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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. 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

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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

  11. 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.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. A Stochastic Diffusion Process for the Dirichlet Distribution

    DOE PAGES

    Bakosi, J.; Ristorcelli, J. R.

    2013-01-01

    The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled 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 of N variablesmore » subject to a conservation principle. 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

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. Digital set point control of nonlinear stochastic systems

    NASA Technical Reports Server (NTRS)

    Moose, R. L.; Vanlandingham, H. F.; Zwicke, P. E.

    1978-01-01

    A technique for digital control of nonlinear stochastic plants is presented. The development achieves a practical digital algorithm with which the closed-loop system behaves in a classical Type I manner even with gross nonlinearities in the plant structure and low signal-to-noise power ratios. The design procedure is explained in detail and illustrated by an example whose simulated responses testify to the practicality of the approach.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  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. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Prediction Theory of Periodically Correlated Stochastic Processes

    DTIC Science & Technology

    2015-05-12

    SECURITY CLASSIFICATION OF: The research dealt with the prediction problem for periodically correlated sequences, that is the stochastic sequences...was to develop an alternative technique for analysis such sequences . In the first published paper we 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Aug-2014 Approved for Public Release; Distribution Unlimited Final Report: Prediction Theory of Periodically Correlated Stochastic Processes. The

  15. 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

  16. 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.

  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. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  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. 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.

  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. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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?

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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).

  1. 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.

  2. 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.

  3. 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

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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}.

  1. Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

    Junaid, Ali Khan; Muhammad, Asif Zahoor Raja; Ijaz Mansoor, Qureshi

    2011-02-01

    We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations (NLODEs). The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error. The training of these networks is achieved by a hybrid intelligent algorithm, a combination of global search with genetic algorithm and local search by pattern search technique. The applicability of this approach ranges from single order NLODEs, to systems of coupled differential equations. We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods. The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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

  4. 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.

  5. 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.

  6. 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

  7. 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,

  8. 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.

  9. 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.

  10. 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.

  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. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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…

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  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. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. An Extended Stochastic Petri Nets Modeling Method for Collaborative Workflow Process

    NASA Astrophysics Data System (ADS)

    Yi, Yang

    Workflow process modeling is important for BPR; some classic process modeling methods have many defects, such as weakness description ability, high modeling complex, and so on. In this paper, we explore an extended stochastic Petri Nets modeling method based on basic Petri Nets. This method can model concurrency collaborative workflow process under stochastic environment.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  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 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  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. 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.

  6. 1/f noise in a thin stochastic layer described by the discrete nonlinear Schrödinger equation.

    PubMed

    Pando L, C L; Doedel, E J

    2007-01-01

    We investigate the nonlinear dynamics in a trimer, described by the one-dimensional discrete nonlinear Schrödinger equation, with periodic boundary conditions in the presence of a single on-site defect. We make use of numerical continuation to study different families of stationary and periodic solutions in this Hamiltonian system. Taking into account a suitable Poincaré section, we are able to study the dynamics of a generic thin stochastic layer in this conservative system. Our results strongly suggest that intermittency, on the one hand, and transport between two almost invariant sets, on the other hand, are relevant features of the chaotic dynamics. This behavior arises as a result of the formation of the above mentioned stochastic layer connecting two hyperbolic fixed points of the Poincaré return map. We find that the transit times, the time intervals to traverse some suitable sets in phase space, generate 1/f noise. Its origin is explained in terms of a hopping mechanism in a suitable discrete state space of transit times. A qualitatively similar behavior is also found in the standard map, which shows the generic nature of this mechanism. As a physical application of our results, we consider a possible experiment in a ring of weakly coupled Bose-Einstein condensates (BECs) with attractive interactions, where intermittent bursts of the relative phase of two spatially symmetric BECs take place.

  7. 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)

  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. 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.

  10. 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.

  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. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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).

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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,

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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

  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. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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

  10. 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.

  11. 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.

  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. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  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. 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.

  20. 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

  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. 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.

  3. Nonlinear Real-Time Optical Signal Processing

    DTIC Science & Technology

    1990-09-01

    parallelism and 3D global free interconnection capabilities. Finally, the instruction set and the programming of the DOCPs are illustrated. C 195 Academic ...Intelligence, Seattle, October, 1987, pp. 19-26. 2. J. Serra, Image Analysis and Mathematical Morphology, Academic Press. New York, 1982. 3. R. M...Technolo . for Parallel Image Processing (S. Levialdi, Ed.), pp. 79-100, Academic Press, New York, 1985. 13. J. Klein and J. Serra, The texture analyzer

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Stochastic thermodynamics for Ising chain and symmetric exclusion process

    NASA Astrophysics Data System (ADS)

    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.

  13. Modeling laser velocimeter signals as triply stochastic Poisson processes

    NASA Technical Reports Server (NTRS)

    Mayo, W. T., Jr.

    1976-01-01

    Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

  14. Estimation for time-changed self-similar stochastic processes

    NASA Astrophysics Data System (ADS)

    Arroum, W.; Jones, O. D.

    2005-12-01

    We consider processes of the form X(t) = X ~(θ(t)) where X ~ is a self-similar process with stationary increments and θ is a deterministic subordinator with a periodic activity function a = θ'> 0. Such processes have been proposed as models for high-frequency financial data, such as currency exchange rates, where there are known to be daily and weekly periodic fluctuations in the volatility, captured here by the periodic activity function. We review an existing estimator for the activity function then propose three new methods for estimating it and present some experimental studies of their performance. We finish with an application to some foreign exchange and FTSE100 futures data.

  15. Learning process mapping heuristics under stochastic sampling overheads

    NASA Technical Reports Server (NTRS)

    Ieumwananonthachai, Arthur; Wah, Benjamin W.

    1991-01-01

    A statistical method was developed previously for improving process mapping heuristics. The method systematically explores the space of possible heuristics under a specified time constraint. Its goal is to get the best possible heuristics while trading between the solution quality of the process mapping heuristics and their execution time. The statistical selection method is extended to take into consideration the variations in the amount of time used to evaluate heuristics on a problem instance. The improvement in performance is presented using the more realistic assumption along with some methods that alleviate the additional complexity.

  16. An Introduction to the Theory of Self-Similar Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Embrechts, Paul; Maejima, Makoto

    Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence. Naturally, these processes are closely related to the notion of renormalization in statistical and high energy physics. They are also increasingly important in many other fields of application, as there are economics and finance. This paper starts with some basic aspects on self-similar processes and discusses several topics from the point of view of probability theory.

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

    PubMed

    Sainudiin, Raazesh; Welch, David

    2016-12-07

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

  18. Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report

    SciTech Connect

    Tataronis, J. A.

    2004-06-01

    This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.

  19. Process and meaning: nonlinear dynamics and psychology in visual art.

    PubMed

    Zausner, Tobi

    2007-01-01

    Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life.

  20. Nonlinear transport processes in tokamak plasmas. I. The collisional regimes

    NASA Astrophysics Data System (ADS)

    Sonnino, Giorgio; Peeters, Philippe

    2008-06-01

    An application of the thermodynamic field theory (TFT) to transport processes in L-mode tokamak plasmas is presented. The nonlinear corrections to the linear ("Onsager") transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the Pfirsch-Schlüter (P-S) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for Joint European Torus (JET) plasmas are also reported. It is found that the nonlinear electron P-S transport coefficients exceed the values provided by neoclassical theory by a factor that may be of the order 102. The nonlinear classical coefficients exceed the neoclassical ones by a factor that may be of order 2. For JET, the discrepancy between experimental and theoretical results for the electron losses is therefore significantly reduced by a factor 102 when the nonlinear contributions are duly taken into account but, there is still a factor of 102 to be explained. This is most likely due to turbulence. The expressions of the ion transport coefficients, determined by the neoclassical theory in these two regimes, remain unaltered. The low-collisional regimes, i.e., the plateau and the banana regimes, are analyzed in the second part of this work.

  1. Stochastic dilution effects weaken deterministic effects of niche-based processes in species rich forests.

    PubMed

    Wang, Xugao; Wiegand, Thorsten; Kraft, Nathan J B; Swenson, Nathan G; Davies, Stuart J; Hao, Zhanqing; Howe, Robert; Lin, Yiching; Ma, Keping; Mi, Xiangcheng; Su, Sheng-Hsin; Sun, I-fang; Wolf, Amy

    2016-02-01

    Recent theory predicts that stochastic dilution effects may result in species-rich communities with statistically independent species spatial distributions, even if the underlying ecological processes structuring the community are driven by deterministic niche differences. Stochastic dilution is a consequence of the stochastic geometry of biodiversity where the identities of the nearest neighbors of individuals of a given species are largely unpredictable. Under such circumstances, the outcome of deterministic species interactions may vary greatly among individuals of a given species. Consequently, nonrandom patterns in the biotic neighborhoods of species, which might be expected from coexistence or community assembly theory (e.g., individuals of a given species are neighbored by phylogenetically similar species), are weakened or do not emerge, resulting in statistical independence of species spatial distributions. We used data on phylogenetic and functional similarity of tree species in five large forest dynamics plots located across a gradient of species richness to test predictions of the stochastic dilution hypothesis. To quantify the biotic neighborhood of a focal species we used the mean phylogenetic (or functional) dissimilarity of the individuals of the focal species to all species within a local neighborhood. We then compared the biotic neighborhood of species to predictions from stochastic null models to test if a focal species was surrounded by more or less similar species than expected by chance. The proportions of focal species that showed spatial independence with respect to their biotic neighborhoods increased with total species richness. Locally dominant, high-abundance species were more likely to be surrounded by species that were statistically more similar or more dissimilar than expected by chance. Our results suggest that stochasticity may play a stronger role in shaping the spatial structure of species rich tropical forest communities than it

  2. Stochastic behavior of cooling processes in hot nuclei

    SciTech Connect

    de Oliveira, P.M.; Sa Martins, J.S.

    1997-06-01

    The collapse of structure effects observed in hot nuclei is interpreted in terms of a dynamic lattice model which describes the process of nucleon (clusters) evaporation from a hot nucleus, predicting the final mass distribution. Results are compared with experimental data for the {sup 10}B+{sup 9}Be and {sup 10}B+{sup 10}B reactions, and indicate that the structures observed in the low-energy mass distributions in both simulation and experiment are a consequence of the competition between the residual interactions and the thermalization dissipative process. As a characteristic feature of complex evolving systems, this competition leads to long term memory during the dissipative path, the observables becoming thus insensitive to the actual microscopic interactions. {copyright} {ital 1997} {ital The American Physical Society}

  3. Supersymmetric formulation of multiplicative white-noise stochastic processes.

    PubMed

    Arenas, Zochil González; Barci, Daniel G

    2012-04-01

    We present a supersymmetric formulation of Markov processes, represented by a family of Langevin equations with multiplicative white noise. The hidden symmetry encodes equilibrium properties such as fluctuation-dissipation relations. The formulation does not depend on the particular prescription to define the Wiener integral. In this way, different equilibrium distributions, reached at long times for each prescription, can be formally treated on the same footing.

  4. Infinite Order Autoregressive Representations of Multivariate Stationary Stochastic Processes.

    DTIC Science & Technology

    1984-09-01

    FIL -T7 -- SBS Autoregressive and moving average representation; q-variate stationary processes; spectral density matrix; Abel and 1] Cesaro ...has a mean Abel n summable or mean--compounded Cesaro summable autoregressive representation. *20 OISTRISUTION AvAILABILiTy O~F ABSTRACT 121...different reason (motivated by a computational problem in prediction theory) for the feasibility of the compounded Cesaro %%,’..,.: -7- summability method

  5. Evaluation of computing systems using functionals of a Stochastic process

    NASA Technical Reports Server (NTRS)

    Meyer, J. F.; Wu, L. T.

    1980-01-01

    An intermediate model was used to represent the probabilistic nature of a total system at a level which is higher than the base model and thus closer to the performance variable. A class of intermediate models, which are generally referred to as functionals of a Markov process, were considered. A closed form solution of performability for the case where performance is identified with the minimum value of a functional was developed.

  6. Anomalous diffusion and scaling in coupled stochastic processes

    SciTech Connect

    Bel, Golan; Nemenman, Ilya

    2009-01-01

    Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. The diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.

  7. Optimal finite-time processes in stochastic thermodynamics.

    PubMed

    Schmiedl, Tim; Seifert, Udo

    2007-03-09

    For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicit solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and at the end of the process.

  8. Aquatic bacterial assemblage structure in Pozas Azules, Cuatro Cienegas Basin, Mexico: Deterministic vs. stochastic processes.

    PubMed

    Espinosa-Asuar, Laura; Escalante, Ana Elena; Gasca-Pineda, Jaime; Blaz, Jazmín; Peña, Lorena; Eguiarte, Luis E; Souza, Valeria

    2015-06-01

    The aim of this study was to determine the contributions of stochastic vs. deterministic processes in the distribution of microbial diversity in four ponds (Pozas Azules) within a temporally stable aquatic system in the Cuatro Cienegas Basin, State of Coahuila, Mexico. A sampling strategy for sites that were geographically delimited and had low environmental variation was applied to avoid obscuring distance effects. Aquatic bacterial diversity was characterized following a culture-independent approach (16S sequencing of clone libraries). The results showed a correlation between bacterial beta diversity (1-Sorensen) and geographic distance (distance decay of similarity), which indicated the influence of stochastic processes related to dispersion in the assembly of the ponds' bacterial communities. Our findings are the first to show the influence of dispersal limitation in the prokaryotic diversity distribution of Cuatro Cienegas Basin.

  9. Multiobjective optimization in structural design with uncertain parameters and stochastic processes

    NASA Technical Reports Server (NTRS)

    Rao, S. S.

    1984-01-01

    The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

  10. Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times.

    PubMed

    Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

    2016-01-01

    This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.

  11. Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times

    PubMed Central

    Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

    2016-01-01

    This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems. PMID:27907163

  12. Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

    NASA Astrophysics Data System (ADS)

    Allen, Bruce; Romano, Joseph D.

    1999-05-01

    We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation that was used to ``experimentally'' verify the theoretical calculations derived in the paper, and which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. This information consists of graphs of the noise power spectra, overlap reduction functions, and optimal filter functions; also included are tables of the signal-to-noise ratios and sensitivity levels for cross-correlation measurements between different detector pairs. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.

  13. FITTING NONLINEAR ORDINARY DIFFERENTIAL EQUATION MODELS WITH RANDOM EFFECTS AND UNKNOWN INITIAL CONDITIONS USING THE STOCHASTIC APPROXIMATION EXPECTATION–MAXIMIZATION (SAEM) ALGORITHM

    PubMed Central

    Chow, Sy- Miin; Lu, Zhaohua; Zhu, Hongtu; Sherwood, Andrew

    2014-01-01

    The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed. PMID:25416456

  14. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

    PubMed

    Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

    2016-03-01

    The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

  15. Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

    PubMed

    Hua, Changchun; Zhang, Liuliu; Guan, Xinping

    2017-01-01

    This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

  16. Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession.

    PubMed

    Dini-Andreote, Francisco; Stegen, James C; van Elsas, Jan Dirk; Salles, Joana Falcão

    2015-03-17

    Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages--which provide a larger spatiotemporal scale relative to within stage analyses--revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended--and experimentally testable--conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems.

  17. Measuring Edge Importance: A Quantitative Analysis of the Stochastic Shielding Approximation for Random Processes on Graphs

    PubMed Central

    2014-01-01

    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. PMID:24742077

  18. Determining the Stationarity Distance via a Reversible Stochastic Process

    PubMed Central

    Poulos, Marios

    2016-01-01

    The problem of controlling stationarity involves an important aspect of forecasting, in which a time series is analyzed in terms of levels or differences. In the literature, non-parametric stationary tests, such as the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests, have been shown to be very important; however, they are affected by problems with the reliability of lag and sample size selection. To date, no theoretical criterion has been proposed for the lag-length selection for tests of the null hypothesis of stationarity. Their use should be avoided, even for the purpose of so-called ‘confirmation’. The aim of this study is to introduce a new method that measures the distance by obtaining each numerical series from its own time-reversed series. This distance is based on a novel stationary ergodic process, in which the stationary series has reversible symmetric features, and is calculated using the Dynamic Time-warping (DTW) algorithm in a self-correlation procedure. Furthermore, to establish a stronger statistical foundation for this method, the F-test is used as a statistical control and is a suggestion for future statistical research on resolving the problem of a sample of limited size being introduced. Finally, as described in the theoretical and experimental documentation, this distance indicates the degree of non-stationarity of the times series. PMID:27764103

  19. A common stochastic process in solar and stellar flares

    NASA Astrophysics Data System (ADS)

    Li, Chuan; Fang, Cheng

    2015-08-01

    Solar flares, with energies of 1027 - 1032 ergs, are believed to be powered by sudden release of magnetic energy stored in the corona. Stellar flares, observationally 102 - 106 more intense than solar flares, are generally assumed to release energy through the same underlying mechanism: magnetic reconnection. It is thus expected similar statistical properties between two groups of flares. The selected candidates are 23400 solar flares observed over one solar cycle by GOES spacecraft and 3140 stellar flares from Kepler data adapted from the catalog of Balona (MNRAS, 447, 2714, 2015). We examine the flare frequency as a function of duration, energy, and waiting time. The distributions of flare duration and energy can be well understood in the context of the avalanche model of a self-organized criticality (SOC) system (Aschwanden, A&A, 539, 2, 2012). The waiting time distribution of the SOC system can be explained by a non-stationary Poisson process (Li et al. ApJ Letters, 792, 26, 2014).

  20. Optimal Signal Processing in Small Stochastic Biochemical Networks

    PubMed Central

    Ziv, Etay; Nemenman, Ilya; Wiggins, Chris H.

    2007-01-01

    We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the “cross-talk” phenomenon as well as the previously unexplained observation that transcription factors that undergo proteolysis are more likely to be auto-repressive. PMID:17957259

  1. A study of the nonlinear response of the upper atmosphere to episodic and stochastic acoustic-gravity wave forcing

    NASA Astrophysics Data System (ADS)

    Lin, Cissi Y.; Deng, Yue; Sheng, Cheng; Drob, Douglas P.

    2017-01-01

    Perturbations caused by geophysical and anthropogenic events on the ground have been observed to propagate upward and impact the upper atmosphere. Gravity waves with wavelengths less than 750 km are known to be responsible for the total electron content (TEC) perturbations and to play a significant role in the mass, momentum, and energy budgets of the mesosphere and lower thermosphere. These waves are, however, difficult to continuously measure, globally resolve, and deterministically specify in first-principle ionosphere-thermosphere (IT) models. In this study, we investigate IT response to induced acoustic-gravity waves resulting from strong time-varying lower atmospheric wave forcing, including a traveling wave packet (TWP) and stochastic gravity wave (SGW) fields using the nonlinear Global Ionosphere Thermosphere Model (GITM) with high-resolution grids of 0.08° in longitude and latitude. When TWP and SGW forcing occurs concurrently, the induced gravity waves (GWs) cause variation of ±8.8% in neutral, ±6.2% in electron density, and ±1.5% in TEC. The magnitudes decrease by 2.4% (from ±8.8% to ±6.4%) with the SGW effects simulated separately and subtracted; importantly, interactions between TWP and SGW contribute to ±1.4% of the perturbations. On the other hand, the induced acoustic waves (AWs) cause variation of ±13.9% in neutral, ±2.1% in electron density, and ±0.4% in TEC. Furthermore, GWs sustain tens of minutes after the TWP has passed through the lower atmosphere and clear traveling ionospheric disturbances and traveling atmospheric disturbances are developed. We demonstrate that clear wave structures from an episodic event can be isolated even under a ubiquitously and overwhelmingly perturbed atmosphere.

  2. Relative frequencies of constrained events in stochastic processes: An analytical approach

    NASA Astrophysics Data System (ADS)

    Rusconi, S.; Akhmatskaya, E.; Sokolovski, D.; Ballard, N.; de la Cal, J. C.

    2015-10-01

    The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈104 ). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

  3. Relative frequencies of constrained events in stochastic processes: An analytical approach.

    PubMed

    Rusconi, S; Akhmatskaya, E; Sokolovski, D; Ballard, N; de la Cal, J C

    2015-10-01

    The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈10(4)). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

  4. Strong perturbations in nonlinear systems. The case of stochastic-like resonance and its biological relevance from a complex system's perspective

    NASA Astrophysics Data System (ADS)

    Basios, Vasileios

    2016-09-01

    A novel case of probabilistic coupling for hybrid stochastic systems with chaotic components via Markovian switching is presented. We study its stability in the norm, in the sense of Lyapunov and present a quantitative scheme for detection of stochastic stability in the mean. In particular we examine the stability of chaotic dynamical systems in which a representative parameter undergoes a Markovian switching between two values corresponding to two qualitatively different attractors. To this end we employ, as case studies, the behaviour of two representative chaotic systems (the classic Rössler and the Thomas-Rössler models) under the influence of a probabilistic switch which modifies stochastically their parameters. A quantitative measure, based on a Lyapunov function, is proposed which detects regular or irregular motion and regimes of stability. In connection to biologically inspired models (Thomas-Rössler models), where strong fluctuations represent qualitative structural changes, we observe the appearance of stochastic resonance-like phenomena i.e. transitions that lead to orderly behavior when the noise increases. These are attributed to the nonlinear response of the system.

  5. Minimal representation of matrix valued white stochastic processes and U-D factorisation of algorithms for optimal control

    NASA Astrophysics Data System (ADS)

    Van Willigenburg, L. Gerard; De Koning, Willem L.

    2013-02-01

    Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others. Another, that is more general and concise, uses Kronecker products instead. This article relates the statistics of both descriptions and shows their advantages and disadvantages. As to the first description, an important result that comes out is the minimum number of matrices multiplied by scalar, independent, stochastic processes needed to represent a certain matrix valued white stochastic process, together with an associated minimal representation. As to the second description, an important result concerns the generation of all Kronecker products that represent relevant statistics. Both results facilitate the specification of statistics of systems with white stochastic parameters. The second part of this article further exploits these results to perform an U-D factorisation of an algorithm to compute optimal dynamic output feedback controllers (optimal compensators) for linear discrete-time systems with white stochastic parameters and quadratic sum criteria. U-D factorisation of this type of algorithm is new. By solving several numerical examples, the U-D factored algorithm is compared with a conventional algorithm.

  6. Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes

    PubMed Central

    Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D.

    2016-01-01

    This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. PMID:26993062

  7. SAR processing with non-linear FM chirp waveforms.

    SciTech Connect

    Doerry, Armin Walter

    2006-12-01

    Nonlinear FM (NLFM) waveforms offer a radar matched filter output with inherently low range sidelobes. This yields a 1-2 dB advantage in Signal-to-Noise Ratio over the output of a Linear FM (LFM) waveform with equivalent sidelobe filtering. This report presents details of processing NLFM waveforms in both range and Doppler dimensions, with special emphasis on compensating intra-pulse Doppler, often cited as a weakness of NLFM waveforms.

  8. Tracking instantaneous entropy in heartbeat dynamics through inhomogeneous point-process nonlinear models.

    PubMed

    Valenza, Gaetano; Citi, Luca; Scilingo, Enzo Pasquale; Barbieri, Riccardo

    2014-01-01

    Measures of entropy have been proved as powerful quantifiers of complex nonlinear systems, particularly when applied to stochastic series of heartbeat dynamics. Despite the remarkable achievements obtained through standard definitions of approximate and sample entropy, a time-varying definition of entropy characterizing the physiological dynamics at each moment in time is still missing. To this extent, we propose two novel measures of entropy based on the inho-mogeneous point-process theory. The RR interval series is modeled through probability density functions (pdfs) which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through such probability functions, the proposed indices are able to provide instantaneous tracking of autonomic nervous system complexity. Of note, the distance between the time-varying phase-space vectors is calculated through the Kolmogorov-Smirnov distance of two pdfs. Experimental results, obtained from the analysis of RR interval series extracted from ten healthy subjects during stand-up tasks, suggest that the proposed entropy indices provide instantaneous tracking of the heartbeat complexity, also allowing for the definition of complexity variability indices.

  9. Signature of nonlinear damping in geometric structure of a nonequilibrium process

    NASA Astrophysics Data System (ADS)

    Kim, Eun-jin; Hollerbach, Rainer

    2017-02-01

    We investigate the effect of nonlinear interaction on the geometric structure of a nonequilibrium process. Specifically, by considering a driven-dissipative system where a stochastic variable x is damped either linearly (∝x ) or nonlinearly (∝x3 ) while driven by a white noise, we compute the time-dependent probability density functions (PDFs) during the relaxation towards equilibrium from an initial nonequilibrium state. From these PDFs, we quantify the information change by the information length L , which is the total number of statistically distinguishable states which the system passes through from the initial state to the final state. By exploiting different initial PDFs and the strength D of the white-noise forcing, we show that for a linear system, L increases essentially linearly with an initial mean value y0 of x as L ∝y0 , demonstrating the preservation of a linear geometry. In comparison, in the case of a cubic damping, L has a power-law scaling as L ∝y0m , with the exponent m depending on D and the width of the initial PDF. The rate at which information changes also exhibits a robust power-law scaling with time for the cubic damping.

  10. Temporal Beta Diversity of Bird Assemblages in Agricultural Landscapes: Land Cover Change vs. Stochastic Processes.

    PubMed

    Baselga, Andrés; Bonthoux, Sébastien; Balent, Gérard

    2015-01-01

    Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cover change that occurred between 1982 and 2007 on (i) the species composition (presence/absence) of bird assemblages and (ii) the spatial pattern of taxonomic beta diversity. We also compared the observed temporal change of bird assemblages with a null model accounting for the effect of stochastic dynamics on temporal beta diversity. Temporal assemblage dissimilarity was partitioned into two separate components, accounting for the replacement of species (i.e. turnover) and for the nested species losses (or gains) from one time to the other (i.e. nestedness-resultant dissimilarity), respectively. Neither the turnover nor the nestedness-resultant components of temporal variation were accurately explained by any of the measured variables accounting for land cover change (r(2)<0.06 in all cases). Additionally, the amount of spatial assemblage heterogeneity in the region did not significantly change between 1982 and 2007, and site-specific observed temporal dissimilarities were larger than null expectations in only 1% of sites for temporal turnover and 13% of sites for nestedness-resultant dissimilarity. Taken together, our results suggest that land cover change in this agricultural landscape had little impact on temporal beta diversity of bird assemblages. Although other unmeasured deterministic process could be driving the observed patterns, it is also possible that the observed changes in presence/absence species composition of local bird assemblages might be the consequence of stochastic processes in which species populations appeared and disappeared from specific localities in

  11. Stochastic analysis and simulation of hydrometeorological processes for optimizing hybrid renewable energy systems

    NASA Astrophysics Data System (ADS)

    Tsekouras, Georgios; Ioannou, Christos; Efstratiadis, Andreas; Koutsoyiannis, Demetris

    2013-04-01

    The drawbacks of conventional energy sources including their negative environmental impacts emphasize the need to integrate renewable energy sources into energy balance. However, the renewable sources strongly depend on time varying and uncertain hydrometeorological processes, including wind speed, sunshine duration and solar radiation. To study the design and management of hybrid energy systems we investigate the stochastic properties of these natural processes, including possible long-term persistence. We use wind speed and sunshine duration time series retrieved from a European database of daily records and we estimate representative values of the Hurst coefficient for both variables. We conduct simultaneous generation of synthetic time series of wind speed and sunshine duration, on yearly, monthly and daily scale. To this we use the Castalia software system which performs multivariate stochastic simulation. Using these time series as input, we perform stochastic simulation of an autonomous hypothetical hybrid renewable energy system and optimize its performance using genetic algorithms. For the system design we optimize the sizing of the system in order to satisfy the energy demand with high reliability also minimizing the cost. While the simulation scale is the daily, a simple method allows utilizing the subdaily distribution of the produced wind power. Various scenarios are assumed in order to examine the influence of input parameters, such as the Hurst coefficient, and design parameters such as the photovoltaic panel angle.

  12. The Tool for Designing Engineering Systems Using a New Optimization Method Based on a Stochastic Process

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

    The conventional optimization methods were based on a deterministic approach, since their purpose is to find out an exact solution. However, these methods have initial condition dependence and risk of falling into local solution. In this paper, we propose a new optimization method based on a concept of path integral method used in quantum mechanics. The method obtains a solutions as an expected value (stochastic average) using a stochastic process. The advantages of this method are not to be affected by initial conditions and not to need techniques based on experiences. We applied the new optimization method to a design of the hang glider. In this problem, not only the hang glider design but also its flight trajectory were optimized. The numerical calculation results showed that the method has a sufficient performance.

  13. Design Tool Using a New Optimization Method Based on a Stochastic Process

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

    Conventional optimization methods are based on a deterministic approach since their purpose is to find out an exact solution. However, such methods have initial condition dependence and the risk of falling into local solution. In this paper, we propose a new optimization method based on the concept of path integrals used in quantum mechanics. The method obtains a solution as an expected value (stochastic average) using a stochastic process. The advantages of this method are that it is not affected by initial conditions and does not require techniques based on experiences. We applied the new optimization method to a hang glider design. In this problem, both the hang glider design and its flight trajectory were optimized. The numerical calculation results prove that performance of the method is sufficient for practical use.

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

    PubMed

    Finley, Benjamin J; Kilkki, Kalevi

    2014-01-01

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

  15. Some Results on the Analysis of Stochastic Processes with Uncertain Transition Probabilities and Robust Optimal Control

    SciTech Connect

    Keyong Li; Seong-Cheol Kang; I. Ch. Paschalidis

    2007-09-01

    This paper investigates stochastic processes that are modeled by a finite number of states but whose transition probabilities are uncertain and possibly time-varying. The treatment of uncertain transition probabilities is important because there appears to be a disconnection between the practice and theory of stochastic processes due to the difficulty of assigning exact probabilities to real-world events. Also, when the finite-state process comes as a reduced model of one that is more complicated in nature (possibly in a continuous state space), existing results do not facilitate rigorous analysis. Two approaches are introduced here. The first focuses on processes with one terminal state and the properties that affect their convergence rates. When a process is on a complicated graph, the bound of the convergence rate is not trivially related to that of the probabilities of individual transitions. Discovering the connection between the two led us to define two concepts which we call 'progressivity' and 'sortedness', and to a new comparison theorem for stochastic processes. An optimality criterion for robust optimal control also derives from this comparison theorem. In addition, this result is applied to the case of mission-oriented autonomous robot control to produce performance estimate within a control framework that we propose. The second approach is in the MDP frame work. We will introduce our preliminary work on optimistic robust optimization, which aims at finding solutions that guarantee the upper bounds of the accumulative discounted cost with prescribed probabilities. The motivation here is to address the issue that the standard robust optimal solution tends to be overly conservative.

  16. Nonlinear optical polymers for electro-optic signal processing

    NASA Technical Reports Server (NTRS)

    Lindsay, Geoffrey A.

    1991-01-01

    Photonics is an emerging technology, slated for rapid growth in communications systems, sensors, imagers, and computers. Its growth is driven by the need for speed, reliability, and low cost. New nonlinear polymeric materials will be a key technology in the new wave of photonics devices. Electron-conjubated polymeric materials offer large electro-optic figures of merit, ease of processing into films and fibers, ruggedness, low cost, and a plethora of design options. Several new broad classes of second-order nonlinear optical polymers were developed at the Navy's Michelson Laboratory at China Lake, California. Polar alignment in thin film waveguides was achieved by electric-field poling and Langmuir-Blodgett processing. Our polymers have high softening temperatures and good aging properties. While most of the films can be photobleached with ultraviolet (UV) light, some have excellent stability in the 500-1600 nm range, and UV stability in the 290-310 nm range. The optical nonlinear response of these polymers is subpicosecond. Electro-optic switches, frequency doublers, light modulators, and optical data storage media are some of the device applications anticipated for these polymers.

  17. Nonlinear Statistical Signal Processing: A Particle Filtering Approach

    SciTech Connect

    Candy, J

    2007-09-19

    A introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations.

  18. Direct real-space observation of nearly stochastic behavior in magnetization reversal process on a nanoscale

    SciTech Connect

    Im, M.-Y.; Kim, D.-H.; Lee, K.-D.; Fischer, P.; Shin, S.-C.

    2007-06-01

    We report a non-deterministic nature in the magnetization reversal of nanograins of CoCrPt alloy film. Magnetization reversal process of CoCrPt alloy film is investigated using high resolution soft X-ray microscopy which provides real space images with a spatial resolution of 15 nm. Domain nucleation sites mostly appear stochastically distributed within repeated hysteretic cycles, where the correlation increases as the strength of the applied magnetic field increases in the descending and ascending branches of the major hysteresis loop. In addition, domain configuration is mostly asymmetric with inversion of an applied magnetic field in the hysteretic cycle. Nanomagnetic simulation considering thermal fluctuations of the magnetic moments of the grains explains the nearly stochastic nature of the domain nucleation behavior observed in CoCrPt alloy film. With the bit size in high-density magnetic recording media approaching nanometer length scale, one of the fundamental and crucial issues is whether the domain nucleation during magnetization reversal process exhibits a deterministic behavior. Repeatability of local domain nucleation and deterministic switching behavior are basic and essential factors for achieving high performance in high-density magnetic recording [1-3]. Most experimental studies on this issue reported so far have been mainly performed by indirect probes through macroscopic hysteresis loop and Barkhausen pattern measurements, which provide the ensemble-average magnetization. Thus, they are inadequate to gain insight into the domain-nucleation behavior on a nanometer length scale during the magnetization reversal process [4-6]. Very recently, coherent X-ray speckle metrology, where the speckle pattern observed in reciprocal space acts as a fingerprint of the domain configurations, was adopted to investigate stochastic behavior in the magnetization reversal of a Co/Pt multilayer film [7,8]. However, no direct observation on the stochastic behavior of

  19. Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing.

    PubMed

    Hänggi, Peter

    2002-03-12

    Noise is usually thought of as the enemy of order rather than as a constructive influence. In nonlinear systems that possess some sort of threshold, random noise plays a beneficial role in enhancing the detection of weak information-carrying signals. This phenomenon, termed stochastic resonance, does find useful applications in physical, biological, and biomedical contexts. Certain biological systems may even use this effect for optimizing function and behavior.

  20. Exploring Empirical Rank-Frequency Distributions Longitudinally through a Simple Stochastic Process

    PubMed Central

    Finley, Benjamin J.; Kilkki, Kalevi

    2014-01-01

    The frequent appearance of empirical rank-frequency laws, such as Zipf’s law, in a wide range of domains reinforces the importance of understanding and modeling these laws and rank-frequency distributions in general. In this spirit, we utilize a simple stochastic cascade process to simulate several empirical rank-frequency distributions longitudinally. We focus especially on limiting the process’s complexity to increase accessibility for non-experts in mathematics. The process provides a good fit for many empirical distributions because the stochastic multiplicative nature of the process leads to an often observed concave rank-frequency distribution (on a log-log scale) and the finiteness of the cascade replicates real-world finite size effects. Furthermore, we show that repeated trials of the process can roughly simulate the longitudinal variation of empirical ranks. However, we find that the empirical variation is often less that the average simulated process variation, likely due to longitudinal dependencies in the empirical datasets. Finally, we discuss the process limitations and practical applications. PMID:24755621

  1. Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

    NASA Astrophysics Data System (ADS)

    Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

    2016-12-01

    We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

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

    SciTech Connect

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir

    2014-05-28

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

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

    NASA Astrophysics Data System (ADS)

    Monràs, Alex; Winter, Andreas

    2016-01-01

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

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

    SciTech Connect

    Monràs, Alex; Winter, Andreas

    2016-01-15

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

  5. Experimental characterization of nonlinear processes of whistler branch waves

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

    Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.

  6. Low Doses of Traditional Nanophytomedicines for Clinical Treatment: Manufacturing Processes and Nonlinear Response Patterns.

    PubMed

    Bell, Iris R; Sarter, Barbara; Standish, Leanna J; Banerji, Prasanta; Banerji, Pratip

    2015-06-01

    The purpose of the present paper is to (a) summarize evidence for the nanoparticle nature and biological effects of traditional homeopathically-prepared medicines at low and ultralow doses; (b) provide details of historically-based homeopathic green manufacturing materials and methods, relating them to top-down mechanical attrition and plant-based biosynthetic processes in modern nanotechnology; (c) outline the potential roles of nonlinear dose-responses and dynamical interactions with complex adaptive systems in generating endogenous amplification processes during low dose treatment. Possible mechanisms of low dose effects, for which there is evidence involving nanoparticles and/or homeopathically-manufactured medicines, include hormesis, time-dependent sensitization, and stochastic resonance. All of the proposed mechanisms depend upon endogenous nonlinear amplification processes in the recipient organism in interaction with the salient, albeit weak signal properties of the medicine. Conventional ligand-receptor mechanisms relevant to higher doses are less likely involved. Effects, especially for homeopathically-prepared nanophytomedicines, include bidirectional host state-dependent changes in function. Homeopathic clinicians report successful treatment of serious infections and cancers. Preclinical biological evidence is consistent with such claims. Controlled biological data on homeopathically-prepared medicines indicate modulation of gene expression and biological signaling pathways regulating cell cycles, immune reactions, and central nervous system function from studies on cells, animals, and human subjects. As a 200-year old system of traditional medicine used by millions of people worldwide, homeopathy offers a pulsed low dose treatment strategy and strong safety record to facilitate progress in translational nanomedicine with plants and other natural products. In turn, modern nanotechnology methods can improve homeopathic manufacturing procedures

  7. The full penetration hole as a stochastic process: controlling penetration depth in keyhole laser-welding processes

    NASA Astrophysics Data System (ADS)

    Blug, A.; Abt, F.; Nicolosi, L.; Heider, A.; Weber, R.; Carl, D.; Höfler, H.; Tetzlaff, R.

    2012-07-01

    Although laser-welding processes are frequently used in industrial production the quality control of these processes is not satisfactory yet. Until recently, the "full penetration hole" was presumed as an image feature which appears when the keyhole opens at the bottom of the work piece. Therefore it was used as an indicator for full penetration only. We used a novel camera based on "cellular neural networks" which enables measurements at frame rates up to 14 kHz. The results show that the occurrence of the full penetration hole can be described as a stochastic process. The probability to observe it increases near the full penetration state. In overlap joints, a very similar image feature appears when the penetration depth reaches the gap between the sheets. This stochastic process is exploited by a closed-loop system which controls penetration depth near the bottom of the work piece ("full penetration") or near the gap in overlap joints ("partial penetration"). It guides the welding process at the minimum laser power necessary for the required penetration depth. As a result, defects like spatters are reduced considerably and the penetration depth becomes independent of process drifts such as feeding rate or pollution on protection glasses.

  8. Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems

    SciTech Connect

    Stimming, H.-P.; Mauser, N. J.; Mazets, I. E.

    2010-07-02

    We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.

  9. The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

    NASA Astrophysics Data System (ADS)

    Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

    2012-06-01

    A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

  10. Real-Time Implementation of Nonlinear Processing Functions.

    DTIC Science & Technology

    1981-08-01

    release; 8 1 1 06 054 distribution Ualmlted, K REA-IA WOME ~ENTATION FNOLIEA 15CTrJ 7-. 14Srl8 VT TC@SNO NO: RCIPTIENT Ca ANT0 NUMBER5 Malibu CA 93065 epc...nonlinear filtering for trajectory control and guid- ance, "smart" sensing, picture processing, and bandwidth compression. These technologies could benefit ...4. P.K. Watson, J.M. Pollack and J.B. Flannery, "Liquid Crystals and Ordered Fluids, Vol. 3, p. 421, (1977). 5. I.G. Chistyakov and L.K. Vistin, Soy

  11. Flow prediction using stochastic emulators of flood wave propagation process: middle Vistula case study

    NASA Astrophysics Data System (ADS)

    Romanowicz, Renata; Karamuz, Emilia; Kochanek, Krzysztof

    2014-05-01

    Flow predictions along the river reach are required for flood protection, flood risk assessment and also for the planning of water infrastructures and water management. Due to uncertainties involved in hydro-meteorological observations and mathematical modelling, the predictions are always uncertain. Their uncertainty increases with an increase of the time horizon of the prediction - e.g. when forecasts of flow are required many days ahead. Apart from the uncertainty, also the speed of forecast acquisition might also be of concern, in particular when fast preventive actions should be taken to issue flood warning to the public, or some water management actions should be performed. In these cases, the stochastic emulators of flood wave propagation might be very useful. The emulators can be based on available data but also be built using the modelled flows along the river in the absence of the required observations. The middle River Vistula reach stretches between Zawichost and Warsaw and is 100 km long. Two distributed flow routing models were built for the reach based on the detailed river channel and floodplain geometry data. These models are used for the temporal and spatial interpolation of the water level observations available at only 5 cross-sections and in the form of daily averages of water levels. The observations span over 50 years, but they are irregular, with long periods missing either flow or level data. The observed and modelled water level data were used to build stochastic emulators in the form of a nonlinear transformation of water levels at cross-sections along the river reach. The validation of the emulators and the comparison of their performance are done using the available observations of water levels at those cross-sections. A discussion is given on the uncertainty of predictions and the application of emulators to on-line forecasting. This work was partly supported by the project "Stochastic flood forecasting system (The River Vistula reach

  12. Nonlinear processes reinforce extreme Indian Ocean Dipole events

    NASA Astrophysics Data System (ADS)

    Ng, Benjamin; Cai, Wenju; Walsh, Kevin; Santoso, Agus

    2015-06-01

    Under global warming, climate models show an almost three-fold increase in extreme positive Indian Ocean Dipole (pIOD) events by 2100. These extreme pIODs are characterised by a westward extension of cold sea surface temperature anomalies (SSTAs) which push the downstream atmospheric convergence further west. This induces severe drought and flooding in the surrounding countries, but the processes involved in this projected increase have not been fully examined. Here we conduct a detailed heat budget analysis of 19 models from phase 5 of the Coupled Model Intercomparison Project and show that nonlinear zonal and vertical heat advection are important for reinforcing extreme pIODs. Under greenhouse warming, these nonlinear processes do not change significantly in amplitude, but the frequency of occurrences surpassing a threshold increases. This is due to the projected weakening of the Walker circulation, which leads to the western tropical Indian Ocean warming faster than the east. As such, the magnitude of SSTAs required to shift convection westward is relatively smaller, allowing these convection shifts to occur more frequently in the future. The associated changes in wind and ocean current anomalies support the zonal and vertical advection terms in a positive feedback process and consequently, moderate pIODs become more extreme-like.

  13. Nonlinear processes reinforce extreme Indian Ocean Dipole events.

    PubMed

    Ng, Benjamin; Cai, Wenju; Walsh, Kevin; Santoso, Agus

    2015-06-26

    Under global warming, climate models show an almost three-fold increase in extreme positive Indian Ocean Dipole (pIOD) events by 2100. These extreme pIODs are characterised by a westward extension of cold sea surface temperature anomalies (SSTAs) which push the downstream atmospheric convergence further west. This induces severe drought and flooding in the surrounding countries, but the processes involved in this projected increase have not been fully examined. Here we conduct a detailed heat budget analysis of 19 models from phase 5 of the Coupled Model Intercomparison Project and show that nonlinear zonal and vertical heat advection are important for reinforcing extreme pIODs. Under greenhouse warming, these nonlinear processes do not change significantly in amplitude, but the frequency of occurrences surpassing a threshold increases. This is due to the projected weakening of the Walker circulation, which leads to the western tropical Indian Ocean warming faster than the east. As such, the magnitude of SSTAs required to shift convection westward is relatively smaller, allowing these convection shifts to occur more frequently in the future. The associated changes in wind and ocean current anomalies support the zonal and vertical advection terms in a positive feedback process and consequently, moderate pIODs become more extreme-like.

  14. StochPy: a comprehensive, user-friendly tool for simulating stochastic biological processes.

    PubMed

    Maarleveld, Timo R; Olivier, Brett G; Bruggeman, Frank J

    2013-01-01

    Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. There is a demand for versatile, stochastic modeling environments with extensive, preprogrammed statistics functions and plotting capabilities that hide the mathematics from the novice users and offers low-level programming access to the experienced user. Here we present StochPy (Stochastic modeling in Python), which is a flexible software tool for stochastic simulation in cell biology. It provides various stochastic simulation algorithms, SBML support, analyses of the probability distributions of molecule copy numbers and event waiting times, analyses of stochastic time series, and a range of additional statistical functions and plotting facilities for stochastic simulations. We illustrate the functionality of StochPy with stochastic models of gene expression, cell division, and single-molecule enzyme kinetics. StochPy has been successfully tested against the SBML stochastic test suite, passing all tests. StochPy is a comprehensive software package for stochastic simulation of the molecular control networks of living cells. It allows novice and experienced users to study stochastic phenomena in cell biology. The integration with other Python software makes StochPy both a user-friendly and easily extendible simulation tool.

  15. A simple nonlinear PD controller for integrating processes.

    PubMed

    Dey, Chanchal; Mudi, Rajani K; Simhachalam, Dharmana

    2014-01-01

    Many industrial processes are found to be integrating in nature, for which widely used Ziegler-Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.

  16. Nonlinear Markov Semigroups and Interacting Lévy Type Processes

    NASA Astrophysics Data System (ADS)

    Kolokoltsov, Vassili N.

    2007-02-01

    Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B( X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space R d (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.

  17. Stochastic Convection Parameterizations

    NASA Technical Reports Server (NTRS)

    Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios

    2012-01-01

    computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts

  18. URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries

    PubMed Central

    2012-01-01

    Background Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. Results We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic

  19. Whole-field visual motion drives swimming in larval zebrafish via a stochastic process.

    PubMed

    Portugues, Ruben; Haesemeyer, Martin; Blum, Mirella L; Engert, Florian

    2015-05-01

    Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds (<10 mm s(-1)) and then plateaus for higher values. Typical latencies are >1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models.

  20. Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models

    SciTech Connect

    Curtis, J.H.; Michelotti, M.D.; Riemer, N.; Heath, M.T.; West, M.

    2016-10-01

    Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions. While particle-resolved methods have substantial benefits for highly detailed simulations, these techniques suffer from high computational cost, motivating efforts to improve their algorithmic efficiency. Here we formulate an algorithm for accelerating particle removal processes by aggregating particles of similar size into bins. We present the Binned Algorithm for particle removal processes and analyze its performance with application to the atmospherically relevant process of aerosol dry deposition. We show that the Binned Algorithm can dramatically improve the efficiency of particle removals, particularly for low removal rates, and that computational cost is reduced without introducing additional error. In simulations of aerosol particle removal by dry deposition in atmospherically relevant conditions, we demonstrate about 50-times increase in algorithm efficiency.

  1. Monolithic high voltage nonlinear transmission line fabrication process

    DOEpatents

    Cooper, G.A.

    1994-10-04

    A process for fabricating sequential inductors and varistor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varistor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process. 6 figs.

  2. Monolithic high voltage nonlinear transmission line fabrication process

    DOEpatents

    Cooper, Gregory A.

    1994-01-01

    A process for fabricating sequential inductors and varactor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varactor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process.

  3. High-gain nonlinear observer for simple genetic regulation process

    NASA Astrophysics Data System (ADS)

    Torres, L. A.; Ibarra-Junquera, V.; Escalante-Minakata, P.; Rosu, H. C.

    2007-07-01

    High-gain nonlinear observers occur in the nonlinear automatic control theory and are in standard usage in chemical engineering processes. We apply such a type of analysis in the context of a very simple one-gene regulation circuit. In general, an observer combines an analytical differential-equation-based model with partial measurement of the system in order to estimate the non-measured state variables. We use one of the simplest observers, that of Gauthier et al., which is a copy of the original system plus a correction term which is easy to calculate. For the illustration of this procedure, we employ a biological model, recently adapted from Goodwin's old book by De Jong, in which one plays with the dynamics of the concentrations of the messenger RNA coding for a given protein, the protein itself, and a single metabolite. Using the observer instead of the metabolite, it is possible to rebuild the non-measured concentrations of the mRNA and the protein.

  4. Multivariate moment closure techniques for stochastic kinetic models

    SciTech Connect

    Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.

    2015-09-07

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

  5. Multivariate moment closure techniques for stochastic kinetic models.

    PubMed

    Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H

    2015-09-07

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

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

    PubMed

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

    2017-02-01

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

  7. Personality as continuous stochastic process: what Western personality theory can learn from classical confucianism.

    PubMed

    Giordano, Peter J

    2014-06-01

    An important objective of personality psychology is to provide compelling descriptions and explanations of intraindividual personality dynamics that capture the unique qualities of persons. Among contemporary Western personality theories, the Five-Factor Model enjoys prominence in describing individual differences in personality traits. It falls short, however, in its ability to work with intraindividual personality function. This article argues that classical Confucianism, originating 2500 years ago in mainland China, offers Western personality psychologists important theoretical resources for capturing the complex and dynamic processes inherent in human personality. The Confucian perspective emphasizes a behaviorally anchored, continuous, stochastic, process-oriented understanding of the self as relationally constructed and proposes an elegant description of the relational virtuosity of exemplary persons. The article concludes with five characteristics of a Confucian inspired model of personality and questions the viability of a universal theory of personality.

  8. How baryonic feedback processes can affect dark matter halos: a stochastic model

    NASA Astrophysics Data System (ADS)

    Freundlich, J.; El-Zant, A.; Combes, F.

    2016-12-01

    Feedback processes from stars and active galactic nuclei result in gas density fluctuations which can contribute to `heating' dark matter haloes, decrease their density at the center and hence form more realistic `cores' than the steep `cusps' predicted by cold dark matter (CDM) simulations. We present a theoretical model deriving this effect from first principles: stochastic density variations in the gas distribution perturb the gravitational potential and hence affect the halo particles. We analytically derive the velocity dispersion imparted to the CDM particles and the corresponding relaxation time, and further perform numerical simulations to show that the assumed process can indeed lead to the formation of a core in an initially cuspy halo within a timescale comparable to the derived relaxation time. This suggests that feedback-induced cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrized in relatively simple terms.

  9. Accelerating the Gillespie Exact Stochastic Simulation Algorithm using hybrid parallel execution on graphics processing units.

    PubMed

    Komarov, Ivan; D'Souza, Roshan M

    2012-01-01

    The Gillespie Stochastic Simulation Algorithm (GSSA) and its variants are cornerstone techniques to simulate reaction kinetics in situations where the concentration of the reactant is too low to allow deterministic techniques such as differential equations. The inherent limitations of the GSSA include the time required for executing a single run and the need for multiple runs for parameter sweep exercises due to the stochastic nature of the simulation. Even very efficient variants of GSSA are prohibitively expensive to compute and perform parameter sweeps. Here we present a novel variant of the exact GSSA that is amenable to acceleration by using graphics processing units (GPUs). We parallelize the execution of a single realization across threads in a warp (fine-grained parallelism). A warp is a collection of threads that are executed synchronously on a single multi-processor. Warps executing in parallel on different multi-processors (coarse-grained parallelism) simultaneously generate multiple trajectories. Novel data-structures and algorithms reduce memory traffic, which is the bottleneck in computing the GSSA. Our benchmarks show an 8×-120× performance gain over various state-of-the-art serial algorithms when simulating different types of models.

  10. Intrinsic Information Processing and Energy Dissipation in Stochastic Input-Output Dynamical Systems

    DTIC Science & Technology

    2015-07-09

    intelligent” control can convert information to energy. However, these approaches have yet to account for the diverse kinds of information that complex...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 input-output processes, controlled thermodynamics systems, nonlinear...be subject to any oenalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE

  11. Nonlinear diffusion and exclusion processes with contact interactions

    NASA Astrophysics Data System (ADS)

    Fernando, Anthony E.; Landman, Kerry A.; Simpson, Matthew J.

    2010-01-01

    Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C) . We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

  12. Nonlinear diffusion and exclusion processes with contact interactions.

    PubMed

    Fernando, Anthony E; Landman, Kerry A; Simpson, Matthew J

    2010-01-01

    Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

  13. A multi-nano-dot circuit and structure using thermal-noise-assisted tunneling for stochastic associative processing.

    PubMed

    Morie, Takashi; Matsuura, Tomohiro; Nagata, Makoto; Iwata, Atsushi

    2002-01-01

    The single-electron circuit and nanostructure described in this paper are designed for stochastic associative processing, which is an expanded version of ordinary associative memory processing. In stochastic associative processing, the association probability of each stored pattern depends on the similarity between the stored pattern and the input pattern. Such unique processing is useful for sequential stochastic association and for clustering for vector quantization. Conventional single-electron circuits operate only at very low temperature for practical junction capacitance (i.e., 30 K for 0.1 aF) because the charging energy in these circuits is directly related to the tunnel junction capacitance. Our multi-nano-dot circuit and structure operate at room temperature with a junction capacitance around 0.1 aF through tunneling processes assisted by thermal noise. We analyze the operation of this circuit in detail and propose for it a stochastic associative processing operation, where the detection timing of the electron position controls the association probability distribution.

  14. Stochastic proximity embedding on graphics processing units: taking multidimensional scaling to a new scale.

    PubMed

    Yang, Eric; Liu, Pu; Rassokhin, Dimitrii N; Agrafiotis, Dimitris K

    2011-11-28

    Stochastic proximity embedding (SPE) was developed as a method for efficiently calculating lower dimensional embeddings of high-dimensional data sets. Rather than using a global minimization scheme, SPE relies upon updating the distances of randomly selected points in an iterative fashion. This was found to generate embeddings of comparable quality to those obtained using classical multidimensional scaling algorithms. However, SPE is able to obtain these results in O(n) rather than O(n²) time and thus is much better suited to large data sets. In an effort both to speed up SPE and utilize it for even larger problems, we have created a multithreaded implementation which takes advantage of the growing general computing power of graphics processing units (GPUs). The use of GPUs allows the embedding of data sets containing millions of data points in interactive time scales.

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

    PubMed Central

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

    2017-01-01

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

  16. Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses

    SciTech Connect

    Amoruso, C.; Moore, M. A.; Hartmann, A. K.; Hastings, M. B.

    2006-12-31

    We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.

  17. Leaf optical system modeled as a stochastic process. [solar radiation interaction with terrestrial vegetation

    NASA Technical Reports Server (NTRS)

    Tucker, C. J.; Garratt, M. W.

    1977-01-01

    A stochastic leaf radiation model based upon physical and physiological properties of dicot leaves has been developed. The model accurately predicts the absorbed, reflected, and transmitted radiation of normal incidence as a function of wavelength resulting from the leaf-irradiance interaction over the spectral interval of 0.40-2.50 micron. The leaf optical system has been represented as Markov process with a unique transition matrix at each 0.01-micron increment between 0.40 micron and 2.50 micron. Probabilities are calculated at every wavelength interval from leaf thickness, structure, pigment composition, and water content. Simulation results indicate that this approach gives accurate estimations of actual measured values for dicot leaf absorption, reflection, and transmission as a function of wavelength.

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

    PubMed

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Golosovsky, Michael; Solomon, Sorin

    2012-08-01

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

  20. Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications

    NASA Astrophysics Data System (ADS)

    Daley, K.

    2009-08-01

    A re-visitation of QFT is first cited, deriving the Feynman integral from the theory of active stochastic processes (Glueck and Hueffler, Phys. Lett. B. 659(1-2):447-451, 2008; Hueffel and Kelnhofer, Phys. Lett. B 588(1-2):145-150, 2004). We factor the lie group “generator” of the inverse wavefunction over an entropy-maximizing basis. Performing term-by-term Ito-integration leads us to an analytical, evaluable trajectory for a charged particle in an arbitrary field given a Maximum-Entropy distribution. We generalize this formula to many-body electrodynamics. In theory, it is capable of predicting plasma’s thermodynamic properties from ionic spectral data and thermodynamic and optical distributions. Blessed with the absence of certain limitations (e.g., renormalization) strongly present in competing formalisms and the incorporation of research related to many different phenomena, we outline a candidate quantum gravity theory based on these developments.

  1. Nonlinear closure relations theory for transport processes in nonequilibrium systems.

    PubMed

    Sonnino, Giorgio

    2009-05-01

    A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ("Onsager") transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

  2. Adaptive neural network tracking control for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis

    NASA Astrophysics Data System (ADS)

    Niu, Ben; Qin, Tian; Fan, Xiaodong

    2016-10-01

    In this paper, an adaptive neural network tracking control approach is proposed for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis. In the design procedure, an affine variable is constructed, which avoids the use of the mean value theorem, and the additional first-order low-pass filter is employed to deal with the problem of explosion of complexity. Then, a common Lyapunov function and a state feedback controller are explicitly obtained for all subsystems. It is proved that the proposed controller that guarantees all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error remains an adjustable neighbourhood of the origin. Finally, simulation results show the effectiveness of the presented control design approach.

  3. Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation

    NASA Astrophysics Data System (ADS)

    Zhuang, Guangming; Li, Yongmin; Li, Ze

    2016-05-01

    This paper considers the problem of robust H∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.

  4. Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.

    NASA Technical Reports Server (NTRS)

    Larsen, Curtis E.

    1988-01-01

    A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.

  5. Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

    NASA Technical Reports Server (NTRS)

    Menga, G.

    1975-01-01

    An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

  6. Double resonant processes in 1D nonlinear periodic media

    NASA Astrophysics Data System (ADS)

    Kuzmiak, Vladimir; Konotop, Vladimir

    2001-03-01

    We consider one-dimensional periodic structure consisting of alternating layers fabricated from the materials possessing \\chi^(2) nonlinearity and assume that the filling fraction and the dielectric permittivities of the slabs are chosen in such a way that resonant contions for the generation for the second and third harmonic are satisfied simultaneously. The possibility of such process is demonstrated in the structure consisting of the alternating slabs of AlGaAs and InSb. The wave evolution is described in terms of envelope function approach. By taking account three resonant waves one obtains a system of coupled-mode differential equations. One of the solutions which is of special importance is that of having a constant amplitude and the first and third harmonic having zero amplitude. We analyze the stability of the solutions and show that the use of the double resonance allows one to obtain difference generation. A particular example of such a process is fractional conversion ω arrow (2/3)ω which takes place with the participation of the mode with the frequency ω/3.

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

    PubMed Central

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

    2016-01-01

    Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor. PMID:27346701

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  9. All-optical image processing with nonlinear liquid crystals

    NASA Astrophysics Data System (ADS)

    Hong, Kuan-Lun

    Liquid crystals are fascinating materials because of several advantages such as large optical birefringence, dielectric anisotropic, and easily compatible to most kinds of materials. Compared to the electro-optical properties of liquid crystals widely applied in displays and switching application, transparency through most parts of wavelengths also makes liquid crystals a better candidate for all-optical processing. The fast response time of liquid crystals resulting from multiple nonlinear effects, such as thermal and density effect can even make real-time processing realized. In addition, blue phase liquid crystals with spontaneously self-assembled three dimensional cubic structures attracted academic attention. In my dissertation, I will divide the whole contents into six parts. In Chapter 1, a brief introduction of liquid crystals is presented, including the current progress and the classification of liquid crystals. Anisotropy and laser induced director axis reorientation is presented in Chapter 2. In Chapter 3, I will solve the electrostrictive coupled equation and analyze the laser induced thermal and density effect in both static and dynamic ways. Furthermore, a dynamic simulation of laser induced density fluctuation is proposed by applying finite element method. In Chapter 4, two image processing setups are presented. One is the intensity inversion experiment in which intensity dependent phase modulation is the mechanism. The other is the wavelength conversion experiment in which I can read the invisible image with a visible probe beam. Both experiments are accompanied with simulations to realize the matching between the theories and practical experiment results. In Chapter 5, optical properties of blue phase liquid crystals will be introduced and discussed. The results of grating diffractions and thermal refractive index gradient are presented in this chapter. In addition, fiber arrays imaging and switching with BPLCs will be included in this chapter

  10. Noise in Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Moss, Frank; McClintock, P. V. E.

    2009-08-01

    List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.

  11. Neural field theory of nonlinear wave-wave and wave-neuron processes

    NASA Astrophysics Data System (ADS)

    Robinson, P. A.; Roy, N.

    2015-06-01

    Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.

  12. Stochastic Chemical Evolution of Sub-Halos and the Origin of r-Process Elements

    NASA Astrophysics Data System (ADS)

    Ojima, Takuya; Ishimaru, Yuhri; Wanajo, Shinya; Prantzos, Nikos

    The main origin of r-process elements is still uncertain, but recent nucleosynthesis studies show that neutron star mergers (NSMs) are capable of naturally explaining the solar r-process abundance. Though, previous chemical evolution models hold conflict with the NSM scenario because the long NSM coalescence timescale causes an [r/Fe] enhancement at higher metallicity compared to the observed Galactic halo stars in the [r/Fe] vs [Fe/H] plane. However, it is not the case if assuming the formation of the Galactic halo by clusterings of sub-halos with varying star formation histories. We construct a chemical evolution model of sub-halos, where NSM occurring in each sub-halos are computed stochastically. Our results are in good agreement with the Galactic halo stars, explaining the observed dispersion and trend. Also, the abundance ratio pattern of the low mass sub-halos is in consistency with Reticulum II, a dwarf galaxy that might have been contaminated by a single r-process event.

  13. Emergence of patterns in random processes. II. Stochastic structure in random events

    NASA Astrophysics Data System (ADS)

    Newman, William I.

    2014-06-01

    Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equation of statistical mechanics as a device for connecting the two limiting sets of behaviors, which we then compared with a variety of observations from the physical and social sciences. Here, we establish a probabilistic framework via the Smoluchowski equation for exploring the Langevin equation and its expected peak-to-peak sequence lengths, and we introduce a concept we call "stochastic structure in random events," or SSRE. We extend the Brownian model to include antipersistent processes via autoregressive (AR) models. We relate the latter to describe the behavior of Old Faithful Geyser in Yellowstone National Park, and we devise a further test for the validity of the Langevin and AR models. Given our analytic results, we show how the Langevin equation can be adapted to describe population cycles of three to four years observed among many mammalian species in biology.

  14. Aggregation Processes on Networks: Deterministic Equations, Stochastic Model and Numerical Simulation

    SciTech Connect

    Guias, Flavius

    2008-09-01

    We introduce an infinite system of equations modeling the time evolution of the growth process of a network. The nodes are characterized by their degree k(set-membership sign)N and a fitness parameter f(set-membership sign)[0,h]. Every new node which emerges becomes a fitness f' according to a given distribution P and attaches to an existing node with fitness f and degree k at rate fA{sub k}, where A{sub k} are positive coefficients, growing sub-linearly in k. If the parameter f takes only one value, the dynamics of this process can be described by a variant of the Becker-Doering equations, where the l growth of the size of clusters of size k occurs only with increment 1. In contrast l to the established Becker-Doering equations, the system considered here is nonconservative, since mass (i.e. links) is continuously added. Nevertheless, it has the property of linearity, which is a natural consequence of the process which is being modeled. The purpose of this paper is to construct a solution of the system based on a stochastic approximation algorithm, which allows also a numerical simulation in order to get insight into its qualitative behaviour. In particular we show analytically and numerically the property of Bose-Einstein condensation, which was observed in the literature on random graphs and which can be described as an emergence of a huge cluster which captures a macroscopic fraction of the total link density.

  15. Stochastic Transients as a Source of Quasi-periodic Processes in the Solar Atmosphere

    NASA Astrophysics Data System (ADS)

    Yuan, Ding; Su, Jiangtao; Jiao, Fangran; Walsh, Robert W.

    2016-06-01

    Solar dynamics and turbulence occur at all heights of the solar atmosphere and could be described as stochastic processes. We propose that finite-lifetime transients recurring at a certain place could trigger quasi-periodic processes in the associated structures. In this study, we developed a mathematical model for finite-lifetime and randomly occurring transients, and found that quasi-periodic processes with periods longer than the timescale of the transients, are detectable intrinsically in the form of trains. We simulate their propagation in an empirical solar atmospheric model with chromosphere, transition region, and corona. We found that, due to the filtering effect of the chromospheric cavity, only the resonance period of the acoustic resonator is able to propagate to the upper atmosphere; such a scenario is applicable to slow magnetoacoustic waves in sunspots and active regions. If the thermal structure of the atmosphere is less wild and acoustic resonance does not take place, the long-period oscillations could propagate to the upper atmosphere. Such a case would be more likely to occur in polar plumes.

  16. Emergence of patterns in random processes. II. Stochastic structure in random events.

    PubMed

    Newman, William I

    2014-06-01

    Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equation of statistical mechanics as a device for connecting the two limiting sets of behaviors, which we then compared with a variety of observations from the physical and social sciences. Here, we establish a probabilistic framework via the Smoluchowski equation for exploring the Langevin equation and its expected peak-to-peak sequence lengths, and we introduce a concept we call "stochastic structure in random events," or SSRE. We extend the Brownian model to include antipersistent processes via autoregressive (AR) models. We relate the latter to describe the behavior of Old Faithful Geyser in Yellowstone National Park, and we devise a further test for the validity of the Langevin and AR models. Given our analytic results, we show how the Langevin equation can be adapted to describe population cycles of three to four years observed among many mammalian species in biology.

  17. Investigation of the fatigue process using nonlinear ultrasound

    NASA Astrophysics Data System (ADS)

    Ellwood, R.; Stratoudaki, T.; Sharples, S. D.; Clark, M.; Somekh, M. G.

    2011-01-01

    During normal usage components are subject to stresses that while not sufficient to cause fracture cause fatigue, which gradually weakens the component. Linear ultrasonic methods have been shown to be poor at detecting fatigue. However, there is evidence that the accumulation of damage gives the material a nonlinear elastic response that can be probed by ultrasound. By measuring the change in a material's nonlinear properties a measure of the fatigue can be obtained. Several methods of detecting material nonlinearity using acoustic waves have been proposed. The collinear mixing technique is used here. By measuring the velocity change of a probe wave due to the induced stress from a second pump wave, a measure of the nonlinearity is obtained. By generating the probe wave and detecting both waves using laser ultrasound techniques we gain the benefits of high spatial and temporal resolution. This is important when investigating the nonlinear response of a material as there is evidence that the microstructure affects the nonlinear response of a material. The change in nonlinearity over a region of a specimen (aluminium) has been monitored over several fatigue levels to investigate any relation. Early stage results are given with a discussion on the development of the technique.

  18. A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement

    NASA Astrophysics Data System (ADS)

    Liu, Dan; Liu, Yurong; Alsaadi, Fuad E.

    2016-07-01

    In this paper, we are concerned with the problem of analysis and synthesis for a class of output feedback control system. The system under consideration is a discrete-time stochastic system with time-varying delay. It is assumed that the measurement of system is quantized via a logarithmic quantizer before it is transmitted, and the measurement data would be missing from time to time which can be described by a Bernoulli distributed white sequence. In addition, the nonlinearities are assumed to satisfy the sector conditions. The problem addressed is to design an output feedback controller such that the resulting closed-loop system is exponentially stable in the mean square. By employing Lyapunov theory and some new techniques, a new framework is established to cope with the design of output feedback controller for nonlinear systems involving quantization and missing measurement. Sufficient conditions are derived to guarantee the existence of the desired controllers, and the controller parameters are given in an explicit expression as well. A numerical example is exploited to show the usefulness of the results obtained.

  19. Random-order fractional bistable system and its stochastic resonance

    NASA Astrophysics Data System (ADS)

    Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

    2017-01-01

    In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

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

    PubMed Central

    Martinez, Alexander S.; Faist, Akasha M.

    2016-01-01

    Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species) and belowground (species active in organic and mineral soil layers) arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community) and modified Winkler funnels (belowground community) and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity) among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the aboveground arthropod

  1. Nonlinear Theoretical Tools for Fusion-related Microturbulence: Historical Evolution, and Recent Applications to Stochastic Magnetic Fields, Zonal-flow Dynamics, and Intermittency

    SciTech Connect

    J.A. Krommes

    2009-05-19

    Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.

  2. Stochastic production phase design for an open pit mining complex with multiple processing streams

    NASA Astrophysics Data System (ADS)

    Asad, Mohammad Waqar Ali; Dimitrakopoulos, Roussos; van Eldert, Jeroen

    2014-08-01

    In a mining complex, the mine is a source of supply of valuable material (ore) to a number of processes that convert the raw ore to a saleable product or a metal concentrate for production of the refined metal. In this context, expected variation in metal content throughout the extent of the orebody defines the inherent uncertainty in the supply of ore, which impacts the subsequent ore and metal production targets. Traditional optimization methods for designing production phases and ultimate pit limit of an open pit mine not only ignore the uncertainty in metal content, but, in addition, commonly assume that the mine delivers ore to a single processing facility. A stochastic network flow approach is proposed that jointly integrates uncertainty in supply of ore and multiple ore destinations into the development of production phase design and ultimate pit limit. An application at a copper mine demonstrates the intricacies of the new approach. The case study shows a 14% higher discounted cash flow when compared to the traditional approach.

  3. Phylogenetic beta diversity in bacterial assemblages across ecosystems: deterministic versus stochastic processes

    SciTech Connect

    Wang, Jianjun; Shen, Jianhaua; Wu, Yucheng; Tu, Chen; Soininen , Janne; Stegen, James C.; He, Jizheng; Liu, Xingqi; Zhang, Lu; Zhang, Enlou

    2013-02-28

    Increasing evidence emerged for non-random spatial distributions for microbes, but the underlying processes resulting in microbial assemblage variation among and within Earth’s ecosystems is still lacking. For instance, some studies showed that the deterministic processes by habitat specialization are important, while other studies hold that bacterial communities are assembled by neutral forces. Here we examine the relative importance of deterministic and stochastic processes for bacterial communities from subsurface environments, as well as stream biofilm, lake water, lake sediment and soil using pyrosequencing of 16S rRNA gene. We show that there is a general pattern in phylogenetic signal in species niches across recent evolutionary time for all studied habitats, enabling us to infer the influences of community assembly processes from patterns of phylogenetic turnover in community composition. The phylogenetic dissimilarities among habitat types were significantly higher than within them, and the communities were clustered according to their original habitat types. For communities within habitat types, the highest phylogenetic turnover rate through space was observed in subsurface environments, followed by stream biofilm on mountainsides, whereas the sediment assemblages across regional scales showed the lowest turnover rate. Quantifying phylogenetic turnover as the deviation from a null expectation suggested that measured environmental variables imposed strong selection on bacterial communities for nearly all sample groups, and for three sample groups, that spatial distance reflects unmeasured environmental variables that impose selection, as opposed to spatial isolation. Such characterization of spatial and environmental variables proved essential for proper interpretation of partial mantel results based on observed beta diversity metrics. In summary, our results clearly indicate a dominant role of deterministic processes on bacterial assemblages and

  4. Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics.

    PubMed

    D'Onofrio, Giuseppe; Pirozzi, Enrica

    2016-09-26

    We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.

  5. Relative importance of deterministic and stochastic processes in driving arbuscular mycorrhizal fungal assemblage during the spreading of a toxic plant.

    PubMed

    Shi, Guoxi; Liu, Yongjun; Mao, Lin; Jiang, Shengjing; Zhang, Qi; Cheng, Gang; An, Lizhe; Du, Guozhen; Feng, Huyuan

    2014-01-01

    Both deterministic and stochastic processes are expected to drive the assemblages of arbuscular mycorrhizal (AM) fungi, but little is known about the relative importance of these processes during the spreading of toxic plants. Here, the species composition and phylogenetic structure of AM fungal communities colonizing the roots of a toxic plant, Ligularia virgaurea, and its neighborhood plants, were analyzed in patches with different individual densities of L. virgaurea (represents the spreading degree). Community compositions of AM fungi in both root systems were changed significantly by the L. virgaurea spreading, and also these communities fitted the neutral model very well. AM fungal communities in patches with absence and presence of L. virgaurea were phylogenetically random and clustered, respectively, suggesting that the principal ecological process determining AM fungal assemblage shifted from stochastic process to environmental filtering when this toxic plant was present. Our results indicate that deterministic and stochastic processes together determine the assemblage of AM fungi, but the dominant process would be changed by the spreading of toxic plants, and suggest that the spreading of toxic plants in alpine meadow ecosystems might be involving the mycorrhizal symbionts.

  6. Relative Importance of Deterministic and Stochastic Processes in Driving Arbuscular Mycorrhizal Fungal Assemblage during the Spreading of a Toxic Plant

    PubMed Central

    Mao, Lin; Jiang, Shengjing; Zhang, Qi; Cheng, Gang; An, Lizhe; Du, Guozhen; Feng, Huyuan

    2014-01-01

    Both deterministic and stochastic processes are expected to drive the assemblages of arbuscular mycorrhizal (AM) fungi, but little is known about the relative importance of these processes during the spreading of toxic plants. Here, the species composition and phylogenetic structure of AM fungal communities colonizing the roots of a toxic plant, Ligularia virgaurea, and its neighborhood plants, were analyzed in patches with different individual densities of L. virgaurea (represents the spreading degree). Community compositions of AM fungi in both root systems were changed significantly by the L. virgaurea spreading, and also these communities fitted the neutral model very well. AM fungal communities in patches with absence and presence of L. virgaurea were phylogenetically random and clustered, respectively, suggesting that the principal ecological process determining AM fungal assemblage shifted from stochastic process to environmental filtering when this toxic plant was present. Our results indicate that deterministic and stochastic processes together determine the assemblage of AM fungi, but the dominant process would be changed by the spreading of toxic plants, and suggest that the spreading of toxic plants in alpine meadow ecosystems might be involving the mycorrhizal symbionts. PMID:24748393

  7. Disentangling Mechanisms That Mediate the Balance Between Stochastic and Deterministic Processes in Microbial Succession

    SciTech Connect

    Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan D.; Falcao Salles, Joana

    2015-03-17

    Despite growing recognition that deterministic and stochastic factors simultaneously influence bacterial communities, little is known about mechanisms shifting their relative importance. To better understand underlying mechanisms, we developed a conceptual model linking ecosystem development during primary succession to shifts in the stochastic/deterministic balance. To evaluate the conceptual model we coupled spatiotemporal data on soil bacterial communities with environmental conditions spanning 105 years of salt marsh development. At the local scale there was a progression from stochasticity to determinism due to Na accumulation with increasing ecosystem age, supporting a main element of the conceptual model. At the regional-scale, soil organic matter (SOM) governed the relative influence of stochasticity and the type of deterministic ecological selection, suggesting scale-dependency in how deterministic ecological selection is imposed. Analysis of a new ecological simulation model supported these conceptual inferences. Looking forward, we propose an extended conceptual model that integrates primary and secondary succession in microbial systems.

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

    SciTech Connect

    Angstmann, C.N.; Donnelly, I.C.; Henry, B.I.; Jacobs, B.A.; Langlands, T.A.M.; Nichols, J.A.

    2016-02-15

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

  9. Protein-protein ratchets: stochastic simulation and application to processive enzymes.

    PubMed Central

    Brokaw, C J

    2001-01-01

    Interaction between a protein and a series of binding sites on a cytoskeletal substrate can create a resistance, or "protein friction," as the protein is moved along the substrate. If attachment and detachment rates are specified asymmetrically, this resistance can depend on the direction of movement, and the binding interaction acts as a ratchet. Stochastic computer simulations have been used to examine this type of protein-protein interaction. The performance of a protein-protein ratchet in the piconewton and nanometer range is significantly limited by thermal fluctuations, which in experimental measurements with single molecules are evident as Brownian motion. Simulations with a two-component model combining a conventional motor enzyme model with a protein-protein ratchet confirm previous suggestions that the processive movement of a single motor enzyme molecule against a load, as seen in experiments with inner arm dynein molecules, might be made possible by an accessory protein interaction that prevents backward slippage. When this accessory protein interaction is defined so that it acts as a ratchet, backward slippage can be prevented with minimal interference with forward progression. PMID:11509349

  10. Stochastic parametrization of multiscale processes using a dual-grid approach.

    PubMed

    Shutts, Glenn; Allen, Thomas; Berner, Judith

    2008-07-28

    Some speculative proposals are made for extending current stochastic sub-gridscale parametrization methods using the techniques adopted from the field of computer graphics and flow visualization. The idea is to emulate sub-filter-scale physical process organization and time evolution on a fine grid and couple the implied coarse-grained tendencies with a forecast model. A two-way interaction is envisaged so that fine-grid physics (e.g. deep convective clouds) responds to forecast model fields. The fine-grid model may be as simple as a two-dimensional cellular automaton or as computationally demanding as a cloud-resolving model similar to the coupling strategy envisaged in 'super-parametrization'. Computer codes used in computer games and visualization software illustrate the potential for cheap but realistic simulation where emphasis is placed on algorithmic stability and visual realism rather than pointwise accuracy in a predictive sense. In an ensemble prediction context, a computationally cheap technique would be essential and some possibilities are outlined. An idealized proof-of-concept simulation is described, which highlights technical problems such as the nature of the coupling.

  11. Stochastic gradient processes: A survey of convergence theory using Lyapunov second method

    SciTech Connect

    Nakonechnyi, A.N.

    1995-09-01

    In the present article, our aim is to provide a comprehensive survey and analysis of the convergence conditions of known gradient type algorithms described by process in terms of the Lyapunov function v(z) = min/y {element_of} Y {parallel} z - y {parallel}{sup 2}, where Y is a closed bounded subset in R{sup l}, i.e., the conditions that ensure the equality P (lim/k{r_arrow}{infinity} min/y{element_of}Y {parallel} z{sup k}-y{parallel}{sup 2} = O) = 1. Alongside qualitative results, the article also focuses on comparison of specific gradient type stochastic algorithms on test examples, practical evaluation of the accuracy of the results, and acceleration of convergence by the averaging operation on the trajectory, which is defined by the recurrence u{sup k+1}=u{sup {center_dot}k} + (z{sup k}-u{sup k})/k, k {ge} 1, u{sup 1} = z{sup 1}.

  12. On the use of stochastic process-based methods for the analysis of hyperspectral data

    NASA Technical Reports Server (NTRS)

    Landgrebe, David A.

    1992-01-01

    Further development in remote sensing technology requires refinement of information system design aspects, i.e., the ability to specify precisely the data to collect and the means to extract increasing amounts of information from the increasingly rich and complex data stream created. One of the principal directions of advance is that data from much larger numbers of spectral bands can be collected, but with significantly increased signal-to-noise ratio. The theory of stochastic or random processes may be applied to the modeling of second-order variations. A multispectral data set with a large number of spectral bands is analyzed using standard pattern recognition techniques. The data were classified using first a single spectral feature, then two, and continuing on with greater and greater numbers of features. Three different classification schemes are used: a standard maximum likelihood Gaussian scheme; the same approach with the mean values of all classes adjusted to be the same; and the use of a minimum distance to means scheme such that mean differences are used.

  13. Evidence that the process of murine melanoma metastasis is sequential and selective and contains stochastic elements.

    PubMed

    Price, J E; Aukerman, S L; Fidler, I J

    1986-10-01

    Malignant neoplasms are heterogeneous for many different biological characteristics, including invasion and metastasis. The pathogenesis of metastasis involves a series of sequential steps which must be completed by metastatic cells. In the present study we examined the metastatic behavior of three highly metastatic and three nonmetastatic subpopulations isolated from the K-1735 melanoma syngeneic to the C3H/HeN mouse. Cells were labeled with [125I]iodo-2'-deoxyuridine, and their initial organ distribution, fate, and production of experimental metastases were determined. Highly metastatic cells survived in lung parenchyma to produce metastases, whereas nonmetastatic cells did not. However, even with the highly metastatic cells only 2% of the original inoculum was responsible for the final production of metastases. The results support the concept that the fate of tumor cells released into the bloodstream is determined by sequential and selective events and introduces a third regulatory factor. Cells endowed with metastatic properties have a higher probability of forming metastases than cells not so endowed, but this probability is not 100%. Hence, metastasis should be considered as a sequential, selective, and stochastic process.

  14. Quantifying Measurement Fluctuations from Stochastic Surface Processes on Sensors with Heterogeneous Sensitivity

    NASA Astrophysics Data System (ADS)

    Charmet, Jérôme; Michaels, Thomas C. T.; Daly, Ronan; Prasad, Abhinav; Thiruvenkathanathan, Pradyumna; Langley, Robin S.; Knowles, Tuomas P. J.; Seshia, Ashwin A.

    2016-06-01

    Recent advances in micro- and nanotechnology have enabled the development of ultrasensitive sensors capable of detecting small numbers of species. In general, however, the response induced by the random adsorption of a small number of objects onto the surface of such sensors results in significant fluctuations due to the heterogeneous sensitivity inherent to many such sensors coupled to statistical fluctuations in the particle number. At present, this issue is addressed by considering either the limit of very large numbers of analytes, where fluctuations vanish, or the converse limit, where the sensor response is governed by individual analytes. Many cases of practical interest, however, fall between these two limits and remain challenging to analyze. Here, we address this limitation by deriving a general theoretical framework for quantifying measurement variations on mechanical resonators resulting from statistical-number fluctuations of analyte species. Our results provide insights into the stochastic processes in the sensing environment and offer opportunities to improve the performance of mechanical-resonator-based sensors. This metric can be used, among others, to aid in the design of robust sensor platforms to reach ultrahigh-resolution measurements using an array of sensors. These concepts, illustrated here in the context of biosensing, are general and can therefore be adapted and extended to other sensors with heterogeneous sensitivity.

  15. Nonlinear acoustic/seismic waves in earthquake processes

    SciTech Connect

    Johnson, Paul A.

    2012-09-04

    Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering-one of the most fascinating topics in seismology today-which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge-the granular material located between the fault blocks-is key to the triggering phenomenon.

  16. Stochastic differential equations

    SciTech Connect

    Sobczyk, K. )

    1990-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Goad, Clyde C.; Chadwell, C. David

    1993-01-01

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

  18. Stochastic resonance in nanomechanical systems

    NASA Astrophysics Data System (ADS)

    Badzey, Robert L.

    The phenomenon of stochastic resonance is a counter-intuitive one: adding noise to a noisy nonlinear system under the influence of a modulation results in coherent behavior. The signature of the effect is a resonance in the signal-to-noise ratio of the response over a certain range of noise power; this behavior is absent if either the modulation or the noise are absent. Stochastic resonance has attracted considerable interest over the past several decades, having been seen in a great number of physical and biological systems. Here, observation of stochastic resonance is reported for nanomechanical systems consisting of a doubly-clamped beam resonators fabricated from single-crystal silicon. Such oscillators have been found to display nonlinear and bistable behavior under the influence of large driving forces. This bistability is exploited to produce a controllable nanomechanical switch, a device that may be used as the basis for a new generation of computational memory elements. These oscillators possess large intrinsic resonance frequencies (MHz range or higher) due to their small size and relatively high stiffness; thus they have the potential to rival the current state-of-the-art of electronic and magnetic storage technologies. This small size also allows them to be packed in densities which meet or exceed the superparamagnetic limit for magnetic storage media of 100 GB/in2. Two different doubly-clamped beams were cooled to low temperatures (300 mK--4 K), and excited with a magnetomotive technique. They were driven into the nonlinear response regime, and then modulated to induce switching between their bistable states. When the modulation was reduced, the switching died out. Application of noise, either with an external broadband source or via an increase in temperature, resulted in a distinct resonance in the signal-to-noise ratio. Aside from establishing the phenomenon of stochastic resonance in yet another physical system, the observation of this effect has

  19. Identification of a class of Wiener and Hammerstein-type nonlinear processes with monotonic static gains.

    PubMed

    Mehta, Utkal; Majhi, Somanath

    2010-10-01

    In this paper a non-iterative approach to identifying Wiener and Hammerstein models, including model structure and parameters, is proposed. A single symmetrical relay test is conducted to determine the structure and then the parameters of the block-oriented nonlinear model possessing a static nonlinearity and a linear process in cascade. The static nonlinearity block is represented by a memoryless and monotonic function and the linear process by a second order transfer function model. A relay with hysteresis induces the limit cycle output signal and one cycle data of the output signal is used to identify the block-oriented nonlinear model. The proposed identification method is simple and gives better performance than previous methods for processes with static nonlinearity.

  20. Amplitude-dependent phononic processes in a diatomic granular chain in the weakly nonlinear regime.

    PubMed

    Cabaret, Jérémy; Tournat, Vincent; Béquin, Philippe

    2012-10-01

    Nonlinear acoustic processes of second harmonic generation and nonlinear resonances in a diatomic granular chain (a granular phononic crystal) with static precompression are reported. The observed nonlinear self-action process which manifests itself as shifts in resonance frequencies of the chain leads to amplitude-dependent band edges: the properties of the phononic crystal change as a function of wave amplitude. Observed nonlinear effects at the band edges are exceptionally strong (self-induced attenuation and self-induced transparency) due to the peculiar frequency dependence of the attenuation in these frequency regions. The reported effects open the way for applications in wave tailoring by nonlinear phononic crystals, using amplitude-dependent processes, such as passive amplitude-dependent attenuators or amplifiers and various logical elements.

  1. The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss

    NASA Astrophysics Data System (ADS)

    Nazarov, V. E.; Kiyashko, S. B.

    2016-07-01

    We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.

  2. Nonlinear giant magnetoimpedance and the asymmetric circumferential magnetization process in soft magnetic wires

    NASA Astrophysics Data System (ADS)

    Gómez-Polo, C.; Duque, J. G. S.; Knobel, M.

    2004-07-01

    The magnetoimpedance effect and its nonlinear terms are analysed for a (Co0.94Fe0.06)72.5Si12.5B15 amorphous wire. In order to enhance the nonlinear contribution the sample was previously subjected to current annealing (Joule heating) to induce a circumferential anisotropy. The effect of the application of a torsional strain on the nonlinear magnetoimpedance is analysed in terms of the torsional dependence of the magnetic permeability, evaluated through experimental circumferential hysteresis loops. The results obtained clearly confirm the direct correlation between the asymmetric circumferential magnetization process and the occurrence of nonlinear second-harmonic terms in the magnetoimpedance voltage.

  3. Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction

    SciTech Connect

    Peletier, Mark A.; Redig, Frank; Vafayi, Kiamars

    2014-09-01

    We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter m (BEP(m)), a Generalized Brownian Energy Process, and the Kipnis-Marchioro-Presutti (KMP) process. The hydrodynamic limit of each of these three processes is a parabolic equation, the linear heat equation in the case of the BEP(m) and the KMP, and a nonlinear heat equation for the Generalized Brownian Energy Process with parameter a (GBEP(a)). We prove the hydrodynamic limit rigorously for the BEP(m), and give a formal derivation for the GBEP(a). We then formally derive the pathwise large-deviation rate functional for the empirical measure of the three processes. These rate functionals imply gradient-flow structures for the limiting linear and nonlinear heat equations. We contrast these gradient-flow structures with those for processes describing the diffusion of mass, most importantly the class of Wasserstein gradient-flow systems. The linear and nonlinear heat-equation gradient-flow structures are each driven by entropy terms of the form -log ρ; they involve dissipation or mobility terms of order ρ² for the linear heat equation, and a nonlinear function of ρ for the nonlinear heat equation.

  4. Nonlinear Perspectives on Family Process: Chaos and Catastrophe Theories.

    ERIC Educational Resources Information Center

    Ward, Margaret; Koopmans, Matthijs

    This paper explores the principal features of nonlinear dynamical systems and applies the theory to parents' acceptance of a child adopted at an older age. Although family systems theories tend to be weak in addressing family change, chaos theory and catastrophe theory allow consideration of sudden, discontinuous change. If stable, the family may…

  5. A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

    ERIC Educational Resources Information Center

    Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

    2006-01-01

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

  6. Stochastic dynamics of small ensembles of non-processive molecular motors: the parallel cluster model.

    PubMed

    Erdmann, Thorsten; Albert, Philipp J; Schwarz, Ulrich S

    2013-11-07

    Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.

  7. Beyond Rainfall Multipliers: Describing Input Uncertainty as an Autocorrelated Stochastic Process Improves Inference in Hydrology

    NASA Astrophysics Data System (ADS)

    Del Giudice, D.; Albert, C.; Reichert, P.; Rieckermann, J.

    2015-12-01

    Rainfall is the main driver of hydrological systems. Unfortunately, it is highly variable in space and time and therefore difficult to observe accurately. This poses a serious challenge to correctly estimate the catchment-averaged precipitation, a key factor for hydrological models. As biased precipitation leads to biased parameter estimation and thus to biased runoff predictions, it is very important to have a realistic description of precipitation uncertainty. Rainfall multipliers (RM), which correct each observed storm with a random factor, provide a first step into this direction. Nevertheless, they often fail when the estimated input has a different temporal pattern from the true one or when a storm is not detected by the raingauge. In this study we propose a more realistic input error model, which is able to overcome these challenges and increase our certainty by better estimating model input and parameters. We formulate the average precipitation over the watershed as a stochastic input process (SIP). We suggest a transformed Gauss-Markov process, which is estimated in a Bayesian framework by using input (rainfall) and output (runoff) data. We tested the methodology in a 28.6 ha urban catchment represented by an accurate conceptual model. Specifically, we perform calibration and predictions with SIP and RM using accurate data from nearby raingauges (R1) and inaccurate data from a distant gauge (R2). Results show that using SIP, the estimated model parameters are "protected" from the corrupting impact of inaccurate rainfall. Additionally, SIP can correct input biases during calibration (Figure) and reliably quantify rainfall and runoff uncertainties during both calibration (Figure) and validation. In our real-word application with non-trivial rainfall errors, this was not the case with RM. We therefore recommend SIP in all cases where the input is the predominant source of uncertainty. Furthermore, the high-resolution rainfall intensities obtained with this

  8. Stochastic dynamics of small ensembles of non-processive molecular motors: The parallel cluster model

    SciTech Connect

    Erdmann, Thorsten; Albert, Philipp J.; Schwarz, Ulrich S.

    2013-11-07

    Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.

  9. Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

    NASA Technical Reports Server (NTRS)

    Hsieh, Shang-Hsien

    1993-01-01

    The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

  10. Structural preferential attachment: Stochastic process for the growth of scale-free, modular, and self-similar systems

    NASA Astrophysics Data System (ADS)

    Hébert-Dufresne, Laurent; Allard, Antoine; Marceau, Vincent; Noël, Pierre-André; Dubé, Louis J.

    2012-02-01

    Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity, and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior, and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modeling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.

  11. Determining Stochasticity and Causality of Vegetation Dynamics in the Southwestern Amazon: Non-linear Time Series Analysis and Dynamic Factor Analysis of EVI2 Data

    NASA Astrophysics Data System (ADS)

    Klarenberg, G.

    2015-12-01

    Infrastructure projects such as road paving have proven to bring a variety of (mainly) socio-economic advantages to countries and populations. However, many studies have also highlighted the negative socio-economic and biophysical effects that these developments have at local, regional and even larger scales. The "MAP" area (Madre de Dios in Peru, Acre in Brazil, and Pando in Bolivia) is a biodiversity hotspot in the southwestern Amazon where sections of South America's Inter-Oceanic Highway were paved between 2006 and 2010. We are interested in vegetation dynamics in the area since it plays an important role in ecosystem functions and ecosystem services in socio-ecological systems: it provides information on productivity and structure of the forest. In preparation of more complex and mechanistic simulation of vegetation, non-linear time series analysis and Dynamic Factor Analysis (DFA) was conducted on Enhanced Vegetation Index (EVI) time series - which is a remote sensing product and provides information on vegetation dynamics as it detects chlorophyll (productivity) and structural change. Time series of 30 years for EVI2 (from MODIS and AVHRR) were obtained for 100 communities in the area. Through specific time series cluster analysis of the vegetation data, communities were clustered to facilitate data analysis and pattern recognition. The clustering is spatially consistent, and appears to be driven by median road paving progress - which is different for each cluster. Non-linear time series analysis (multivariate singular spectrum analysis, MSSA) separates common signals (or low-dimensional attractors) across clusters. Despite the presence of this deterministic structure though, time series behavior is mostly stochastic. Granger causality analysis between EVI2 and possible response variables indicates which variables (and with what lags) are to be included in DFA, resulting in unique Dynamic Factor Models for each cluster.

  12. Decorrelation strategies for the integration of finite sequences of a stochastic process into Gauss-Markov models

    NASA Astrophysics Data System (ADS)

    Schuh, Wolf-Dieter; Brockmann, Jan Martin; Kargoll, Boris; Loth, Ina

    2014-05-01

    The modeling of satellite measurements series pose a special challenge because of the huge amount of data and the strong correlations between the measurements. In connection with the large number of parameters the rigorous computation of an appropriate stochastic model is a demanding task. This contribution discusses the large variety of possible strategies to treat correlated measurements with constant sampling rate. At first view the regularly structured covariance matrices suggest fast Toeplitz algorithms. But the equidistant measurement series can be also interpreted as a finite sequence of a time discrete covariance stationary stochastic processes with infinite extension. The stochastic process can be represented and analyzed in different quantities in the time domain as well as in the frequency domain. The signal itself and its autocovariance function in the time domain be accompanied by the periodogram and the spectral distribution/spectral density function in the frequency domain. These four quantities and their relations in between can be clearly represented in form of a "Magic Square", which gives a good basis to analyze the stochastic process, study truncation effects and model the behavior by parametric and non parametric approaches. The focus of this study considers the pro and cons of possible strategies to decorrelate finite sequences of measurements and is motivated by GOCE gradiometer measurements. The measurement series are characterized by large correlations over long time spans with a periodic behavior with respect to the orbital period and a fragmentation of the time series into parts, due to satellite maneuvers and calibration phases. The decorrelation process is crucial for the gravity field estimation. Therefore efficient strategies are necessary to get as much signal as possible also from the highly correlated, fragmented measurements series. Special attentions has to take place to avoid data loss during the warmup phase of recursive

  13. ENISI SDE: A New Web-Based Tool for Modeling Stochastic Processes.

    PubMed

    Mei, Yongguo; Carbo, Adria; Hoops, Stefan; Hontecillas, Raquel; Bassaganya-Riera, Josep

    2015-01-01

    Modeling and simulations approaches have been widely used in computational biology, mathematics, bioinformatics and engineering to represent complex existing knowledge and to effectively generate novel hypotheses. While deterministic modeling strategies are widely used in computational biology, stochastic modeling techniques are not as popular due to a lack of user-friendly tools. This paper presents ENISI SDE, a novel web-based modeling tool with stochastic differential equations. ENISI SDE provides user-friendly web user interfaces to facilitate adoption by immunologists and computational biologists. This work provides three major contributions: (1) discussion of SDE as a generic approach for stochastic modeling in computational biology; (2) development of ENISI SDE, a web-based user-friendly SDE modeling tool that highly resembles regular ODE-based modeling; (3) applying ENISI SDE modeling tool through a use case for studying stochastic sources of cell heterogeneity in the context of CD4+ T cell differentiation. The CD4+ T cell differential ODE model has been published [8] and can be downloaded from biomodels.net. The case study reproduces a biological phenomenon that is not captured by the previously published ODE model and shows the effectiveness of SDE as a stochastic modeling approach in biology in general and immunology in particular and the power of ENISI SDE.

  14. Control of nonlinear processes by using linear model predictive control algorithms.

    PubMed

    Gu, Bingfeng; Gupta, Yash P

    2008-04-01

    Most chemical processes are inherently nonlinear. However, because of their simplicity, linear control algorithms have been used for the control of nonlinear processes. In this study, the use of the dynamic matrix control algorithm and a simplified model predictive control algorithm for control of a bench-scale pH neutralization process is investigated. The nonlinearity is handled by dividing the operating region into sub-regions and by switching the controller model as the process moves from one sub-region to another. A simple modification for model predictive control algorithms is presented to handle the switching. The simulation and experimental results show that the modification can provide a significant improvement in the control of nonlinear processes.

  15. Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.

    PubMed

    Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt

    2012-12-01

    Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.

  16. Nonlinear stochastic regularization to characterize tissue residue function in bolus-tracking MRI: assessment and comparison with SVD, block-circulant SVD, and Tikhonov.

    PubMed

    Zanderigo, Francesca; Bertoldo, Alessandra; Pillonetto, Gianluigi; Cobelli Ast, Claudio

    2009-05-01

    An accurate characterization of tissue residue function R(t) in bolus-tracking magnetic resonance imaging is of crucial importance to quantify cerebral hemodynamics. R(t) estimation requires to solve a deconvolution problem. The most popular deconvolution method is singular value decomposition (SVD). However, SVD is known to bear some limitations, e.g., R(t) profiles exhibit nonphysiological oscillations and take on negative values. In addition, SVD estimates are biased in presence of bolus delay and dispersion. Recently, other deconvolution methods have been proposed, in particular block-circulant SVD (cSVD) and Tikhonov regularization (TIKH). Here we propose a new method based on nonlinear stochastic regularization (NSR). NSR is tested on simulated data and compared with SVD, cSVD, and TIKH in presence and absence of bolus dispersion. A clinical case in one patient has also been considered. NSR is shown to perform better than SVD, cSVD, and TIKH in reconstructing both the peak and the residue function, in particular when bolus dispersion is considered. In addition, differently from SVD, cSVD, and TIKH, NSR always provides positive and smooth R(t).

  17. Stochastic-convective transport with nonlinear reaction and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media.

    PubMed

    Ginn, T R; Murphy, E M; Chilakapati, A; Seeboonruang, U

    2001-03-01

    Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.

  18. Stochastic-convective transport with nonlinear reaction and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media

    NASA Astrophysics Data System (ADS)

    Ginn, T. R.; Murphy, E. M.; Chilakapati, A.; Seeboonruang, U.

    2001-03-01

    Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.

  19. Long-time relaxation processes in the nonlinear Schroedinger equation

    SciTech Connect

    Ovchinnikov, Yu. N.; Sigal, I. M.

    2011-03-15

    The nonlinear Schroedinger equation, known in low-temperature physics as the Gross-Pitaevskii equation, has a large family of excitations of different kinds. They include sound excitations, vortices, and solitons. The dynamics of vortices strictly depends on the separation between them. For large separations, some kind of adiabatic approximation can be used. We consider the case where an adiabatic approximation can be used (large separation between vortices) and the opposite case of a decay of the initial state, which is close to the double vortex solution. In the last problem, no adiabatic parameter exists (the interaction is strong). Nevertheless, a small numerical parameter arises in the problem of the decay rate, connected with an existence of a large centrifugal potential, which leads to a small value of the increment. The properties of the nonlinear wave equation are briefly considered in the Appendix A.

  20. Describing the catchment-averaged precipitation as a stochastic process improves parameter and input estimation

    NASA Astrophysics Data System (ADS)

    Del Giudice, Dario; Albert, Carlo; Rieckermann, Jörg; Reichert, Peter

    2016-04-01

    Rainfall input uncertainty is one of the major concerns in hydrological modeling. Unfortunately, during inference, input errors are usually neglected, which can lead to biased parameters and implausible predictions. Rainfall multipliers can reduce this problem but still fail when the observed input (precipitation) has a different temporal pattern from the true one or if the true nonzero input is not detected. In this study, we propose an improved input error model which is able to overcome these challenges and to assess and reduce input uncertainty. We formulate the average precipitation over the watershed as a stochastic input process (SIP) and, together with a model of the hydrosystem, include it in the likelihood function. During statistical inference, we use "noisy" input (rainfall) and output (runoff) data to learn about the "true" rainfall, model parameters, and runoff. We test the methodology with the rainfall-discharge dynamics of a small urban catchment. To assess its advantages, we compare SIP with simpler methods of describing uncertainty within statistical inference: (i) standard least squares (LS), (ii) bias description (BD), and (iii) rainfall multipliers (RM). We also compare two scenarios: accurate versus inaccurate forcing data. Results show that when inferring the input with SIP and using inaccurate forcing data, the whole-catchment precipitation can still be realistically estimated and thus physical parameters can be "protected" from the corrupting impact of input errors. While correcting the output rather than the input, BD inferred similarly unbiased parameters. This is not the case with LS and RM. During validation, SIP also delivers realistic uncertainty intervals for both rainfall and runoff. Thus, the technique presented is a significant step toward better quantifying input uncertainty in hydrological inference. As a next step, SIP will have to be combined with a technique addressing model structure uncertainty.