original non-Markov problem into a Markov one is based on the appended Markov chain corresponding to the introduced auxiliary pure jump stochastic process. The derivation of the set of integro-differential equations for response probability density and also a moment equations technique are based on the forward integro-differential Chapman-Kolmogorov equation. An illustrating numerical example is also included.

  18. 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

  19. Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

    PubMed

    Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

    2007-12-01

    By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

  20. Stochastic thermodynamics for Ising chain and symmetric exclusion process.

    PubMed

    Toral, R; Van den Broeck, C; Escaff, D; Lindenberg, Katja

    2017-03-01

    We verify the finite-time fluctuation theorem for a linear Ising chain in contact with heat reservoirs at its ends. Analytic results are derived for a chain consisting of two spins. The system can be mapped onto a model for particle transport, namely, the symmetric exclusion process in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.