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Sample records for nonlinear stochastic process

  1. 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.

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

    PubMed

    Ohkubo, Jun

    2015-10-01

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

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

    PubMed

    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

  4. 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

  5. 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.

  6. On controllability of nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Sakthivel, R.; Kim, J.-H.; Mahmudov, N. I.

    2006-12-01

    In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.

  7. Stochastic inflation and nonlinear gravity

    NASA Astrophysics Data System (ADS)

    Salopek, D. S.; Bond, J. R.

    1991-02-01

    We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background. We derive a Fokker-Planck equation which describes how the probability distribution of scalar field values at a given spatial point evolves in T. Analytic Green's-function solutions obtained for a single scalar field self-interacting through an exponential potential are used to demonstrate (1) if the initial condition of the Hubble parameter is chosen to be consistent with microwave-background limits, H(φ0)/mρ<~10-4, then the fluctuations obey Gaussian statistics to a high precision, independent of the time hypersurface choice and operator-ordering ambiguities in the Fokker-Planck equation, and (2) for scales much larger than our present observable patch of the Universe, the distribution is non-Gaussian, with a tail extending to large energy densities; although there are no observable manifestations, it does show eternal inflation. Lattice simulations of our Langevin network for the exponential potential demonstrate how spatial correlations are incorporated. An initially

  8. Quantum Stochastic Processes

    SciTech Connect

    Spring, William Joseph

    2009-04-13

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

  9. 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.

  10. 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.

  11. 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.

  12. Turbulence and Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Celani, Antonio; Mazzino, Andrea; Pumir, Alain

    sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.

  13. 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.

  14. Stochastic resonance for nonlinear sensors with saturation.

    PubMed

    Rousseau, David; Rojas Varela, Julio; Chapeau-Blondeau, François

    2003-02-01

    We analyze the transmission of a noisy signal by sensor devices which are linear for small inputs and saturate at large inputs. Large information-carrying signals are thus distorted in their transmission. We demonstrate conditions where addition of noise to such large input signals can reduce the distortion that they undergo in the transmission. This is established for periodic, as well as aperiodic, and random information-carrying signals. Various measures characterizing the transmission, such as signal-to-noise ratio, input-output cross correlation, and mutual information, are shown improvable by addition of noise. These results constitute another instance of the nonlinear phenomenon of stochastic resonance where addition of noise enhances the signal. PMID:12636648

  15. Stochastic resonance for nonlinear sensors with saturation

    NASA Astrophysics Data System (ADS)

    Rousseau, David; Rojas Varela, Julio; Chapeau-Blondeau, François

    2003-02-01

    We analyze the transmission of a noisy signal by sensor devices which are linear for small inputs and saturate at large inputs. Large information-carrying signals are thus distorted in their transmission. We demonstrate conditions where addition of noise to such large input signals can reduce the distortion that they undergo in the transmission. This is established for periodic, as well as aperiodic, and random information-carrying signals. Various measures characterizing the transmission, such as signal-to-noise ratio, input-output cross correlation, and mutual information, are shown improvable by addition of noise. These results constitute another instance of the nonlinear phenomenon of stochastic resonance where addition of noise enhances the signal.

  16. 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

  17. Digital simulation and modeling of nonlinear stochastic systems

    SciTech Connect

    Richardson, J M; Rowland, J R

    1981-04-01

    Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.

  18. Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

    NASA Technical Reports Server (NTRS)

    Tsitsiklis, J. N.; Athans, M.

    1984-01-01

    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.

  19. 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.

  20. Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings

    NASA Astrophysics Data System (ADS)

    Cunha, Americo; Soize, Christian; Sampaio, Rubens

    2015-11-01

    This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

  1. 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.

  2. 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.

  3. Wavelet entropy of stochastic processes

    NASA Astrophysics Data System (ADS)

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

    2007-06-01

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

  4. Stochastic 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. Nonlinear dynamics of accretion disks with stochastic viscosity

    SciTech Connect

    Cowperthwaite, Philip S.; Reynolds, Christopher S.

    2014-08-20

    We present a nonlinear numerical model for a geometrically thin accretion disk with the addition of stochastic nonlinear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the disk angular momentum transport. We show that this simple model is capable of reproducing several observed phenomenologies of accretion-driven systems. The most notable of these is the observed linear rms-flux relationship in the disk luminosity. This feature is not formally captured by the linearized disk equations used in previous work. A Fourier analysis of the dissipation and mass accretion rates across disk radii show coherence for frequencies below the local viscous frequency. This is consistent with the coherence behavior observed in astrophysical sources such as Cygnus X-1.

  14. 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.

  15. Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure

    SciTech Connect

    Morozov, E Yu; Chirkin, Anatolii S

    2004-03-31

    A theory of the interaction between light waves in polydomain crystals with a random variation in the domain thickness described by a random telegraph process is developed. The second harmonic generation and parametric amplification upon high-frequency pumping are considered. It is found that the maximum efficiency of nonlinear conversion is achieved when the phase mismatch between the interacting waves is equal to the doubled spatial frequency at which the nonlinearity sign is changed (the condition of stochastic quasi-phase matching). (nonlinear optical phenomena)

  16. Designing a Stochastic Adaptive Impulsive Observer for Stochastic Linear and Nonlinear Impulsive Systems

    SciTech Connect

    Ayati, Moosa; Alwan, Mohamad; Liu Xinzhi; Khaloozadeh, Hamid

    2011-11-30

    State observation (estimation) is a very important issue in system analysis and control. This paper develops a new observer called Stochastic Adaptive Impulsive Observer (SAIO) for the state estimation of impulsive systems. The proposed observer is applicable to linear and nonlinear stochastic impulsive systems. In addition, the effect of parametric uncertainty is considered and unknown parameters of the system are estimated by suitable adaptation laws. Impulsive system theory, particularly stochastic Lyapunov-like function, is used to analyze the stability and convergence of the state estimations. The main advantages of the proposed observer are: 1) it gives continuous estimation from discrete time measurements of the system output, and 2) it is useful for state estimation when continuous measurements are impossible or expensive. Simulation results show the effectiveness of the proposed observer and we believe that it has many applications in control and estimation theories.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Stochastic acceleration of charged particle in nonlinear wave field

    NASA Astrophysics Data System (ADS)

    He, Kaifen

    2003-04-01

    Possibility of stochastic acceleration of charged particle by nonlinear waves is investigated. Spatially regular (SR) and spatiotemporal chaotic (STC) wave solutions evolving from saddle steady wave are tested as the fields. In the non-steady SR field the particle is finally trapped by the wave and averagely gains its group velocity, while in the STC field the particle motion displays trapped-free phases with its averaged velocity larger or smaller than the group velocity depending on the charge sign. A simplified model is established to investigate the acceleration mechanism. By analogy with motor protein, it is found that the virtual pattern of saddle steady wave plays a role of asymmetric potential, which and the nonlinear varying perturbation wave are the two sufficient ingredients for the acceleration in our case.

  2. Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Agarwal, S.; Wettlaufer, J. S.

    2014-12-01

    We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

  3. M-ary suprathreshold stochastic resonance: Generalization and scaling beyond binary threshold nonlinearities

    NASA Astrophysics Data System (ADS)

    McDonnell, Mark D.; Gao, Xiao

    2014-12-01

    Suprathreshold stochastic resonance is a form of noise-enhanced processing that is observed only when more than one noisy nonlinear signal processing element is combined in a parallel array, such as in biological and engineered sensory transduction. The case of binary threshold nonlinearities combined into arrays of independently noisy components has previously been studied extensively, and quantified in terms of how information transmission through the array varies with the input noise level, and the number of elements, N. Here we generalise this setup to arrays of N identical M-ary threshold nonlinearities. We show that enhanced suprathreshold stochastic resonance occurs for M≥ 1 and N > 1, implying that M identical quantizing sensors can be combined to provide higher resolution than a single sensor, provided they are independently noisy. We also study the system's scaling with M and N and conclude that although binary quantizing nonlinearities are superior to M-ary nonlinearities in the presence of large noise, the opposite holds in the presence of small noise. This suggests that multiple identical but coarse-resolution sensors can be useful for acquiring low SNR signals while few high-resolution identical sensors are superior for high SNR signals.

  4. 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.

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

    PubMed

    Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem

    2015-01-01

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

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

    PubMed Central

    Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem

    2015-01-01

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

  7. 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.

  8. 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. PMID:24483536

  9. 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.

  10. Absolute phase image reconstruction: a stochastic nonlinear filtering approach.

    PubMed

    Leitão, J N; Figueiredo, M A

    1998-01-01

    This paper formulates and proposes solutions to the problem of estimating/reconstructing the absolute (not simply modulo-2pi) phase of a complex random field from noisy observations of its real and imaginary parts. This problem is representative of a class of important imaging techniques such as interferometric synthetic aperture radar, optical interferometry, magnetic resonance imaging, and diffraction tomography. We follow a Bayesian approach; then, not only a probabilistic model of the observation mechanism, but also prior knowledge concerning the (phase) image to be reconstructed, are needed. We take as prior a nonsymmetrical half plane autoregressive (NSHP AR) Gauss-Markov random field (GMRF). Based on a reduced order state-space formulation of the (linear) NSHP AR model and on the (nonlinear) observation mechanism, a recursive stochastic nonlinear filter is derived, The corresponding estimates are compared with those obtained by the extended Kalman-Bucy filter, a classical linearizing approach to the same problem. A set of examples illustrate the effectiveness of the proposed approach. PMID:18276299

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

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

    SciTech Connect

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-06-20

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

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

    NASA Astrophysics Data System (ADS)

    Ganapathysubramanian, Baskar; Zabaras, Nicholas

    2008-06-01

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

  19. Cellular Biology in Terms of Stochastic Nonlinear Biochemical Dynamics: Emergent Properties, Isogenetic Variations and Chemical System Inheritability

    NASA Astrophysics Data System (ADS)

    Qian, Hong

    2010-12-01

    Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a "ghost" of the extinction phenomenon. We argue the thermal fluctuations inherent in molecular processes do not disappear in mesoscopic cell-sized nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical variations in terms of the stochastic attractors can have extremely long lifetime. Transitions among discrete stochastic attractors spend most of the time in "waiting", exhibit punctuated equilibria. It can be naturally passed to "daughter cells" via a simple growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing free energy F( t) with external energy drive Q hk ≥0, and total entropy production rate e p =- dF/ dt+ Q hk ≥0. In the thermodynamic limit, with a system's size being infinitely large, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.

  20. 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.

  1. Doubly stochastic Poisson processes in artificial neural learning.

    PubMed

    Card, H C

    1998-01-01

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

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

    PubMed

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

    2014-12-01

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

  3. 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.

  4. Study on high order perturbation-based nonlinear stochastic finite element method for dynamic problems

    NASA Astrophysics Data System (ADS)

    Wang, Qing; Yao, Jing-Zheng

    2010-12-01

    Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

  5. 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.

  6. Stochastic functionals and fluctuation theorem for multikangaroo processes.

    PubMed

    Van den Broeck, C; Toral, R

    2014-06-01

    We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device. PMID:25019742

  7. 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.

  8. INSTRUCTIONAL CONFERENCE ON THE THEORY OF STOCHASTIC PROCESSES: Operator stochastic differential equations and stochastic semigroups

    NASA Astrophysics Data System (ADS)

    Skorokhod, A. V.

    1982-12-01

    CONTENTSIntroduction § 1. The finite-dimensional case § 2. Stochastic semigroups in the L2-strong theory § 3. Homogeneous strongly continuous semigroups with the group of the first moments § 4. Stochastic equations of diffusion type with constant coefficients § 5. Continuous homogeneous stochastic semigroups in the presence of two moments References

  9. Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise.

    PubMed

    Chen, Po-Wei; Chen, Bor-Sen

    2011-08-01

    Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods. PMID:21624379

  10. Stochastic simulation of pulverized coal (PC) processes

    SciTech Connect

    Salazar, J.; Diwekar, U.; Zitney, S.

    2010-01-01

    An increasing population and electricity demand in the U.S. require capacity expansion of power systems. The National Energy Technology Laboratory (NETL), U.S. Department of Energy (DOE), has invested considerable efforts on research and development to improve the design and simulation of these power plants. Incorporation of novel process synthesis techniques and realistic simulation methodologies yield optimal flowsheet configurations and accurate estimation of their performance parameters. To provide a better estimation of such performance indicators, simulation models should predict the process behavior based on not only deterministic values of well-known input parameters but also uncertain variables associated with simulation assumptions. In this work, the stochastic simulation of a load-following pulverized coal (PC) power plant takes into account the variation of three input variables, namely, atmospheric air temperature, atmospheric air humidity, and generation load. These uncertain variables are characterized with probability density functions (pdfs) obtained from available atmospheric and electrical energy generation data. The stochastic simulation is carried out by obtaining a sample of values from the pdfs that generates a set of scenarios under which the model is run. An efficient sampling technique [Hammersley sequence sampling (HSS)] guarantees a set of scenarios uniformly distributed throughout the uncertain variable range. Then, each model run generates results on performance parameters as cycle efficiency, carbon emissions, sulfur emissions, and water consumption that are statistically analyzed after all runs are completed. Among these parameters, water consumption is of importance because an increasing demand has been observed mostly in arid regions of the country and, therefore, constrains the operability of the processes. This water consumption is significantly affected by atmospheric uncertainties. The original deterministic process model

  11. 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. PMID:24732236

  12. 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.

  13. 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.

  14. 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.

  15. Correlation functions in conformal invariant stochastic processes

    NASA Astrophysics Data System (ADS)

    Alcaraz, Francisco C.; Rittenberg, Vladimir

    2015-11-01

    We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one considers systems with periodic boundary conditions, the observables are described by boundary operators. From our experience with equilibrium problems one would have expected bulk operators. Boundary operators have correlators having critical exponents being half of those of bulk operators. If one studies the space-time dependence of the two-point function, one has to consider one boundary and one bulk operators. The Raise and Peel model has conformal invariance as can be shown in the spin 1/2 basis of the Hamiltonian which gives the time evolution of the system. This is an XXZ quantum chain with twisted boundary condition and local interactions. This Hamiltonian is integrable and the spectrum is known in the finite-size scaling limit. In the stochastic base in which the process is defined, the Hamiltonian is not local anymore. The mapping into an SOS model, helps to define new local operators. As a byproduct some new properties of the SOS model are conjectured. The predictions of conformal invariance are discussed in the new framework and compared with Monte Carlo simulations.

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

    SciTech Connect

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

    2013-01-15

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

  17. 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.

  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. 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.

  20. Reliability analysis of roadway departure risk using stochastic processes

    NASA Astrophysics Data System (ADS)

    Rey, G.; Clair, D.; Fogli, M.; Bernardin, F.

    2011-05-01

    The work presented here aims to develop a warning device to prevent roadway departure while cornering. Given the random variability arising from the driver, the vehicle and the infrastructure at the entrance of the curve, a probabilistic strategy is adopted to assess the roadway departure risk. Random variables and processes are introduced in a specifically developed vehicle dynamics model. The driver's behaviours are deduced from real traffic measurements. Structural reliability methods are employed to compute a roadway departure risk index, used to take the decision of an alarm triggering. Particular care is brought to the reduction of the computational cost. Refinements made on the standard reliability methods to handle with the model non-linearities and the stochastic dimension are presented.

  1. Mapping stochastic processes onto complex networks

    NASA Astrophysics Data System (ADS)

    Shirazi, A. H.; Reza Jafari, G.; Davoudi, J.; Peinke, J.; Reza Rahimi Tabar, M.; Sahimi, Muhammad

    2009-07-01

    We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and white noise. The networks are further studied by contrasting their geometrical properties, such as the mean length, diameter, clustering, and average number of connections per node. By comparing the network properties of the original time series investigated with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series on the networks constructed. Most importantly, we demonstrate that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks.

  2. THE LOSS OF ACCURACY OF STOCHASTIC COLLOCATION METHOD IN SOLVING NONLINEAR DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA

    SciTech Connect

    Webster, Clayton G; Tran, Hoang A; Trenchea, Catalin S

    2013-01-01

    n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.

  3. 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.

  4. Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

    NASA Astrophysics Data System (ADS)

    Duan, Zhaoxia; Xiang, Zhengrong; Karimi, Hamid Reza

    2014-07-01

    This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality-based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.

  5. 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.

  6. Nonlinear biochemical signal processing via noise propagation.

    PubMed

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

    2013-10-14

    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.

  7. 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.

  8. Nonlinear and stochastic effects in ENSO variability: From observations to intermediate models

    NASA Astrophysics Data System (ADS)

    Chekroun, Mickael David; Kondrashov, Dmitri; Neelin, David; Ghil, Michael

    2010-05-01

    The El-Nino/Southern-Oscillation (ENSO) phenomenon dominates interannual climate signals in and around the Tropical Pacific and affects the atmospheric circulation and air-sea interaction over many parts of the globe. Observational campaigns over the last decades have helped infer the most relevant processes, time scales and spatial patterns. A hierarchy of models has been developed to understand these processes and their interaction. These models have been, by-and-large, either deterministic and nonlinear or stochastic and linear, and have been applied to the prediction of future variability as well. The purpose of our work is to combine these two complementary points of view, and thus account for (i) the most robust and relevant aspects of the observations; (ii) the advances in understanding the nonlinear, deterministic interactions between the largest and most energetic scales; and (iii) the impact of small-scale ("noise") and remote ("external") processes. The main thrust of our approach is based on the concepts and tools of the theory of random dynamical systems (RDS). So far, two of the co-authors (MC & MG), in collaboration with E. Simonnet, have successfully applied RDS theory to, and described in detail the random attractors of several idealized climate models, such as the Lorenz (JAS, 1963) model of convection and the ENSO model of Timmermann and Jin (GRL, 2002). In the present work, we are extending these results to more detailed and realistic models, on the way to their eventual application to IPCC-class general circulation models (GCMs). Specifically, we address here two classes of such intermediate models. The first class is that of nonlinear inverse models derived by empirical mode reduction (EMR), as developed by two of the co-authors (MG and DK), in collaboration with S. Kravtsov, A. W. Robertson and others. In particular, we are studying the random attractor of the ENSO model derived in 2005 from sea surface temperature data over the past century

  9. 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.

  10. Stochastic Impulse Control of Non-Markovian Processes

    SciTech Connect

    Djehiche, Boualem; Hamadene, Said Hdhiri, Ibtissam

    2010-02-15

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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    This paper is concerned with a stochastic delayed SEIR epidemic model with nonlinear incidence. Firstly we verify that there exists a unique global positive solution of the system. Then by constructing some suitable Lyapunov functions, we study the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium respectively.

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

    PubMed

    Rifhat, Ramziya; Ge, Qing; Teng, Zhidong

    2016-01-01

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

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

    PubMed Central

    Rifhat, Ramziya; Ge, Qing; Teng, Zhidong

    2016-01-01

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

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  1. 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

  2. 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

  3. Economic-oriented stochastic optimization in advanced process control of chemical processes.

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  5. Stochastic Car-Following Model for Explaining Nonlinear Traffic Phenomena

    NASA Astrophysics Data System (ADS)

    Meng, Jianping; Song, Tao; Dong, Liyun; Dai, Shiqiang

    There is a common time parameter for representing the sensitivity or the lag (response) time of drivers in many car-following models. In the viewpoint of traffic psychology, this parameter could be considered as the perception-response time (PRT). Generally, this parameter is set to be a constant in previous models. However, PRT is actually not a constant but a random variable described by the lognormal distribution. Thus the probability can be naturally introduced into car-following models by recovering the probability of PRT. For demonstrating this idea, a specific stochastic model is constructed based on the optimal velocity model. By conducting simulations under periodic boundary conditions, it is found that some important traffic phenomena, such as the hysteresis and phantom traffic jams phenomena, can be reproduced more realistically. Especially, an interesting experimental feature of traffic jams, i.e., two moving jams propagating in parallel with constant speed stably and sustainably, is successfully captured by the present model.

  6. 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.

  7. 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

  8. Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

    NASA Astrophysics Data System (ADS)

    Han, Qun; Xu, Wei; Sun, Jian-Qiao

    2016-09-01

    The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

  9. 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.

  10. 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.

  11. 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.

  12. On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

    SciTech Connect

    Motta, Monica; Sartori, Caterina

    2011-08-15

    In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.

  13. 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.

  14. 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.

  15. 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

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

    NASA Astrophysics Data System (ADS)

    Wang, Yong; Jin, Xiaoling; Huang, Zhilong

    2016-02-01

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

  17. 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.

  18. Analyzing stochastic dependence of cognitive processes in multidimensional source recognition.

    PubMed

    Meiser, Thorsten

    2014-01-01

    Stochastic dependence among cognitive processes can be modeled in different ways, and the family of multinomial processing tree models provides a flexible framework for analyzing stochastic dependence among discrete cognitive states. This article presents a multinomial model of multidimensional source recognition that specifies stochastic dependence by a parameter for the joint retrieval of multiple source attributes together with parameters for stochastically independent retrieval. The new model is equivalent to a previous multinomial model of multidimensional source memory for a subset of the parameter space. An empirical application illustrates the advantages of the new multinomial model of joint source recognition. The new model allows for a direct comparison of joint source retrieval across conditions, it avoids statistical problems due to inflated confidence intervals and does not imply a conceptual imbalance between source dimensions. Model selection criteria that take model complexity into account corroborate the new model of joint source recognition.

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

    PubMed

    Herzallah, Randa

    2015-03-01

    Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. PMID:25562567

  20. 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.

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

    SciTech Connect

    Keanini, R.G.

    2011-04-15

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

  2. Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

    This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

  3. 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.

  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. Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles

    NASA Astrophysics Data System (ADS)

    Kiselev, S. A.; Phillips, Andy; Gabitov, I.

    2000-07-01

    This Letter investigates the stochastic dynamics of a simplified agent-based microscopic model describing stock market evolution. Our mathematical model includes a stochastic market and a sealed-bid double auction. The dynamics of the model are determined by the game of two types of traders: (i) `intelligent' traders whose strategy is based on nonlinear technical data analysis 1 and (ii) `random' traders that act without a consistent strategy. We demonstrate the effect of time-scale separations on the market dynamics. We study the characteristics of the market relaxation in response to perturbations caused by large cash flows generated between these two groups of traders. We also demonstrate that our model exhibits the formation of a price bubble 2 and the subsequent transition to a bear market 3. Bear market - a macroscopically long stage of a market evolution when the stock price declines significantly, 15% or more.

  6. 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.

  7. 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.

  8. ? filtering for stochastic systems driven by Poisson processes

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  9. 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.

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

    PubMed

    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

  11. 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

  12. 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. PMID:15787159

  13. A space-time cluster algorithm for stochastic processes.

    SciTech Connect

    Gulbahce, N.

    2003-01-01

    We introduce a space-time cluster algorithm that will generate histories of stochastic processes. Michael Zimmer introduced a spacetime MC algorithm for stochastic classical dynamics and he applied it to simulate Ising model with Glauber dynamics. Following his steps, we extended Brower and Tamayo's embedded {phi}{sup 4} dynamics to space and time. We believe our algorithm can be applied to more general stochastic systems. Why space-time? To be able to study nonequilibrium systems, we need to know the probability of the 'history' of a nonequilibrium state. Histories are the entire space-time configurations. Cluster algorithms first introduced by SW, are useful to overcome critical slowing down. Brower and Tamayo have mapped continous field variables to Ising spins, and have grown and flipped SW clusters to gain speed. Our algorithm is an extended version of theirs to space and time.

  14. 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.

  15. 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.

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

    PubMed

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

    2015-02-01

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

  17. 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.

  18. Hybrid processing of stochastic and subjective uncertainty data

    SciTech Connect

    Cooper, J.A.; Ferson, S.; Ginzburg, L.

    1995-11-01

    Uncertainty analyses typically recognize separate stochastic and subjective sources of uncertainty, but do not systematically combine the two, although a large amount of data used in analyses is partly stochastic and partly subjective. We have developed methodology for mathematically combining stochastic and subjective data uncertainty, based on new ``hybrid number`` approaches. The methodology can be utilized in conjunction with various traditional techniques, such as PRA (probabilistic risk assessment) and risk analysis decision support. Hybrid numbers have been previously examined as a potential method to represent combinations of stochastic and subjective information, but mathematical processing has been impeded by the requirements inherent in the structure of the numbers, e.g., there was no known way to multiply hybrids. In this paper, we will demonstrate methods for calculating with hybrid numbers that avoid the difficulties. By formulating a hybrid number as a probability distribution that is only fuzzy known, or alternatively as a random distribution of fuzzy numbers, methods are demonstrated for the full suite of arithmetic operations, permitting complex mathematical calculations. It will be shown how information about relative subjectivity (the ratio of subjective to stochastic knowledge about a particular datum) can be incorporated. Techniques are also developed for conveying uncertainty information visually, so that the stochastic and subjective constituents of the uncertainty, as well as the ratio of knowledge about the two, are readily apparent. The techniques demonstrated have the capability to process uncertainty information for independent, uncorrelated data, and for some types of dependent and correlated data. Example applications are suggested, illustrative problems are worked, and graphical results are given.

  19. Modeling of Ultra-Short Soliton Propagation in Deterministic and Stochastic Nonlinear Cubic Media

    NASA Astrophysics Data System (ADS)

    Kurt, Levent

    We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We investigate the numerical proof for the exact solitary solution of the short pulse equation. Moreover, we demonstrate that the short pulse solitons approximate the solution of the Maxwell equation numerically. Our numerical experiments prove the particle-like behaviour of the short pulse solitons. Furthermore, we derive a short pulse equation in the higher order. A stochastic counterpart of the short pulse equation is also derived through the use of the multiple scale expansion method for more realistic situations where stochastic perturbations in the dispersion are present. We numerically show that the short pulse solitary waves persist even in the presence of the randomness. The numerical schemes developed demonstrate that the statistics of the coarse-graining noise of the short pulse equation over the slow scale, and the microscopic noise of the nonlinear wave equation over the fast scale, agree to fairly good accuracy.

  20. Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond.

    PubMed

    Ge, Hao; Qian, Hong

    2011-01-01

    A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation-dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the 'free energy function', Lee-Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network.

  1. Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

    PubMed Central

    Ge, Hao; Qian, Hong

    2011-01-01

    A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

  2. Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

    NASA Astrophysics Data System (ADS)

    Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

    2016-05-01

    Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

  3. Using Multi-Objective Genetic Programming to Synthesize Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Ross, Brian; Imada, Janine

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

  4. 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

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

    PubMed Central

    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 R2 = 0 .99396. PMID:25920547

  6. 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.

  7. 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

  8. 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.

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

    NASA Astrophysics Data System (ADS)

    Yadav, Avinash Chand

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-02-01

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

  11. Stochastic 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

  12. NOVEL SIGNAL PROCESSING WITH NONLINEAR TRANSMISSION LINES

    SciTech Connect

    D. REAGOR; ET AL

    2000-08-01

    Nonlinear dielectrics offer uniquely strong and tunable nonlinearities that make them attractive for current devices (for example, frequency-agile microwave filters) and for future signal-processing technologies. The goal of this project is to understand pulse propagation on nonlinear coplanar waveguide prototype devices. We have performed time-domain and frequency-domain experimental studies of simple waveguide structures and pursued a theoretical understanding of the propagation of signals on these nonlinear waveguides. To realistically assess the potential applications, we used a time-domain measurement and analysis technique developed during this project to perform a broadband electrodynamics characterization in terms of nonlinear, dispersive, and dissipative effects. We completed a comprehensive study of coplanar waveguides made from high-temperature superconducting thin-film YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} electrodes on nonlinear dielectric single-crystal SrTiO{sub 3} substrates. By using parameters determined from small-signal (linear) transmission characteristics of the waveguides, we develop a model equation that successfully predicts and describes large-signal (nonlinear) behavior.

  13. Identification of chaotic and stochastic processes by permutation entropy analysis

    NASA Astrophysics Data System (ADS)

    Maggs, J. E.; Morales, G. J.

    2013-10-01

    The dynamical nature of time signals can be determined by the simultaneous use of entropy and statistical complexity. These key measures can be implemented using the amplitude permutation probability introduced by Bandt and Pompe. Stochastic and chaotic processes are distinguished because they occupy different regions of the entropy-complexity plane. Permutation entropy analysis is used to demonstrate that temperature fluctuations observed in a basic heat transport experiment arise from chaotic dynamics. Locations of various known stochastic and chaotic processes in the entropy-complexity plane are presented and the important technique of `sub-sampling' for the amelioration of noise is discussed. The permutation entropy analysis can be applied to any time signal as no pre-processing or a priori conditions are required. This signal analysis technique has the potential to uncover new features in a wide range of fusion and basic plasma experiments. Supported by a DOE-NSF cooperative agreement, and by DOE grant SC0004663.

  14. The maximal process of nonlinear shot noise

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo; Klafter, Joseph

    2009-05-01

    In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay-surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay-surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay-surge structure, and its correlation structure. All results are obtained analytically and in closed-form.

  15. Simulating river meandering processes using stochastic bank erosion coefficient

    NASA Astrophysics Data System (ADS)

    Posner, Ari J.; Duan, Jennifer G.

    2012-08-01

    This study first compares the first order analytical solutions for flow field by Ikeda et. al. (1981) and Johanesson and Parker (1989b). Ikeda et. al.'s (1981) linear model of bank erosion was implemented to predict the rate of bank erosion in which the bank erosion coefficient is treated as a stochastic variable that varies with physical properties of the bank (e.g. cohesiveness, stratigraphy, vegetation density). The developed model was used to predict the evolution of meandering planforms. Then, the modeling results were analyzed and compared to the observed data. Because the migration of meandering channels consists of downstream translation, lateral expansion, and downstream or upstream rotations, several measures are formulated to determine which of the resulting planform is closest to the experimental measured one. Results from the deterministic model highly depend on the calibrated erosion coefficient. Because field measurements are always limited, the stochastic model yielded more realistic predictions of meandering planform evolutions. Because the coefficient of bank erosion is a random variable, the meandering planform evolution is a stochastic process that can only be accurately predicted by a stochastic model.

  16. 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,

  17. 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.

  18. Stochastic linearisation approach to performance analysis of feedback systems with asymmetric nonlinear actuators and sensors

    NASA Astrophysics Data System (ADS)

    Kabamba, P. T.; Meerkov, S. M.; Ossareh, H. R.

    2015-01-01

    This paper considers feedback systems with asymmetric (i.e., non-odd functions) nonlinear actuators and sensors. While the stability of such systems can be investigated using the theory of absolute stability and its extensions, the current paper provides a method for their performance analysis, i.e., reference tracking and disturbance rejection. Similar to the case of symmetric nonlinearities considered in earlier work, the development is based on the method of stochastic linearisation (which is akin to the describing functions, but intended to study general properties of dynamics, rather than periodic regimes). Unlike the symmetric case, however, the nonlinearities considered here must be approximated not only by a quasilinear gain, but a quasilinear bias as well. This paper derives transcendental equations for the quasilinear gain and bias, provides necessary and sufficient conditions for existence of their solutions, and, using simulations, investigates the accuracy of these solutions as a tool for predicting the quality of reference tracking and disturbance rejection. The method developed is then applied to performance analysis of specific systems, and the effect of asymmetry on their behaviour is investigated. In addition, this method is used to justify the recently discovered phenomenon of noise-induced loss of tracking in feedback systems with PI controllers, anti-windup, and sensor noise.

  19. 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.

  20. Novel mapping in non-equilibrium stochastic processes

    NASA Astrophysics Data System (ADS)

    Heseltine, James; Kim, Eun-jin

    2016-04-01

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

  1. 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.

  2. Adaptive control of stochastic Hammerstein-Wiener nonlinear systems with measurement noise

    NASA Astrophysics Data System (ADS)

    Zhang, Bi; Mao, Zhizhong

    2016-01-01

    This paper deals with the adaptive control of a class of stochastic Hammerstein-Wiener nonlinear systems with measurement noise. Despite the fundamental progress achieved so far, a general theory framework about adaptive control of Hammerstein-Wiener models is still absent. Such situation is mainly due to the lack of an appropriate parameterisation model. To this end, this paper presents a novel parameterisation model that is to replace unmeasurable internal variables with their estimations. Then, the adaptive control algorithm to be applied is derived on the basis of self-tuning control. In addition, due to the use of the internal variable estimations, the stability and convergence properties are different from the self-tuning control. Our aim, in theoretical analysis, is to discover what limitations are in using the estimations instead of the true values in a control algorithm. Representative numerical examples are given and the simulation results verify the theoretical analysis.

  3. Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate

    NASA Astrophysics Data System (ADS)

    Teng, Zhidong; Wang, Lei

    2016-06-01

    In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is investigated. It is shown that the extinction and persistence of the disease in probability are determined by a threshold value R˜0. That is, if R˜0 < 1 and an additional condition holds then disease dies out, and if R˜0 > 1 then disease is weak permanent with probability one. To obtain the permanence in the mean of the disease, a new quantity R̂0 is introduced, and it is proved that if R̂0 > 1 the disease is permanent in the mean with probability one. Furthermore, the numerical simulations are presented to illustrate some open problems given in Remarks 1-3 and 5 of this paper.

  4. 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.

  5. Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics

    SciTech Connect

    Burić, Nikola Popović, Duška B.; Radonjić, Milan; Prvanović, Slobodan

    2014-04-15

    A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.

  6. 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.

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

    PubMed

    Xu, Hao; Jagannathan, Sarangapani

    2015-03-01

    The stochastic optimal control of nonlinear networked control systems (NNCSs) using neuro-dynamic programming (NDP) over a finite time horizon is a challenging problem due to terminal constraints, system uncertainties, and unknown network imperfections, such as network-induced delays and packet losses. Since the traditional iteration or time-based infinite horizon NDP schemes are unsuitable for NNCS with terminal constraints, a novel time-based NDP scheme is developed to solve finite horizon optimal control of NNCS by mitigating the above-mentioned challenges. First, an online neural network (NN) identifier is introduced to approximate the control coefficient matrix that is subsequently utilized in conjunction with the critic and actor NNs to determine a time-based stochastic optimal control input over finite horizon in a forward-in-time and online manner. Eventually, Lyapunov theory is used to show that all closed-loop signals and NN weights are uniformly ultimately bounded with ultimate bounds being a function of initial conditions and final time. Moreover, the approximated control input converges close to optimal value within finite time. The simulation results are included to show the effectiveness of the proposed scheme. PMID:25720004

  8. 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.

  9. Vibrotactile sensitivity threshold: nonlinear stochastic mechanotransduction model of the Pacinian Corpuscle.

    PubMed

    Biswas, Abhijit; Manivannan, M; Srinivasan, Mandayam A

    2015-01-01

    Based on recent discoveries of stretch and voltage activated ion channels in the receptive area of the Pacinian Corpuscle (PC), this paper describes a two-stage mechanotransduction model of its near threshold Vibrotactile (VT) sensitivity valid over 10 Hz to a few kHz. The model is based on the nonlinear and stochastic behavior of the ion channels represented as dependent charge sources loaded with membrane impedance. It simulates the neural response of the PC considering the morphological and statistical properties of the receptor potential and action potential with the help of an adaptive relaxation pulse frequency modulator. This model also simulates the plateaus and nonmonotonic saturation of spike rate characteristics. The stochastic simulation based on the addition of mechanical and neural noise describes that the VT Sensitivity Threshold (VTST) at higher frequencies is more noise dependent. Above 800 Hz even a SNR = 150 improves the neurophysiological VTST more than 3 dBμ. In that frequency range, an absence of the entrainment threshold and a lower sensitivity index near the absolute threshold make the upper bound of the psychophysical VTST more dependent on the experimental protocol and physical set-up. This model can be extended to simulate the neural response of a group of PCs.

  10. Fractal dimension and nonlinear dynamical processes

    NASA Astrophysics Data System (ADS)

    McCarty, Robert C.; Lindley, John P.

    1993-11-01

    Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

  11. 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…

  12. Nonequilibrium dynamics of stochastic point processes with refractoriness

    NASA Astrophysics Data System (ADS)

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

    2010-08-01

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

  13. Chaotic signal processes and associated nonlinear filters

    NASA Astrophysics Data System (ADS)

    McCarty, Robert C.

    1997-04-01

    A chaotic signal process is generated by use of a continuous but nowhere differentiable Weierstrass function as a force function in Duffing's second-order nonlinear differential equation. In the particular cases where Duffing's equation represents the mechanical behavior of a simple pendulum where only the mass of the 'bob' changes in time, an analytical solution is obtained by the use of Hammerstein integrals. In the more-complicated case where the mass of the 'bob' and the length of the pendulum rod are both changing in time, the resulting solution is obtained numerically. In any detailed analysis of a chaotic signal process, nonlinear filters are used to determine the existence and nature of an attractor or repeller as discussed. By a simple change of parametric values in the Weierstrass function, other chaotic signal processes are easily generated.

  14. 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.

  15. 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.

  16. 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.

  17. Relative efficiency of Gaussian stochastic process sampling procedures

    NASA Astrophysics Data System (ADS)

    Cameron, Chris

    2003-12-01

    Various methods for sampling stationary, Gaussian stochastic processes are investigated and compared with an emphasis on applications to processes with power law energy spectra. Several approaches are considered, including a Riemann summation using left endpoints, the use of random wave numbers to sample a the spectrum in proportion to the energy it contains, and a combination of the two. The Fourier-wavelet method of Elliott et al. is investigated and compared with other methods, all of which are evaluated in terms of their ability to sample the stochastic process over a large number of decades for a given computational cost. The Fourier-wavelet method has accuracy which increases linearly with the computational complexity, while the accuracy of the other methods grows logarithmically. For the Kolmogorov spectrum, a hybrid quadrature method is as efficient as the Fourier-wavelet method, if no more than eight decades of accuracy are required. The effectiveness of this hybrid method wanes when one samples fields whose energy spectrum decays more rapidly near the origin. The Fourier-wavelet method has roughly the same behavior independently of the exponent of the power law. The Fourier-wavelet method returns samples which are Gaussian over the range of values where the structure function is well approximated. By contrast, (multi-point) Gaussianity may be lost at the smaller length scales when one uses methods with random wave numbers.

  18. 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. PMID:26940822

  19. Estimating partial observability and nonlinear climate effects on stochastic community dynamics of migratory waterfowl.

    PubMed

    Almaraz, Pablo; Green, Andy J; Aguilera, Eduardo; Rendón, Miguel A; Bustamante, Javier

    2012-09-01

    1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (<5%). In general, abiotic conditions during winter prevailed over conditions experienced during breeding and migration. Across species, a pervasive and coherent nonlinear signal of environmental variability on population dynamics suggests weaker forcing at extreme values of abiotic variables. 4. Modelling missing observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when

  20. Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations

    NASA Astrophysics Data System (ADS)

    Nazarov, V. E.

    2016-09-01

    Based on the modification of the linear part of the Granato-Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.

  1. Linking stochastic sediment transport to physical processes (Invited)

    NASA Astrophysics Data System (ADS)

    Jerolmack, D. J.; Martin, R.; Paola, C.; Reitz, M. D.; Schumer, R.

    2010-12-01

    Intermittent transport is the rule rather than the exception in sedimentary systems. Avalanching dynamics in granular flows is known to produce stochastic transport fluctuations over a wide range of scales - for example, the well known power-law distributions of landslide magnitudes. Similar stochastic dynamics can occur in multi-phase flows, e.g., bedload transport in rivers. A generalized theoretical framework for understanding stochastic transport is lacking. A pragmatic alternative is the stochastic processes approach: using (fractional) advection-diffusion equations, conditioned with measured statistics from a real system, to make future predictions about transport. Linking the macroscopic statistics described by such models to the microscopic physics of sediment transport will require a new statistical mechanics approach. We propose to begin by delineating generic categories of transport mechanics - universality classes - and determining their statistical signatures through theory and experiment. A first separation may be drawn between periodic and aperiodic transport fluctuations. Periodic transport fluctuations have been observed in both sand piles and river delta experiments, and appear to arise under conditions of a well-defined transport threshold (e.g., an angle of repose) and limited dissipation. Under these conditions, inertia overwhelms system heterogeneity and gives rise to periodic oscillations having a characteristic magnitude. Aperiodic transport fluctuations often imply a strong control of system heterogeneity, and/or significant dissipation or friction capable of “breaking up” sediment pulses. For example, varying soil properties give rise to a range of critical failure slopes for landslides. Transitions in the dominant transport process from small to large time or space scales are expected to result in transitions in scaling. Bedload transport is super-diffusive at short timescales because of correlated motion due to particle momentum. At

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

    NASA Astrophysics Data System (ADS)

    Le, Thai-Hoa; Caracoglia, Luca

    2015-05-01

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

  3. 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.

  4. 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.

  5. Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays.

    PubMed

    Chen, Weisheng; Jiao, Licheng; Li, Jing; Li, Ruihong

    2010-06-01

    For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.

  6. 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

  7. Laboratory investigation of nonlinear whistler wave processes

    NASA Astrophysics Data System (ADS)

    Amatucci, B.; Tejero, E.; Cothran, C.; Ganguli, G.; Crabtree, C.; Mithiawala, M.; Sotnikov, V.

    2012-10-01

    Nonlinear interactions involving whistler wave turbulence result from processes, including 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.footnotetextCrabtree et al., Phys. Plasmas, 19, Art. No. 032903 (2012). In the magnetosphere, boundary layers often have highly sheared plasma flows and lower hybrid turbulence. Such nonlinear processes are being investigated in the NRL Space Chamber in conditions scaled to match the respective environments. By creating boundary layers with controllable density gradient and transverse electric fields and scale length much smaller than an ion gyroradius, lower hybrid waves consistent with the Electron-Ion Hybrid InstabilityfootnotetextGanguli et al., Phys. Fluids, 31, 2753 (1988). have been observed. 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. Details of the observed wave spectra and mode characteristics will be presented.

  8. State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

    PubMed

    Elenchezhiyan, M; Prakash, J

    2015-09-01

    In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.

  9. Nonlinear stochastic biasing of halos: Analysis of cosmological N-body simulations and perturbation theories

    NASA Astrophysics Data System (ADS)

    Sato, Masanori; Matsubara, Takahiko

    2013-06-01

    It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.

  10. 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

  11. Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

    NASA Astrophysics Data System (ADS)

    El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.

    2015-06-01

    This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.

  12. 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

  13. 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.

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

    PubMed

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

    2011-07-01

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

  15. Suprathreshold stochastic resonance in neural processing tuned by correlation

    NASA Astrophysics Data System (ADS)

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

    2011-07-01

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

  16. 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.

  17. 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.

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

    SciTech Connect

    Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

    2010-08-15

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

  19. INSTRUCTIONAL CONFERENCE ON THE THEORY OF STOCHASTIC PROCESSES: Stochastic partial differential equations and diffusion processes

    NASA Astrophysics Data System (ADS)

    Krylov, N. V.; Rozovskii, B. L.

    1982-12-01

    CONTENTS § 1. Introduction § 2. Solubility of the direct and inverse Cauchy problems § 3. The direct equation of inverse diffusion. The method of variation of constants § 4. The method of characteristics. First integrals and the Liouville equations for diffusion processes § 5. Inverse filtration equations References

  20. Deciphering and modeling interconnections in ecohydrology: The role of scale, thresholds and stochastic storage processes

    NASA Astrophysics Data System (ADS)

    Bartlett, M. S.; McDonnell, J. J.; Porporato, A. M.

    2013-12-01

    Several components of ecohydrological systems are characterized by an interplay of stochastic inputs, finite capacity storage, and nonlinear, threshold-like losses, resulting in a complex partitioning of the rainfall input between the different basin scales. With the goal of more accurate predictions of rainfall partitioning and threshold effects in ecohydrology, we examine ecohydrological processes at the various scales, including canopy interception, soil storage with runoff/percolation, hillslope filling-spilling mechanisms, and the related groundwater recharge and baseflow contribution to streamflow. We apply a probabilistic approach to a hierarchical arrangement of cascading reservoirs that are representative of the components of the basin system. The analytical results of this framework help single out the key parameters controlling the partitioning of rainfall within the storage compartments of river basins. This theoretical framework is a useful learning tool for exploring the physical meaning of known thresholds in ecohydrology.

  1. 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

  2. Reliability-based design optimization under stationary stochastic process loads

    NASA Astrophysics Data System (ADS)

    Hu, Zhen; Du, Xiaoping

    2016-08-01

    Time-dependent reliability-based design ensures the satisfaction of reliability requirements for a given period of time, but with a high computational cost. This work improves the computational efficiency by extending the sequential optimization and reliability analysis (SORA) method to time-dependent problems with both stationary stochastic process loads and random variables. The challenge of the extension is the identification of the most probable point (MPP) associated with time-dependent reliability targets. Since a direct relationship between the MPP and reliability target does not exist, this work defines the concept of equivalent MPP, which is identified by the extreme value analysis and the inverse saddlepoint approximation. With the equivalent MPP, the time-dependent reliability-based design optimization is decomposed into two decoupled loops: deterministic design optimization and reliability analysis, and both are performed sequentially. Two numerical examples are used to show the efficiency of the proposed method.

  3. 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.

  4. 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

  5. Critical behavior of a class of nonlinear stochastic models of diffusion of information

    NASA Astrophysics Data System (ADS)

    Sharma, C. L.; Pathria, R. K.; Karmeshu

    1982-12-01

    A theoretical analysis based on the concepts and techniques of statistical physics is carried out for two nonlinear models of diffusion of information-one in a closed population and the other in an open one. Owing to interpersonal contacts among the members of the population, the models exhibit a cooperative behavior when a certain parameter of the problem approaches a critical value. Mathematical similarities in the behavior of the two models, in the vicinity of the critical point, are so impelling that one is tempted to investigate the corresponding behavior of a generalized model, which can be done by carrying out a systematic system-size expansion of the master equation of the process and thereby deriving a nonlinear Fokker-Planck equation for the relevant probability distribution. This establishes a broader class of systems displaying identical behavior in the critical region and also elucidates the role played by fluctuations in bringing about the cooperative phenomenon.

  6. 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.

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

    USGS Publications Warehouse

    Geist, Eric L.

    2015-01-01

    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.

  8. Superposition of Stochastic Processes and the Resulting Particle Distributions

    NASA Astrophysics Data System (ADS)

    Schwadron, N. A.; Dayeh, M. A.; Desai, M.; Fahr, H.; Jokipii, J. R.; Lee, M. A.

    2010-04-01

    Many observations of suprathermal and energetic particles in the solar wind and the inner heliosheath show that distribution functions scale approximately with the inverse of particle speed (v) to the fifth power. Although there are exceptions to this behavior, there is a growing need to understand why this type of distribution function appears so frequently. This paper develops the concept that a superposition of exponential and Gaussian distributions with different characteristic speeds and temperatures show power-law tails. The particular type of distribution function, f vprop v -5, appears in a number of different ways: (1) a series of Poisson-like processes where entropy is maximized with the rates of individual processes inversely proportional to the characteristic exponential speed, (2) a series of Gaussian distributions where the entropy is maximized with the rates of individual processes inversely proportional to temperature and the density of individual Gaussian distributions proportional to temperature, and (3) a series of different diffusively accelerated energetic particle spectra with individual spectra derived from observations (1997-2002) of a multiplicity of different shocks. Thus, we develop a proof-of-concept for the superposition of stochastic processes that give rise to power-law distribution functions.

  9. 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.

  10. Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

    NASA Astrophysics Data System (ADS)

    Wen, Shiping; Zeng, Zhigang

    2013-09-01

    In this article, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.

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

    PubMed

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

    2014-06-01

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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. Plasma Emission by Nonlinear Electromagnetic Processes

    NASA Astrophysics Data System (ADS)

    Ziebell, L. F.; Yoon, P. H.; Petruzzellis, L. T.; Gaelzer, R.; Pavan, J.

    2015-06-01

    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.

  20. 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.

  1. Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems

    NASA Astrophysics Data System (ADS)

    Moaveni, Babak; Asgarieh, Eliyar

    2012-08-01

    This paper proposes the use of the deterministic-stochastic subspace identification (DSI) method, an input-output parametric linear system identification method, for characterization of nonlinear dynamic structural systems based on their time-varying amplitude-dependent instantaneous (i.e., based on short time-windows) modal parameters. Performance of the DSI method for estimation of instantaneous modal parameters of nonlinear systems is investigated using numerical as well as experimental data. In this study, DSI is used for extracting instantaneous modal parameters of single degree-of-freedom (SDOF) as well as 7-DOF systems with different hysteretic material behavior. Nonlinear responses of the SDOF and 7-DOF systems are simulated due to different seismic excitations using the OpenSees structural analysis software. Modal identification results are compared with those obtained using wavelet transform and the exact values. Effects of four input factors are studied on the variability of identified instantaneous modal parameters: (1) type of material nonlinearity, (2) level of nonlinearity, (3) input excitation, and (4) length of data windows used in the identification. The accuracy of the identified instantaneous modal parameters is evaluated along the response time history while varying the above mentioned input factors. Overall, DSI outperforms the wavelet transform for short-time/instantaneous modal identification of nonlinear structural systems and provides reasonably accurate results especially when the material hysteretic behavior is smooth such as the considered Giuffré-Menegotto-Pinto hysteretic model. Finally, DSI has been applied for short-time modal identification of a full-scale seven-story reinforced concrete shear wall structure based on its measured response to different seismic base excitations on a shake table. The identified instantaneous natural frequencies of the first vibration mode can accurately track the variation in the structure

  2. State-feedback ℋ∞ control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise

    NASA Astrophysics Data System (ADS)

    Li, Huiping; Shi, Yang

    2012-10-01

    This article focuses on the state-feedback ℋ∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton-Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ℋ∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ℋ∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Anomalous pulse delay in microwave propagation: A stochastic process interpretation.

    PubMed

    Ranfagni, A; Ruggeri, R; Agresti, A; Ranfagni, C; Sandri, P

    2002-09-01

    An experiment involving microwave propagation in the near-field region with two horn antennas demonstrated a superluminal behavior which is strongly dependent on the frequency. The models previously proposed are found to be inadequate for interpreting the results. An attempt is made within the framework of a stochastic model, which can be improved by a path-integral analysis.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. On the nature of heart rate variability in a breathing normal subject: A stochastic process analysis

    NASA Astrophysics Data System (ADS)

    Buchner, Teodor; Petelczyc, Monika; Żebrowski, 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.

  14. Neural-Based Adaptive Output-Feedback Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems.

    PubMed

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

    2015-09-01

    In this paper, we consider the problem of observer-based adaptive neural output-feedback control for a class of stochastic nonlinear systems with nonstrict-feedback structure. To overcome the design difficulty from the nonstrict-feedback structure, a variable separation approach is introduced by using the monotonically increasing property of system bounding functions. On the basis of the state observer, and by combining the adaptive backstepping technique with radial basis function neural networks' universal approximation capability, an adaptive neural output feedback control algorithm is presented. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in the sense of mean quartic value. Simulation results are provided to show the effectiveness of the proposed control scheme.

  15. Decentralized Output Feedback Adaptive NN Tracking Control for Time-Delay Stochastic Nonlinear Systems With Prescribed Performance.

    PubMed

    Hua, Changchun; Zhang, Liuliu; Guan, Xinping

    2015-11-01

    This paper studies the dynamic output feedback tracking control problem for stochastic interconnected time-delay systems with the prescribed performance. The subsystems are in the form of triangular structure. First, we design a reduced-order observer independent of time delay to estimate the unmeasured state variables online instead of the traditional full-order observer. Then, a new state transformation is proposed in consideration of the prescribed performance requirement. Using neural network to approximate the composite unknown nonlinear function, the corresponding decentralized output tracking controller is designed. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of uniformly ultimately boundedness and that both transient-state and steady-state performances are preserved. Finally, a simulation example is given, and the result shows the effectiveness of the proposed control design method.

  16. EFFECTS OF ROTATION ON STOCHASTICITY OF GRAVITATIONAL WAVES IN THE NONLINEAR PHASE OF CORE-COLLAPSE SUPERNOVAE

    SciTech Connect

    Kotake, Kei; Iwakami-Nakano, Wakana; Ohnishi, Naofumi

    2011-08-01

    By performing three-dimensional (3D) simulations that demonstrate the neutrino-driven core-collapse supernovae aided by the standing accretion shock instability (SASI), we study how the spiral modes of the SASI can impact the properties of the gravitational-wave (GW) emission. To see the effects of rotation in the nonlinear postbounce phase, we give a uniform rotation on the flow advecting from the outer boundary of the iron core, the specific angular momentum of which is assumed to agree with recent stellar evolution models. We compute fifteen 3D models in which the initial angular momentum and the input neutrino luminosities from the protoneutron star are changed in a systematic manner. By performing a ray-tracing analysis, we accurately estimate the GW amplitudes generated by anisotropic neutrino emission. Our results show that the gravitational waveforms from neutrinos in models that include rotation exhibit a common feature; otherwise, they vary much more stochastically in the absence of rotation. The breaking of the stochasticity stems from the excess of the neutrino emission parallel to the spin axis. This is because the compression of matter is more enhanced in the vicinity of the equatorial plane due to the growth of the spiral SASI modes, leading to the formation of the spiral flows circulating around the spin axis with higher temperatures. We point out that recently proposed future space interferometers like Fabry-Perot-type DECIGO would permit the detection of these signals for a Galactic supernova.

  17. 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.

  18. 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.

  19. 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).

  20. Comparative analysis of nonlinear optofluidic processes in microdroplets.

    PubMed

    Zhang, Peng; Jung, Sunghwan; Lee, Aram; Xu, Yong

    2016-06-01

    Our prior work has shown that high quality (Q) factor whispering gallery modes (WGMs) in liquid microdroplets can potentially induce single-photon-level nonlinear effects through radiation pressure on the interface. However, little is known about the nonlinear effects of other processes involving scattering force and thermocapillarity. In this study, we establish a numerical framework that can calculate the fluid motion and the resultant nonlinearity induced by the optical scattering force and thermocapillarity. Then, we compare the magnitude of various nonlinear optofluidic processes induced by the radiation pressure, the thermocapillary effect, the scattering-induced optical force, and the Kerr effect. Using realistic fluid parameters, we show that the radiation pressure due to the WGM produces the strongest nonlinear optofluidic effect. PMID:27415370

  1. Unifying three perspectives on information processing in stochastic thermodynamics.

    PubMed

    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. PMID:24655235

  2. Energetics of Poisson-Kac Stochastic Processes Possessing Finite Propagation Velocity

    NASA Astrophysics Data System (ADS)

    Brasiello, Antonio; Giona, Massimiliano; Crescitelli, Silvestro

    2016-04-01

    A local fluctuation-dissipation theorem for the power delivered by a stochastic forcing is derived for Ornstein-Uhlenbeck processes driven by smooth, i. e. almost everywhere (a. e.)-differentiable stochastic perturbations (Poisson-Kac processes). An analytic expression for the probability density function of the fluctuational power is obtained in the large time limit. As these processes converge, in the Kac limit, toward classical Langevin equations driven by Wiener processes, a coarse-grained analysis of the statistical properties of the fluctuational work is developed.

  3. Analytical description of nonlinear particle transport in slab turbulence: High particle energies and stochastic acceleration

    SciTech Connect

    Shalchi, A.

    2012-10-15

    Pitch-angle scattering, parallel spatial diffusion, and stochastic acceleration of cosmic rays are investigated analytically. Based on a second-order quasilinear theory, we derive analytical expressions for the aforementioned transport parameters for all possible magnetic field strengths and particle energies. This work complements previous work where only parallel diffusion for low energetic particles was considered. Furthermore, we compute the first time the momentum diffusion coefficient. It is also shown that the relation between the momentum diffusion coefficient and the parallel spatial diffusion coefficient is more complicated than assumed in previous work.

  4. 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.

  5. Disentangling the importance of ecological niches from stochastic processes across scales.

    PubMed

    Chase, Jonathan M; Myers, Jonathan A

    2011-08-27

    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.

  6. 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. PMID:27336169

  7. 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

  8. 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.

  9. Nonlinear signal processing using neural networks: Prediction and system modelling

    SciTech Connect

    Lapedes, A.; Farber, R.

    1987-06-01

    The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

  10. 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

  11. 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. PMID:26270979

  12. Distinguishing between discreteness effects in stochastic reaction processes

    NASA Astrophysics Data System (ADS)

    Haruna, Taichi

    2015-05-01

    The effect of discreteness on stochastic dynamics of chemically reacting systems is studied analytically. We apply the scheme bridging the chemical master equation and the chemical Fokker-Planck equation by a parameter representing the degree of discreteness previously proposed by the author for two concrete systems. One is an autocatalytic reaction system, and the other is a branching-annihilation reaction system. It is revealed that the change in characteristic time scales when discreteness is decreased is yielded between the two systems for different reasons. In the former system, it originates from the boundaries where one of the chemical species is zero, whereas in the latter system, it is due to modification of the most probable extinction path caused by discreteness loss.

  13. Evidence that hematopoiesis may be a stochastic process in vivo.

    PubMed

    Abkowitz, J L; Catlin, S N; Guttorp, P

    1996-02-01

    To study the behavior of hematopoietic stem cells in vivo, hematopoiesis was simulated by assuming that all stem cell decisions (that is, replication, apoptosis, initiation of a differentiation/maturation program) were determined by chance. Predicted outcomes from simulated experiments were compared with data obtained in autologous marrow transplantation studies of glucose 6-phosphate dehydrogenase (G6PD) heterozygous female Safari cats. With this approach, we prove that stochastic differentiation can result in the wide spectrum of discrete outcomes observed in vivo, and that clonal dominance can occur by chance. As the analyses also suggest that the frequency of feline hematopoietic stem cells is only 6 per 10(7) nucleated marrow cells, and that sem cells do not replicate on average more frequently than once every three weeks, these large-animal data challenge clinical strategies for marrow transplantation and gene therapy.

  14. Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics.

    PubMed

    Chorin, Alexandre J; Lu, Fei

    2015-08-11

    Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper we consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori-Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system.

  15. Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics

    PubMed Central

    Chorin, Alexandre J.; Lu, Fei

    2015-01-01

    Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate solvable approximate equations for the variables of greater interest, and use data and statistical methods to account for the impact of the other variables. In the present paper we consider time-dependent problems and introduce a fully discrete solution method, which simplifies both the analysis of the data and the numerical algorithms. The resulting time series are identified by a NARMAX (nonlinear autoregression moving average with exogenous input) representation familiar from engineering practice. The connections with the Mori–Zwanzig formalism of statistical physics are discussed, as well as an application to the Lorenz 96 system. PMID:26216975

  16. 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.

  17. Nonlinear Flow Process: A New Package to Compute Nonlinear Flow in MODFLOW.

    PubMed

    Mayaud, Cyril; Walker, Patrica; Hergarten, Stefan; Birk, Steffen

    2015-01-01

    A new MODFLOW package (Nonlinear Flow Process; NLFP) simulating nonlinear flow following the Forchheimer equation was developed and implemented in MODLFOW-2005. The method is based on an iterative modification of the conductance calculated and used by MODFLOW to obtain an effective Forchheimer conductance. The package is compatible with the different layer types, boundary conditions, and solvers as well as the wetting capability of MODFLOW. The correct implementation is demonstrated using four different benchmark scenarios for which analytical solutions are available. A scenario considering transient flow in a more realistic setting and a larger model domain with a higher number of cells demonstrates that NLFP performs well under more complex conditions, although it converges moderately slower than the standard MODFLOW depending on the nonlinearity of flow. Thus, this new tool opens a field of opportunities to groundwater flow simulation with MODFLOW, especially for core sample simulation or vuggy karstified aquifers as well as for nonlinear flow in the vicinity of pumping wells.

  18. Stochastic resonance

    NASA Astrophysics Data System (ADS)

    Gammaitoni, Luca; Hänggi, Peter; Jung, Peter; Marchesoni, Fabio

    1998-01-01

    Over the last two decades, stochastic resonance has continuously attracted considerable attention. The term is given to a phenomenon that is manifest in nonlinear systems whereby generally feeble input information (such as a weak signal) can be be amplified and optimized by the assistance of noise. The effect requires three basic ingredients: (i) an energetic activation barrier or, more generally, a form of threshold; (ii) a weak coherent input (such as a periodic signal); (iii) a source of noise that is inherent in the system, or that adds to the coherent input. Given these features, the response of the system undergoes resonance-like behavior as a function of the noise level; hence the name stochastic resonance. The underlying mechanism is fairly simple and robust. As a consequence, stochastic resonance has been observed in a large variety of systems, including bistable ring lasers, semiconductor devices, chemical reactions, and mechanoreceptor cells in the tail fan of a crayfish. In this paper, the authors report, interpret, and extend much of the current understanding of the theory and physics of stochastic resonance. They introduce the readers to the basic features of stochastic resonance and its recent history. Definitions of the characteristic quantities that are important to quantify stochastic resonance, together with the most important tools necessary to actually compute those quantities, are presented. The essence of classical stochastic resonance theory is presented, and important applications of stochastic resonance in nonlinear optics, solid state devices, and neurophysiology are described and put into context with stochastic resonance theory. More elaborate and recent developments of stochastic resonance theory are discussed, ranging from fundamental quantum properties-being important at low temperatures-over spatiotemporal aspects in spatially distributed systems, to realizations in chaotic maps. In conclusion the authors summarize the achievements

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

    NASA Astrophysics Data System (ADS)

    Penland, C.

    2013-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

  1. 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.

  2. 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.

  3. A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

    NASA Astrophysics Data System (ADS)

    Pereyra, Marcelo; Schniter, Philip; Chouzenoux, Emilie; Pesquet, Jean-Christophe; Tourneret, Jean-Yves; Hero, Alfred O.; McLaughlin, Steve

    2016-03-01

    Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.

  4. 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.

  5. 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.

  6. 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

  7. Self-Sustaining Nonlinear Dynamo Process in Keplerian Shear Flows

    SciTech Connect

    Rincon, F.; Ogilvie, G. I.; Proctor, M. R. E.

    2007-06-22

    A three-dimensional nonlinear dynamo process is identified in rotating plane Couette flow in the Keplerian regime. It is analogous to the hydrodynamic self-sustaining process in nonrotating shear flows and relies on the magnetorotational instability of a toroidal magnetic field. Steady nonlinear solutions are computed numerically for a wide range of magnetic Reynolds numbers but are restricted to low Reynolds numbers. This process may be important to explain the sustenance of coherent fields and turbulent motions in Keplerian accretion disks, where all its basic ingredients are present.

  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. PMID:24893001

  9. Stationary response of nonlinear magneto-piezoelectric energy harvester systems under stochastic excitation

    NASA Astrophysics Data System (ADS)

    Martens, W.; von Wagner, U.; Litak, G.

    2013-09-01

    Recent years have shown increasing interest of researchers in energy harvesting systems designed to generate electrical energy from ambient energy sources, such as mechanical excitations. In a lot of cases excitation patterns of such systems exhibit random rather than deterministic behaviour with broad-band frequency spectra. In this paper, we study the efficiency of vibration energy harvesting systems with stochastic ambient excitations by solving corresponding Fokker-Planck equations. In the system under consideration, mechanical energy is transformed by a piezoelectric transducer in the presence of mechanical potential functions which are governed by magnetic fields applied to the device. Depending on the magnet positions and orientations the vibrating piezo beam system is subject to characteristic potential functions, including single and double well shapes. Considering random excitation, the probability density function (pdf) of the state variables can be calculated by solving the corresponding Fokker-Planck equation. For this purpose, the pdf is expanded into orthogonal polynomials specially adapted to the problem and the residual is minimized by a Galerkin procedure. The power output has been estimated as a function of basic potential function parameters determining the characteristic pdf shape.

  10. A kinetic theory for age-structured stochastic birth-death processes

    NASA Astrophysics Data System (ADS)

    Chou, Tom; Greenman, Chris

    Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.

  11. Patterns for the waiting time in the context of discrete-time stochastic processes

    NASA Astrophysics Data System (ADS)

    Jamali, Tayeb; Jafari, G. R.; Vasheghani Farahani, S.

    2016-09-01

    The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of the level-crossing method, problems with it correspond to the fact that this method had been developed for analyzing a continuous-time process or at most a multiple continuous-time process in an individual manner. However, since all empirical processes are discrete in time, the already-established level-crossing method may not prove adequate for studying empirical processes. Beyond this, due to the fact that most empirical processes are coupled; their individual study could lead to vague results. To achieve the objectives of this study, we first find an analytical expression for the average frequency of crossing a level in a discrete-time process, giving the measure of the time experienced for two consecutive crossings named as the "waiting time." We then introduce the generalized level-crossing method by which the consideration of coupling between the components of a multiple process becomes possible. Finally, we provide an analytic solution when the components of a multiple stochastic process are independent Gaussian white noises. The comparison of the results obtained for coupled and uncoupled processes measures the strength and efficiency of the coupling, justifying our model and analysis. The advantage of the proposed method is its sensitivity to the slightest coupling and shortest correlation length.

  12. Information transfer with rate-modulated Poisson processes: a simple model for nonstationary stochastic resonance.

    PubMed

    Goychuk, I

    2001-08-01

    Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.

  13. Information transfer with rate-modulated Poisson processes: A simple model for nonstationary stochastic resonance

    NASA Astrophysics Data System (ADS)

    Goychuk, Igor

    2001-08-01

    Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.

  14. 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. PMID:25740683

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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. PMID:26871029

  20. 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. PMID:27085426

  1. 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.

  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. Investigation of Nonlinear Whistler Wave Processes in the Laboratory

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

    Nonlinear interactions involving whistler wave turbulence can strongly effect the dynamics of the radiation belts. The building blocks of whistler wave turbulence are currently being studied in the NRL Space Physics Simulation Chamber (SPSC) under scaled magnetospheric conditions. These processes include parametric three-wave decay and a nonlinear wave-particle scattering off of thermal electrons that can substantially change the wave vector direction and energy flux. In the laboratory experiments, both of these processes have been observed and characterized. The results are consistent with theoretical predictions. Results from continuing laboratory experiments demonstrating triggered emissions and chorus-like emissions via nonlinear whistler wave-energetic particle interactions will be discussed. These chirped whistler waves are also observed to exhibit three-wave decay/coalescence and wave-particle scattering.

  4. Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

    PubMed Central

    2012-01-01

    Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with

  5. Nonlinear Optical Properties in Molecular Systems with Non-Zero Permanent Dipole Moments in Four-Wave Mixing Under Stochastic Considerations

    NASA Astrophysics Data System (ADS)

    Paz, J. L.; Mastrodomenico, A.; Cardenas-Garcia, Jaime F.; Rodriguez, Luis G.; Vera, Cesar Costa

    2016-07-01

    The solvent effects over nonlinear optical properties of a two-level molecular system in presence of a classical electromagnetic field were modeled in this work. The collective effects proper of the thermal reservoir are modeled as a random Bohr frequency, whose manifestation is the broadening of the upper level according to a prescribed random function. A technique of work, based in the use of the cumulant expansions to obtain the average in the Fourier components associated with the coherence and populations, evaluated by the use of the Optical Stochastic Bloch Equations (OSBE), is employed. Analytical expressions for susceptibility, optical properties and non-degenerate Four-Wave Mixing (nd-FWM) signal intensity, were obtained. Numerical calculations were carried out to construct surfaces corresponding to these magnitudes as a function of the pump-probe frequency detuning, values of the permanent dipole moments (PDM), noise parameters and relationships between the longitudinal and transversal relaxation times. Our results show that it is necessary to neglect the Rotating-Wave approximation (RWA) in order to measure the effect of the permanent dipole moments and that the inclusion of these favors two-photon transitions over those with one-photon. In general, the effect of non-zero permanent dipole moments, are reflected in the appearance of new and more complex signals associated with new multiphoton processes.

  6. 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. PMID:19256987

  7. Simple Additivity of Stochastic Psychological Processes: Tests and Measures.

    ERIC Educational Resources Information Center

    Balakrishnan, J. D.

    1994-01-01

    Methods of testing relatively complete (distributional) models of internal psychological processes are described. It is shown that there is a sufficient condition for additive models to imply this property of the likelihood ratio. Also discussed are the examination of hazard rate functions of component processes and change in cumulative…

  8. 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

  9. Recurrence plots of discrete-time Gaussian stochastic processes

    NASA Astrophysics Data System (ADS)

    Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick

    2016-09-01

    We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.

  10. Probabilistic tracking control for non-Gaussian stochastic process using novel iterative learning algorithms

    NASA Astrophysics Data System (ADS)

    Yi, Yang; Sun, ChangYin; Guo, Lei

    2013-07-01

    A new generalised iterative learning algorithm is presented for complex dynamic non-Gaussian stochastic processes. After designed neural networks are used to approximate the output probability density function (PDF) of the stochastic system in the repetitive processes or the batch processes, the complex probabilistic tracking control to the output PDF is simplified into a parameter tuning problem between two adjacent repetitive processes. Under this framework, this article studies a novel model free iterative learning control problem and proposes a convex optimisation algorithm based on a set of designed linear matrix inequalities and L 1 optimisation index. It is noted that such an algorithm can improve the tracking performance and robustness for the closed-loop PDF control. A simulated example is given, which effectively demonstrates the use of the proposed control algorithm.

  11. Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

    PubMed

    Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

    2007-12-01

    By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

  12. Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach

    NASA Astrophysics Data System (ADS)

    Rosso, O. A.; Zunino, L.; Pérez, D. G.; Figliola, A.; Larrondo, H. A.; Garavaglia, M.; Martín, M. T.; Plastino, A.

    2007-12-01

    By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

  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. 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.

  15. Photonic single nonlinear-delay dynamical node for information processing

    NASA Astrophysics Data System (ADS)

    Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

    2012-06-01

    An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

  16. 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.

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

    SciTech Connect

    Sonnino, Giorgio; Peeters, Philippe

    2008-06-15

    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-Schlueter (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 10{sup 2}. 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 10{sup 2} when the nonlinear contributions are duly taken into account but, there is still a factor of 10{sup 2} 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.

  18. 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}

  19. 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.

  20. Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

    NASA Astrophysics Data System (ADS)

    Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

    2013-04-01

    Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

  1. Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

    PubMed

    Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

    2013-04-01

    Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

  2. 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

  3. Sub-diffraction imaging on standard microscopes through photobleaching microscopy with non-linear processing.

    PubMed

    Munck, Sebastian; Miskiewicz, Katarzyna; Sannerud, Ragna; Menchon, Silvia A; Jose, Liya; Heintzmann, Rainer; Verstreken, Patrik; Annaert, Wim

    2012-05-01

    Visualization of organelles and molecules at nanometer resolution is revolutionizing the biological sciences. However, such technology is still limited for many cell biologists. We present here a novel approach using photobleaching microscopy with non-linear processing (PiMP) for sub-diffraction imaging. Bleaching of fluorophores both within the single-molecule regime and beyond allows visualization of stochastic representations of sub-populations of fluorophores by imaging the same region over time. Our method is based on enhancing the probable positions of the fluorophores underlying the images. The random nature of the bleached fluorophores is assessed by calculating the deviation of the local actual bleached fluorescence intensity to the average bleach expectation as given by the overall decay of intensity. Subtracting measured from estimated decay images yields differential images. Non-linear enhancement of maxima in these diffraction-limited differential images approximates the positions of the underlying structure. Summing many such processed differential images yields a super-resolution PiMP image. PiMP allows multi-color, three-dimensional sub-diffraction imaging of cells and tissues using common fluorophores and can be implemented on standard wide-field or confocal systems.

  4. Cycles, randomness, and transport from chaotic dynamics to stochastic processes.

    PubMed

    Gaspard, Pierre

    2015-09-01

    An overview of advances at the frontier between dynamical systems theory and nonequilibrium statistical mechanics is given. Sensitivity to initial conditions is a mechanism at the origin of dynamical randomness-alias temporal disorder-in deterministic dynamical systems. In spatially extended systems, sustaining transport processes, such as diffusion, relationships can be established between the characteristic quantities of dynamical chaos and the transport coefficients, bringing new insight into the second law of thermodynamics. With methods from dynamical systems theory, the microscopic time-reversal symmetry can be shown to be broken at the statistical level of description in nonequilibrium systems. In this way, the thermodynamic entropy production turns out to be related to temporal disorder and its time asymmetry away from equilibrium. PMID:26428559

  5. 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. PMID:26496618

  6. 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.

  7. 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).

  8. 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

  9. Stochastic flows, reaction — Diffusion processes, and morphogenesis

    NASA Astrophysics Data System (ADS)

    Kozak, John J.; Hatlee, Michael D.; Musho, Matthew K.; Politowicz, Philip A.; Walsh, Cecilia A.

    1983-02-01

    Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett. 47:1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processes in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d=2, 3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of "mixing" by showing that the degree of chaos associated with flows in certain lattice systems can be calibrated by monitoring the lattice walks induced by the Poincaré map of a certain parabolic function.

  10. 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.

  11. 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

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

    PubMed Central

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

    2015-01-01

    Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages—which provide a larger spatiotemporal scale relative to within stage analyses—revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended—and experimentally testable—conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems. PMID:25733885

  13. Efficient Nonlinear Programming Algorithms for Chemical Process Control and Operations

    NASA Astrophysics Data System (ADS)

    Biegler, Lorenz T.

    Optimization is applied in numerous areas of chemical engineering including the development of process models from experimental data, design of process flowsheets and equipment, planning and scheduling of chemical process operations, and the analysis of chemical processes under uncertainty and adverse conditions. These off-line tasks require the solution of nonlinear programs (NLPs) with detailed, large-scale process models. Recently, these tasks have been complemented by time-critical, on-line optimization problems with differential-algebraic equation (DAE) process models that describe process behavior over a wide range of operating conditions, and must be solved sufficiently quickly. This paper describes recent advances in this area especially with dynamic models. We outline large-scale NLP formulations and algorithms as well as NLP sensitivity for on-line applications, and illustrate these advances on a commercial-scale low density polyethylene (LDPE) process.

  14. Macroscopic fluxes and local reciprocal relation in second-order stochastic processes far from equilibrium

    NASA Astrophysics Data System (ADS)

    Ge, Hao

    2015-01-01

    A stochastic process is an essential tool for the investigation of the physical and life sciences at nanoscale. In the first-order stochastic processes widely used in chemistry and biology, only the flux of mass rather than that of heat can be well defined. Here we investigate the two macroscopic fluxes in second-order stochastic processes driven by position-dependent forces and temperature gradient. We prove that the thermodynamic equilibrium defined through the vanishing of macroscopic fluxes is equivalent to that defined via time reversibility at mesoscopic scale. In the small noise limit, we find that the entropy production rate, which has previously been defined by the mesoscopic irreversible fluxes on the phase space, matches the classic macroscopic expression as the sum of the products of macroscopic fluxes and their associated thermodynamic forces. Further we show that the two pairs of forces and fluxes in such a limit follow a linear phenomenonical relation and the associated scalar coefficients always satisfy the reciprocal relation for both transient and steady states. The scalar coefficient is proportional to the square of local temperature divided by the local frictional coefficient and originated from the second moment of velocity distribution along each dimension. This result suggests the very close connection between the Soret effect (thermal diffusion) and Dufour effect at nanoscale even far from equilibrium.

  15. 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.

  16. Nonlinear processes in multi-mode optical fibers

    NASA Astrophysics Data System (ADS)

    Pourbeyram Kaleibar, Hamed

    Nonlinear processes in optical fibers can affect data transmission and power carried by optical fibers and can limit the bandwidth and the capacity of optical communications. On the other hand nonlinear phenomena could be utilized to build in-fiber all-optical light sources and amplifiers. In this thesis new peaks inside an optical fiber have been generated using nonlinear processes. An intense green pump laser has been launched into a short fiber and specific modes have been excited to generate two new peaks in red and blue wavelengths, where two pump photons are annihilated to create two new photons in red and blue. The generated peaks are shifted far from pump; therefore they are less polluted by pump and Raman induced noises. The phase matching condition and the photon-flux rate for spontaneous and stimulated FWM have been studied both theoretically and experimentally for a commercial grade SMF-28 fiber. In low power and spontaneous regime new peaks are generated from quantum vacuum noise. Using the same pump laser for a long fiber, up to 21 new peaks spanning from green to Infrared have been generated. These peaks are equally spaced by 13THz. Generation of a Raman cascade spanning the wavelength range of 523 to 1750 nm wavelength range, in a standard telecommunication graded-index multimode optical fiber has been reported. Despite the highly multimode nature of the pump, the Raman peaks are generated in specific modes of the fiber, confirming substantial beam cleanup during the stimulated Raman scattering process.

  17. 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.

  18. 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. PMID:25571453

  19. 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

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. Vibronic coupling simulations for linear and nonlinear optical processes: Theory

    NASA Astrophysics Data System (ADS)

    Silverstein, Daniel W.; Jensen, Lasse

    2012-02-01

    A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.

  5. 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.

  6. 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

  7. Zero-one-only process: A correlated random walk with a stochastic ratchet

    NASA Astrophysics Data System (ADS)

    Baek, Seung Ki; Jeong, Hawoong; Son, Seung-Woo; Kim, Beom Jun

    2014-08-01

    The investigation of random walks is central to a variety of stochastic processes in physics, chemistry and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability p, and stops to change the direction with 1 - p. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

  8. Toward mission-specific service utility estimation using analytic stochastic process models

    NASA Astrophysics Data System (ADS)

    Thornley, David J.; Young, Robert J.; Richardson, James P.

    2009-05-01

    Planning a mission to monitor, control or prevent activity requires postulation of subject behaviours, specification of goals, and the identification of suitable effects, candidate methods, information requirements, and effective infrastructure. In an operation that comprises many missions, it is desirable to base decisions to assign assets and computation time or communications bandwidth on the value of the result of doing so in a particular mission to the operation. We describe initial investigations of a holistic approach for judging the value of candidate sensing service designs by stochastic modeling of information delivery, knowledge building, synthesis of situational awareness, and the selection of actions and achievement of goals. Abstraction of physical and information transformations to interdependent stochastic state transition models enables calculation of probability distributions over uncertain futures using wellcharacterized approximations. This complements traditional Monte Carlo war gaming in which example futures are explored individually, by capturing probability distributions over loci of behaviours that show the importance and value of mission component designs. The overall model is driven by sensing processes that are constructed by abstracting from the physics of sensing to a stochastic model of the system's trajectories through sensing modes. This is formulated by analysing probabilistic projections of subject behaviours against functions which describe the quality of information delivered by the sensing service. This enables energy consumption predictions, and when composed into a mission model, supports calculation of situational awareness formulation and command satisfaction timing probabilities. These outcome probabilities then support calculation of relative utility and value.

  9. Dynamics of coastal cod populations: intra- and intercohort density dependence and stochastic processes

    PubMed Central

    Stenseth, N. C.; rnstad, O. N. Bj; Falck, W.; Fromentin, J.-M.; ter, J. Gj s; Gray, J. S.

    1999-01-01

    Skagerrak populations of Atlantic cod (Gadus morhua L.) have been surveyed at several fixed stations since 1919. These coastal populations consist of local stocks with a low age of maturity and a short life span. We investigated 60 time-series of 0-group juveniles (i.e. young of the year) sampled annually from 1945 to 1994. An age-structured model was developed which incorporates asymmetrical interactions between the juvenile cohorts (0-group and 1-group; i.e. one-year-old juveniles) and stochastic reproduction. The model was expressed in delay coordinates in order to estimate model parameters directly from the time-series and thereby test the model predictions. The autocovariance structure of the time-series was consistent with the delay coordinates model superimposed upon a long-term trend. The model illustrates how both regulatory (density-dependent) and disruptive (stochastic) forces are crucial in shaping the dynamics of the coastal cod populations. The age-structured life cycle acts to resonance the stochasticity inherent in the recruitment process.

  10. 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

  11. 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.

  12. Nonlinear behaviour of power ultrasonic transducers for food processing

    NASA Astrophysics Data System (ADS)

    Riera, E.; Cardoni, A.; Acosta, V. M.; Gallego-Juárez, J. A.

    2012-05-01

    Power ultrasonic systems at laboratory and semi-industrial scale are currently investigated to demonstrate the suitability of ultrasonic waves of high-intensity to industrial applications. It has been shown that intense ultrasonic fields trigger a series of mechanisms in the irradiated media that may enhance and/or accelerate a variety of processes in the food sector. Ultrasonic radiators driven by piezoelectric vibrators have been specifically developed for assisting in drying and extraction operations. Successful industrial scale-up of such tuned systems significantly depends on the control of their nonlinear vibration behaviour at high operational power levels. In this paper we investigated experimentally the nonlinear dynamics of two power ultrasonic transducers: a grooved-plate transducer and a cylindrical radiator transducer. Nonlinear mechanisms affecting the dynamic behaviour of both assemblies such as the appearance of harmonics, combination of resonances, or modal interactions, and response saturation are presented. In particular, energy transfers among system modes that may produce the excitation of nontuned resonant frequencies causing heating, noise and even failures of the transducers are identified and characterised.

  13. 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

  14. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

    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.

  16. Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

    PubMed

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

    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.

  17. 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

  18. Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

    NASA Astrophysics Data System (ADS)

    Katori, Makoto; Tanemura, Hideki

    2004-08-01

    As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of Hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous noncolliding systems of the Bessel processes and a two-parameter family of temporally inhomogeneous noncolliding systems of Yor's generalized meanders and show that all of the ten classes of eigenvalue statistics in the Altland-Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems. As a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process, a stochastic-calculus proof of a version of the Harish-Chandra (Itzykson-Zuber) formula of integral over unitary group is established.

  19. 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.

  20. Nonlinear processes reinforce extreme Indian Ocean Dipole events

    PubMed Central

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

    2015-01-01

    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. PMID:26114441

  1. 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.

  2. Relaxation rate of a stochastic spreading process in a closed ring

    NASA Astrophysics Data System (ADS)

    Hurowitz, Daniel; Cohen, Doron

    2016-06-01

    The relaxation process of a diffusive ring becomes underdamped if the bias (so-called affinity) exceeds a critical threshold value, also known as the delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak link into the circuit and illuminate some subtleties that arise while taking the continuum limit of the discrete model.

  3. Capturing exponential variance using polynomial resources: applying tensor networks to nonequilibrium stochastic processes.

    PubMed

    Johnson, T H; Elliott, T J; Clark, S R; Jaksch, D

    2015-03-01

    Estimating the expected value of an observable appearing in a nonequilibrium stochastic process usually involves sampling. If the observable's variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high-variance observable e^{-βW}, motivated by Jarzynski's equality, with W the work done quenching from equilibrium at inverse temperature β, is exactly and efficiently captured by tensor networks.

  4. 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.

  5. On the Wiener-Masani algorithm for finding the generating function of multivariate stochastic processes

    NASA Technical Reports Server (NTRS)

    Miamee, A. G.

    1988-01-01

    The algorithms developed by Wiener and Masani (1957 and 1958) and Masani (1960) for the characterization of a class of multivariate stationary stochastic processes are investigated analytically. The algorithms permit the determination of (1) the generating function, (2) the prediction-error matrix, and (3) an autoregressive representation of the linear least-squares predictor. A number of theorems and lemmas are proved, and it is shown that the range of validity of the algorithms can be extended significantly beyond that given by Wiener and Masani.

  6. 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.

  7. Nonlinear Optical Microscopy Signal Processing Strategies in Cancer

    PubMed Central

    Adur, Javier; Carvalho, Hernandes F; Cesar, Carlos L; Casco, Víctor H

    2014-01-01

    This work reviews the most relevant present-day processing methods used to improve the accuracy of multimodal nonlinear images in the detection of epithelial cancer and the supporting stroma. Special emphasis has been placed on methods of non linear optical (NLO) microscopy image processing such as: second harmonic to autofluorescence ageing index of dermis (SAAID), tumor-associated collagen signatures (TACS), fast Fourier transform (FFT) analysis, and gray level co-occurrence matrix (GLCM)-based methods. These strategies are presented as a set of potential valuable diagnostic tools for early cancer detection. It may be proposed that the combination of NLO microscopy and informatics based image analysis approaches described in this review (all carried out on free software) may represent a powerful tool to investigate collagen organization and remodeling of extracellular matrix in carcinogenesis processes. PMID:24737930

  8. 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.

  9. StochPy: A Comprehensive, User-Friendly Tool for Simulating Stochastic Biological Processes

    PubMed Central

    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. PMID:24260203

  10. 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.

  11. 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

  12. Nonlinear identification of process dynamics using neural networks

    SciTech Connect

    Parlos, A.G.; Atiya, A.F.; Chong, K.T. . Dept. of Nuclear Engineering); Tsai, W.K. )

    1992-01-01

    In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios.

  13. Final Technical Report - Stochastic Nonlinear Data-Reduction Methods with Detection and Prediction of Critical Rare Event

    SciTech Connect

    Karniadakis, George Em; Vanden-Eijnden, Eric; Lin, Guang; Wan, Xiaoliang

    2013-04-03

    In this project, the collective efforts of all co-PIs aim to address three current limitations in modeling stochastic systems: (1) the inputs are mostly based on ad hoc models, (2) the number of independent parameters is very high, and (3) rare and critical events are difficult to capture with existing algorithms

  14. 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.

  15. 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.

  16. 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

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

    NASA Astrophysics Data System (ADS)

    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.

  18. Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.

    PubMed

    Zhang, Tingting; Kou, S C

    2010-01-01

    Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

  19. 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.

  20. New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

    SciTech Connect

    Venturi, D.; Karniadakis, G.E.

    2012-08-30

    By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.

  1. 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.

  2. Multivariate moment closure techniques for stochastic kinetic models

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    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.

  3. Recovering a stochastic process from super-resolution noisy ensembles of single-particle trajectories.

    PubMed

    Hoze, N; Holcman, D

    2015-11-01

    Recovering a stochastic process from noisy ensembles of single-particle trajectories is resolved here using the coarse-grained Langevin equation as a model. The massive redundancy contained in single-particle tracking data allows recovering local parameters of the underlying physical model. We use several parametric and nonparametric estimators to compute the first and second moments of the process, to recover the local drift, its derivative, and the diffusion tensor, and to deconvolve the instrumental from the physical noise. We use numerical simulations to also explore the range of validity for these estimators. The present analysis allows defining what can exactly be recovered from statistics of super-resolution microscopy trajectories used for characterizing molecular trafficking underlying cellular functions.

  4. Employment of the covariance matrix in parameter estimation for stochastic processes in cell biology

    NASA Astrophysics Data System (ADS)

    Preuss, R.; Dieterich, P.

    2013-08-01

    The dynamics of movements of biological cells can be described with models from correlated stochastic processes. In order to overcome problems from correlated and insufficient data in the determination of the model parameters of such processes we employ the covariance matrix of the data. Since the covariance suffers itself from statistical uncertainty it is corrected by a renormalization treatment [1]. For the example of normal and fractional Brownian motion, which allows both to access all quantities on full theoretical grounds and to generate data similar to experiment, we discuss our results and those of previous works by Gregory [2] and Sivia [3]. The presented approach has the potential to estimate the aging correlation function of observed cell paths and can be applied to more complicated models.

  5. Line-edge roughness and the impact of stochastic processes on lithography scaling for Moore's Law

    NASA Astrophysics Data System (ADS)

    Mack, Chris A.

    2014-09-01

    Moore's Law, the idea that every two years or so chips double in complexity and the cost of a transistor is always in decline, has been the foundation of the semiconductor industry for nearly 50 years. The main technical force behind Moore's Law has been lithography scaling: shrinking of lithographic features at a rate faster than the increase in finished wafer costs. With smaller feature size comes the need for better control of those sizes during manufacturing. Critical dimension and overlay control must scale in proportion to feature size, and has done so for the last 50 years. But in the sub-50-nm feature size regime, a new problem has arisen: line-edge roughness due to the stochastic nature of the lithography process. Despite significant effort, this line-edge roughness has not scaled in proportion to feature size and is thus consuming an ever larger fraction of the feature size control budget. Projection of current trends predicts a collision course between lithography scaling needs and line-edge roughness reality. In the end, stochastic uncertainty in lithography and its manifestation as line-edge roughness will prove the ultimate limiter of resolution in semiconductor manufacturing.

  6. Nonlinear ecological processes driving the distribution of marine decapod larvae

    NASA Astrophysics Data System (ADS)

    Peña, M.; Carbonell, A.; Tor, A.; Alvarez-Berastegui, D.; Balbín, R.; dos Santos, A.; Alemany, F.

    2015-03-01

    The complexity of the natural processes lead to many nonlinear interacting factors that influence the distribution and survival of marine pelagic species, particularly in their larval phase. The management of these ecosystems requires techniques that unveil those interactions by studying the system globally, including all relevant variables and combining both community and environmental data in a single step. Specifically, we apply an unsupervised neural network, the Self-Organising Map (SOM), to a combined dataset of environmental and decapod larvae community data from the Balearic sea, obtained in two years with contrasting environmental scenarios, as an Exploratory Data Analysis (EDA) technique that provides a global and more detailed view of both the environmental processes and their influence on the distribution of such planktonic community. We examine the parental influence on the initial larval distribution by aggregating data by adult habitat, which also increments the signal to noise ratio (mean data patterns over noise due to outliers or measurement errors), and consider the distribution of larvae by development stage (as a proxy of age and hence of potential dispersion). The joined study of parental effect, drifting or concentration events determined by dynamical processes in the whole water column, and lifespan, draws the possible paths followed by larvae, and highlights the more influencing variables in their distribution. Investigation of the different aspects of dynamic height (absolute values, gradients or edges and correlations) clarified the effect of the oceanographic processes on decapods' larvae.

  7. 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.

  8. 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.

  9. Non-linear processes in the Earth atmosphere boundary layer

    NASA Astrophysics Data System (ADS)

    Grunskaya, Lubov; Valery, Isakevich; Dmitry, Rubay

    2013-04-01

    The work is connected with studying electromagnetic fields in the resonator Earth-Ionosphere. There is studied the interconnection of tide processes of geophysical and astrophysical origin with the Earth electromagnetic fields. On account of non-linear property of the resonator Earth-Ionosphere the tides (moon and astrophysical tides) in the electromagnetic Earth fields are kinds of polyharmonic nature. It is impossible to detect such non-linear processes with the help of the classical spectral analysis. Therefore to extract tide processes in the electromagnetic fields, the method of covariance matrix eigen vectors is used. Experimental investigations of electromagnetic fields in the atmosphere boundary layer are done at the distance spaced stations, situated on Vladimir State University test ground, at Main Geophysical Observatory (St. Petersburg), on Kamchatka pen., on Lake Baikal. In 2012 there was continued to operate the multichannel synchronic monitoring system of electrical and geomagnetic fields at the spaced apart stations: VSU physical experimental proving ground; the station of the Institute of Solar and Terrestrial Physics of Russian Academy of Science (RAS) at Lake Baikal; the station of the Institute of volcanology and seismology of RAS in Paratunka; the station in Obninsk on the base of the scientific and production society "Typhoon". Such investigations turned out to be possible after developing the method of scanning experimental signal of electromagnetic field into non- correlated components. There was used a method of the analysis of the eigen vectors ofthe time series covariance matrix for exposing influence of the moon tides on Ez. The method allows to distribute an experimental signal into non-correlated periodicities. The present method is effective just in the situation when energetical deposit because of possible influence of moon tides upon the electromagnetic fields is little. There have been developed and realized in program components

  10. Nonlinear computations shaping temporal processing of precortical vision.

    PubMed

    Butts, Daniel A; Cui, Yuwei; Casti, Alexander R R

    2016-09-01

    Computations performed by the visual pathway are constructed by neural circuits distributed over multiple stages of processing, and thus it is challenging to determine how different stages contribute on the basis of recordings from single areas. In the current article, we address this problem in the lateral geniculate nucleus (LGN), using experiments combined with nonlinear modeling capable of isolating various circuit contributions. We recorded cat LGN neurons presented with temporally modulated spots of various sizes, which drove temporally precise LGN responses. We utilized simultaneously recorded S-potentials, corresponding to the primary retinal ganglion cell (RGC) input to each LGN cell, to distinguish the computations underlying temporal precision in the retina from those in the LGN. Nonlinear models with excitatory and delayed suppressive terms were sufficient to explain temporal precision in the LGN, and we found that models of the S-potentials were nearly identical, although with a lower threshold. To determine whether additional influences shaped the response at the level of the LGN, we extended this model to use the S-potential input in combination with stimulus-driven terms to predict the LGN response. We found that the S-potential input "explained away" the major excitatory and delayed suppressive terms responsible for temporal patterning of LGN spike trains but revealed additional contributions, largely PULL suppression, to the LGN response. Using this novel combination of recordings and modeling, we were thus able to dissect multiple circuit contributions to LGN temporal responses across retina and LGN, and set the foundation for targeted study of each stage. PMID:27334959

  11. 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.

  12. Stochastic dynamical model of a growing citation network based on a self-exciting point process.

    PubMed

    Golosovsky, Michael; Solomon, Sorin

    2012-08-31

    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. PMID:23002894

  13. Stochastic modeling of stock price process induced from the conjugate heat equation

    NASA Astrophysics Data System (ADS)

    Paeng, Seong-Hun

    2015-02-01

    Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

  14. Getting a stochastic process from a conservative Lagrangian: A first approach

    NASA Astrophysics Data System (ADS)

    Ramírez, J. E.; Herrera, J. N.; Martínez, M. I.

    2016-04-01

    The transition probability PV for a stochastic process generated by a conservative Lagrangian L =L0 - εV is obtained at first order from a perturbation series found using a path integral. This PV corresponds to the transition probability for a random walk with a probability density given by the sum of a normal distribution and a perturbation which may be understood as the contribution of the interaction of the random walk with the external field. It is also found that the moment-generating function for PV can be expressed as the generating function of a normal distribution modified by a perturbation. Applications of these results to a linear potential, a harmonic oscillator potential, and an exponentially decaying potential are shown.

  15. 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.

  16. 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.

  17. 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.

  18. Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA

    PubMed Central

    2012-01-01

    Background Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Method Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. Results A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. Conclusions ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of

  19. 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.

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

    PubMed

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

    2016-01-01

    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

  1. 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.

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

    PubMed

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

    2016-06-27

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

  3. 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

  4. 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.

  5. 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.

  6. Constructing the davies process of resonance fluorescence with quantum stochastic calculus

    NASA Astrophysics Data System (ADS)

    Bouten, L.; Maassen, H.; Kümmerer, B.

    2003-06-01

    The starting point is a given semigroup of completely positive maps on the 2×2 matrices. This semigroup describes the irreversible evolution of a decaying two-level atom. By using the integral-sum kernel approach to quantum stochastic calculus, the two-level atom is coupled to an environment, which in this case will be interpreted as the electromagnetic field. The irreversible time evolution of the two-level atom then stems from the reversible time evolution of the atom and the field together. Mathematically speaking, a Markov dilation of the semigroup has been constructed. The next step is to drive the atom by a laser and to count the photons emitted into the field by the decaying two-level atom. For every possible sequence of photon counts, a map is constructed that gives the time evolution of the two-level atom implied by that sequence. The family of maps obtained in this way forms a so-called Davies process. In his book, Davies describes the structure of these processes, which brings us into the field of quantum trajectories. Within the model presented in this paper, the jump operators are calculated and the resulting counting process is briefly described.

  7. 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. PMID:25019731

  8. 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.

  9. Large deviation probabilities for correlated Gaussian stochastic processes and daily temperature anomalies

    NASA Astrophysics Data System (ADS)

    Massah, Mozhdeh; Kantz, Holger

    2016-04-01

    As we have one and only one earth and no replicas, climate characteristics are usually computed as time averages from a single time series. For understanding climate variability, it is essential to understand how close a single time average will typically be to an ensemble average. To answer this question, we study large deviation probabilities (LDP) of stochastic processes and characterize them by their dependence on the time window. In contrast to iid variables for which there exists an analytical expression for the rate function, the correlated variables such as auto-regressive (short memory) and auto-regressive fractionally integrated moving average (long memory) processes, have not an analytical LDP. We study LDP for these processes, in order to see how correlation affects this probability in comparison to iid data. Although short range correlations lead to a simple correction of sample size, long range correlations lead to a sub-exponential decay of LDP and hence to a very slow convergence of time averages. This effect is demonstrated for a 120 year long time series of daily temperature anomalies measured in Potsdam (Germany).

  10. A stochastic model for estimation of mutation rates in multiple-replication proliferation processes.

    PubMed

    Xiong, Xiaoping; Boyett, James M; Webster, Robert G; Stech, Juergen

    2009-08-01

    In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge. PMID:18846374

  11. 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.

  12. Linear processes in stochastic population dynamics: theory and application to insect development.

    PubMed

    Solari, Hernán G; Natiello, Mario A

    2014-01-01

    We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.

  13. 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.

  14. Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development

    PubMed Central

    Solari, Hernán G.; Natiello, Mario A.

    2014-01-01

    We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time. PMID:24696664

  15. Two studies of nonlinear processes in irreversible thermodynamics

    SciTech Connect

    Kestin, J.

    1992-01-01

    The investigation dealt with two lines of research into two well-defined problems of engineering science: a study of two-phase flow and of nonelastic deformations in structural solids. Both topics fall into the broad field of nonlinear irreversible processes. The study of two-phase flow resulted in a complete topological analysis of the canonical mathematical model of one-dimensional flow of a mixture of two phases, now predominantly used in industry, especially the nuclear industry. The topological analysis is confronted with the practice of discretizing the analytic model for the purpose of formulating a numerical computer code. It is shown that in the presence of singular points in the phase space of the differential equations of the model there occur spurious numerical solutions. Such solutions may contain segments which are correct approximations to the exact trajectory, but always include branches which are totally false and misleading. The topological method allows the operator to formulate a subroutine which eliminates spurious solutions. The study of inelastic deformations, i.e., of irreversible processes in structural solids provided a consistent presentation of the local-state approximation erroneously called the method of local equilibrium in the literature. The key concept which impedes the correct use of thermodynamics in this field is the definition of a measurable entropy of a nonequilibrium state. The local state approximation solves this problem by assigning to a nonequilibrium state n the entropy of the accompanying equilibrium state e. The two states, n and e, are linked by having the same values of a specified set of extensive properties. The same principle settles the comparison between the intensive properties of n and e, which are different.

  16. Application of Novel Nonlinear Optical Materials to Optical Processing

    NASA Technical Reports Server (NTRS)

    Banerjee, Partha P.

    1999-01-01

    We describe wave mixing and interactions in nonlinear photorefractive polymers and disodium flourescein. Higher diffracted orders yielding forward phase conjugation can be generated in a two-wave mixing geometry in photorefractive polymers, and this higher order can be used for image edge enhancement and correlation. Four-wave mixing and phase conjugation is studied using nonlinear disodium floureschein, and the nature and properties of gratings written in this material are investigated.

  17. Approximate Controllability of Second-Order Stochastic Differential Equations with Impulsive Effects

    NASA Astrophysics Data System (ADS)

    Sakthivel, Rathinasamy; Ren, Yong; Mahmudov, N. I.

    Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

  18. Stochastic Processes Are Key Determinants of Short-Term Evolution in Influenza A Virus

    PubMed Central

    Nelson, Martha I; Simonsen, Lone; Viboud, Cecile; Miller, Mark A; Taylor, Jill; George, Kirsten St; Griesemer, Sara B; Ghedin, Elodie; Sengamalay, Naomi A; Spiro, David J; Volkov, Igor; Grenfell, Bryan T; Lipman, David J; Taubenberger, Jeffery K; Holmes, Edward C

    2006-01-01

    Understanding the evolutionary dynamics of influenza A virus is central to its surveillance and control. While immune-driven antigenic drift is a key determinant of viral evolution across epidemic seasons, the evolutionary processes shaping influenza virus diversity within seasons are less clear. Here we show with a phylogenetic analysis of 413 complete genomes of human H3N2 influenza A viruses collected between 1997 and 2005 from New York State, United States, that genetic diversity is both abundant and largely generated through the seasonal importation of multiple divergent clades of the same subtype. These clades cocirculated within New York State, allowing frequent reassortment and generating genome-wide diversity. However, relatively low levels of positive selection and genetic diversity were observed at amino acid sites considered important in antigenic drift. These results indicate that adaptive evolution occurs only sporadically in influenza A virus; rather, the stochastic processes of viral migration and clade reassortment play a vital role in shaping short-term evolutionary dynamics. Thus, predicting future patterns of influenza virus evolution for vaccine strain selection is inherently complex and requires intensive surveillance, whole-genome sequencing, and phenotypic analysis. PMID:17140286

  19. Kinetic competition during the transcription cycle results in stochastic RNA processing.

    PubMed

    Coulon, Antoine; Ferguson, Matthew L; de Turris, Valeria; Palangat, Murali; Chow, Carson C; Larson, Daniel R

    2014-01-01

    Synthesis of mRNA in eukaryotes involves the coordinated action of many enzymatic processes, including initiation, elongation, splicing, and cleavage. Kinetic competition between these processes has been proposed to determine RNA fate, yet such coupling has never been observed in vivo on single transcripts. In this study, we use dual-color single-molecule RNA imaging in living human cells to construct a complete kinetic profile of transcription and splicing of the β-globin gene. We find that kinetic competition results in multiple competing pathways for pre-mRNA splicing. Splicing of the terminal intron occurs stochastically both before and after transcript release, indicating there is not a strict quality control checkpoint. The majority of pre-mRNAs are spliced after release, while diffusing away from the site of transcription. A single missense point mutation (S34F) in the essential splicing factor U2AF1 which occurs in human cancers perturbs this kinetic balance and defers splicing to occur entirely post-release. PMID:25271374

  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. 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

  2. Detecting nonlinear oscillations in broadband signals

    NASA Astrophysics Data System (ADS)

    Vejmelka, Martin; Paluš, Milan

    2009-03-01

    A framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modeled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, it can be further analyzed using nonlinear approaches such as phase synchronization analysis. For linear processes standard approaches, such as the coherence analysis, are more appropriate. The method is illustrated in a numerical example and applied to analyze experimentally obtained human electroencephalogram time series from a sleeping subject.

  3. 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.

  4. 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.

  5. 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.

  6. Nonlinear acoustic/seismic waves in earthquake processes

    NASA Astrophysics Data System (ADS)

    Johnson, Paul A.

    2012-09-01

    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.

  7. 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.

  8. Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy

    PubMed Central

    Wise, Frank W.

    2012-01-01

    Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging. PMID:23869163

  9. Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy.

    PubMed

    Wise, Frank W

    2012-01-01

    Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging.

  10. 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.

  11. 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.

  12. 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}.

  13. 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.

  14. Long memory and scaling for multiplicative stochastic processes with application to the study of population oscillations

    NASA Astrophysics Data System (ADS)

    Vlad, Marcel Ovidiu; Lacoursière, Claude; Mackey, Michael C.

    1995-02-01

    An analytically tractable multiplicative random process is introduced based on an analogy between the random phase modulation, wave propagation in a random medium and the population growth in a fluctuating environment. It is assumed that the process depends on a multiplicative random parameter which can be eliminated by introducing an intrinsic time scale; the relation between the intrinsic and the physical (watch) time scales is determined by the stochastic properties of the random parameter. The multitime joint probability densities of the state variables expressed in terms of the physical time can be computed in a closed form in terms of the corresponding joint probability densities expressed in the intrinsic time scale. The theory is applied to the study of age-dependent population oscillations in a random environment. In this case the intrinsic time scale is a biological time which is the same for any physical realization of the random environment. The random fluctuations of the environment lead to a decrease of the intrinsic rate of population growth and generate a temporal analogue of Anderson localization: due to fluctuations the population oscillations are damped. The asymptotic behavior of the process depends on the range of the memory effects of the environmental fluctuations: for short memory the qualitative asymptotic behavior of the population size for large time is the same for a fluctuating as well as for a constant environment; for slowly decaying correlations, however, the exponential increase of the population is outweighed by a compressed exponential decay due to environmental fluctuations and the population eventually becomes extinct.

  15. 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…

  16. 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

  17. 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.

  18. Filamentation processes and dynamical excitation of light condensates in optical media with competing nonlinearities

    SciTech Connect

    Novoa, David; Michinel, Humberto; Tommasini, Daniele; Carpentier, Alicia V.

    2010-04-15

    We analyze both theoretically and by means of numerical simulations the phenomena of filamentation and dynamical formation of self-guided nonlinear waves in media featuring competing cubic and quintic nonlinearities. We provide a theoretical description of recent experiments in terms of a linear stability analysis supported with simulations, showing the possibility of the observation of modulational instability suppression of intense light pulses traveling across such nonlinear media. We also show a mechanism of indirect excitation of light condensates by means of coalescence processes of nonlinear coherent structures produced by managed filamentation of high-power laser beams.

  19. 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.

  20. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

    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.

  3. 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.

  4. The mechanism for stochastic resonance enhancement of mammalian auditory information processing

    PubMed Central

    Hong, Dawei; Martin, Joseph V; Saidel, William M

    2006-01-01

    Background In a mammalian auditory system, when intrinsic noise is added to a subthreshold signal, not only can the resulting noisy signal be detected, but also the information carried by the signal can be completely recovered. Such a phenomenon is called stochastic resonance (SR). Current analysis of SR commonly employs the energies of the subthreshold signal and intrinsic noise. However, it is difficult to explain SR when the energy addition of the signal and noise is not enough to lift the subthreshold signal over the threshold. Therefore, information modulation has been hypothesized to play a role in some forms of SR in sensory systems. Information modulation, however, seems an unlikely mechanism for mammalian audition, since it requires significant a priori knowledge of the characteristics of the signal. Results We propose that the analysis of SR cannot rely solely on the energies of a subthreshold signal and intrinsic noise or on information modulation. We note that a mammalian auditory system expends energy in the processing of a noisy signal. A part of the expended energy may therefore deposit into the recovered signal, lifting it over threshold. We propose a model that in a rigorous mathematical manner expresses this new theoretical viewpoint on SR in the mammalian auditory system and provide a physiological rationale for the model. Conclusion Our result indicates that the mammalian auditory system may be more active than previously described in the literature. As previously recognized, when intrinsic noise is used to generate a noisy signal, the energy carried by the noise is added to the original subthreshold signal. Furthermore, our model predicts that the system itself should deposit additional energy into the recovered signal. The additional energy is used in the processing of the noisy signal to recover the original subthreshold signal. PMID:17140437

  5. 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

  6. 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.

  7. 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

  8. 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. PMID:18255068

  9. Nonlinear Information Processing in a Model Sensory System

    PubMed Central

    Chacron, Maurice J.

    2016-01-01

    Understanding the mechanisms by which sensory neurons encode and decode information remains an important goal in neuroscience. We quantified the performance of optimal linear and nonlinear encoding models in a well-characterized sensory system: the electric sense of weakly electric fish. We show that linear encoding models generally perform better under spatially localized stimulation than under spatially diffuse stimulation. Through pharmacological blockade of feedback input and spatial saturation of the receptive field center, we show that there is significantly less synaptic noise under spatially diffuse stimuli as compared with spatially localized stimuli. Modeling results suggest that pyramidal cells nonlinearly encode sensory information through shunting in their dendrites and clarify the influence of synaptic noise on the performance of linear encoding models. Finally, we used information theory to quantify the performance of linear decoders. While the optimal linear decoder for spatially localized stimuli could capture 60% of the information in pyramidal cell spike trains, the optimal linear decoder for spatially diffuse stimuli could only capture 40% of the information. These results show that nonlinear decoders are necessary to fully access information in pyramidal cell spike trains, and we discuss potential mechanisms by which higher-order neurons could decode this information. PMID:16495358

  10. 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.

  11. An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

    NASA Technical Reports Server (NTRS)

    Parrish, R. S.; Carter, M. C.

    1974-01-01

    This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

  12. Dynamics of a Qubit as a Classical Stochastic Process with Time-Correlated Noise: Minimal Measurement Invasiveness

    NASA Astrophysics Data System (ADS)

    Montina, Alberto

    2012-04-01

    So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this Letter, we present a stochastic model with time-correlated noise that exactly reproduces any unitary evolution of a qubit and requires just four classical states. The invasive updating of only 1 bit during a measurement accounts for the quantum violation of the Leggett-Garg inequalities. Unlike in a pilot-wave theory, the stochastic forces governing the jumps among the four states do not depend on the quantum state but only on the unitary evolution. This model is used to derive a local hidden variable model, augmented by 1 bit of classical communication, for simulating entangled Bell states.

  13. Trickle or clumped infection process? A stochastic model for the infection process of the parasitic roundworm of humans, Ascaris lumbricoides.

    PubMed

    Walker, Martin; Hall, Andrew; Basáñez, María-Gloria

    2010-10-01

    The importance of the mode of acquisition of infectious stages of directly-transmitted parasitic helminths has been acknowledged in population dynamics models; hosts may acquire eggs/larvae singly in a "trickle" type manner or in "clumps". Such models have shown that the mode of acquisition influences the distribution and dynamics of parasite loads, the stability of host-parasite systems and the rate of emergence of anthelmintic resistance, yet very few field studies have allowed these questions to be explored with empirical data. We have analysed individual worm weight data for the parasitic roundworm of humans, Ascaris lumbricoides, collected from a three-round chemo-expulsion study in Dhaka, Bangladesh, with the aim of discerning whether a trickle or a clumped infection process predominates. We found that hosts tend to harbour female worms of a similar weight, indicative of a clumped infection process, but acknowledged that unmeasured host heterogeneities (random effects) could not be completely excluded as a cause. Here, we complement our previous statistical analyses using a stochastic infection model to simulate sizes of individual A. lumbricoides infecting a population of humans. We use the intraclass correlation coefficient (ICC) as a quantitative measure of similarity among simulated worm sizes and explore the behaviour of this statistic under assumptions corresponding to trickle or clumped infections and unmeasured host heterogeneities. We confirm that both mechanisms are capable of generating aggregates of similar-sized worms, but that the particular pattern of ICCs described pre- and post-anthelmintic treatment in the data is more consistent with aggregation generated by clumped infections than by host heterogeneities alone. This provides support to the notion that worms may be acquired in clumps. We discuss our results in terms of the population biology of A. lumbricoides and highlight the significance of our modelling approach for the study of the

  14. Nonlinear dynamics of global atmospheric and earth system processes

    NASA Technical Reports Server (NTRS)

    Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu

    1995-01-01

    During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

  15. Nonlinear processing of radar data for landmine detection

    NASA Astrophysics Data System (ADS)

    Bartosz, Elizabeth E.; DeJong, Keith; Duvoisin, Herbert A.; Solomon, Geoff Z.; Steinway, William J.; Warren, Albert

    2004-09-01

    Outstanding landmine detection has been achieved by the Handheld Standoff Mine Detection System (HSTAMIDS system) in government-run field tests. The use of anomaly detection using principal component analysis (PCA) on the return of ground penetrating radar (GPR) coupled with metal detection is the key to the success of the HSTAMIDS-like system algorithms. Indications of nonlinearities and asymmetries in Humanitarian Demining (HD) data point to modifications to the current PCA algorithm that might prove beneficial. Asymmetries in the distribution of PCA projections of field data have been quantified in Humanitarian Demining (HD) data. An initial correction for the observed asymmetries has improved the False Alarm Rate (FAR) on this data.

  16. Stochastic description of quantum Brownian dynamics

    NASA Astrophysics Data System (ADS)

    Yan, Yun-An; Shao, Jiushu

    2016-08-01

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

  17. On methods for studying stochastic disease dynamics.

    PubMed

    Keeling, M J; Ross, J V

    2008-02-01

    Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters. PMID:17638650

  18. Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

    PubMed Central

    Soltani, Mohammad; Vargas-Garcia, Cesar A.; Antunes, Duarte; Singh, Abhyudai

    2016-01-01

    Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells. PMID:27536771

  19. Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes.

    PubMed

    Soltani, Mohammad; Vargas-Garcia, Cesar A; Antunes, Duarte; Singh, Abhyudai

    2016-08-01

    Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells. PMID:27536771

  20. Transport processes in magnetically confined plasmas in the nonlinear regime

    SciTech Connect

    Sonnino, Giorgio

    2006-06-15

    A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schlueter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schlueter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

  1. Nonlinear natural engine: Model for thermodynamic processes in mesoscale systems

    PubMed Central

    Wheatley, John; Buchanan, D. S.; Swift, G. W.; Migliori, A.; Hofler, T.

    1985-01-01

    To develop intuition on the possible application of concepts from thermodynamic heat engines to mesoscale systems, we have constructed and studied a model thermoacoustic heat engine. The model consists of a chain of coupled nonlinear acoustic vibrators in which the primary thermodynamic medium is argon gas, the secondary thermodynamic medium is constituted by solids bounding the gas, and frequencies are ca. 3 × 102 Hz. The nonlinear elements are the necks, made flexible by means of an oil-loaded DuPont Kapton film, of Helmholtz resonators. When the primary medium is driven uniformly by an acoustic driver at a frequency somewhat below the low-amplitude resonant frequency and at a high enough driving amplitude, stationary localized or solitary states appear irreversibly on the chain. These are characterized by a higher vibrational amplitude than that in surrounding vibrators, where the amplitude can decrease; by the appearance of deep subharmonics of the drive frequency, corresponding to driven low-frequency vibrations of the Kapton film-oil systems; and by the pumping of heat toward the localized states. Possible implications of these results for mesoscale systems consisting of chains of molecular vibrators are then discussed. Images PMID:16593625

  2. Nonlinear and Nonparametric Stochastic Model to Represent Uncertainty of Renewable Generation in Operation and Expansion Planning Studies of Electrical Energy Systems

    NASA Astrophysics Data System (ADS)

    Martins, T. M.; Alberto, J.

    2015-12-01

    The uncertainties of wind and solar generation patterns tends to be a critical factor in operation and expansion planning studies of electrical energy systems, as these generations are highly dependent on atmospheric variables which are difficult to predict. Traditionally, the uncertainty of renewable generation has been represented through scenarios generated by autoregressive parametric models (ARMA, PAR(p), SARIMA, etc.), that have been widely used for simulating the uncertainty of inflows and electrical demand. These methods have 3 disadvantages: (i) it is assumed that the random variables can be modelled through a known probability distribution, usually Weibull, log-normal, or normal, which are not always adequate; (ii) the temporal and spatial coupling of the represented variables are generally constructed from the Pearson Correlation, strictly requiring the hypothesis of data normality, that in the case of wind and solar generation is not met; (iii) there is an exponential increase in the model complexity due to its dimensionality. This work proposes the use of a stochastic model built from the combination of a non-parametric approach of a probability density function (the kernel density estimation method) with a dynamic Bayesian network framework. The kernel density estimation method is used to obtain the probability density function of the random variables directly from historical records, eliminating the need of choosing prior distributions. The Bayesian network allows the representation of nonlinearities in the temporal coupling of the time series, since they allow reproducing a compact probability distribution of a variable, subject to preceding stages. The proposed model was used to the generate wind power scenarios in long-term operation studies of the Brazilian Electric System, in which inflows of major rivers were also represented. The results show a considerable quality gain when compared to scenarios generated by traditional approaches.

  3. Stochastic thermodynamics

    NASA Astrophysics Data System (ADS)

    Eichhorn, Ralf; Aurell, Erik

    2014-04-01

    theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them

  4. Chaotic and stochastic processes in the accretion flows of the black hole X-ray binaries revealed by recurrence analysis

    NASA Astrophysics Data System (ADS)

    Suková, Petra; Grzedzielski, Mikolaj; Janiuk, Agnieszka

    2016-02-01

    Aims: Both the well known microquasar GRS 1915+105, as well as its recently discovered analogue, IGR J17091-3624, exhibit variability that is characteristic of a deterministic chaotic system. Their specific kind of quasi-periodic flares that are observed in some states is intrinsically connected with the global structure of the accretion flow, which are governed by the nonlinear hydrodynamics. One plausible mechanism that is proposed to explain this kind of variability is the thermal-viscous instability that operates in the accretion disk. The purely stochastic variability that occurs because of turbulent conditions in the plasma, is quantified by the power density spectra and appears in practically all types of sources and their spectral states. Methods: We pose a question as to whether these two microquasars are one of a kind, or if the traces of deterministic chaos, and hence the accretion disk instability, may also be hidden in the observed variability of other sources. We focus on the black hole X-ray binaries that accrete at a high rate and are, therefore, theoretically prone to the development of radiation pressure-induced instability. To study the nonlinear behaviour of the X-ray sources and distinguish between the chaotic and stochastic nature of their emission, we propose a novel method, which is based on recurrence analysis. Widely known in other fields of physics, this powerful method is used here for the first time in an astrophysical context. We estimate the indications of deterministic chaos quantitatively, such as the Rényi's entropy for the observed time series, and we compare them with surrogate data. Results: Using the observational data collected by the RXTE satellite, we reveal the oscillations pattern and the observable properties of six black hole systems. For five of them, we confirm the signatures of deterministic chaos being the driver of their observed variability. Conclusions: We test the method and confirm the deterministic nature of

  5. Processing of radar data for landmine detection: nonlinear transformation

    NASA Astrophysics Data System (ADS)

    Bartosz, E. E.; Duvoisin, H.; Konduri, R.; Solomon, G. Z.

    2005-06-01

    The Handheld Standoff Mine Detection System (HSTAMIDS system) has achieved outstanding performance in government-run field tests due to its use of anomaly detection using principal component analysis (PCA) on the return of ground penetrating radar (GPR) coupled with metal detection. Indications of nonlinearities and asymmetries in Humanitarian Demining (HD) data point to modifications to the current PCA algorithm that might prove beneficial. Asymmetries in the distribution of PCA projections of field data have been quantified in Humanitarian Demining (HD) data. The data suggest a logarithmic correction to the data. Such a correction has been applied and has improved the FAR on this data set. The increase in performance is comparable to the increase shown using the simpler asymmetric rescaling method.

  6. A nonlinear optoelectronic filter for electronic signal processing.

    PubMed

    Loh, William; Yegnanarayanan, Siva; Ram, Rajeev J; Juodawlkis, Paul W

    2014-01-01

    The conversion of electrical signals into modulated optical waves and back into electrical signals provides the capacity for low-loss radio-frequency (RF) signal transfer over optical fiber. Here, we show that the unique properties of this microwave-photonic link also enable the manipulation of RF signals beyond what is possible in conventional systems. We achieve these capabilities by realizing a novel nonlinear filter, which acts to suppress a stronger RF signal in the presence of a weaker signal independent of their separation in frequency. Using this filter, we demonstrate a relative suppression of 56 dB for a stronger signal having a 1-GHz center frequency, uncovering the presence of otherwise undetectable weaker signals located as close as 3.5 Hz away. The capabilities of the optoelectronic filter break the conventional limits of signal detection, opening up new possibilities for radar and communication systems, and for the field of precision frequency metrology. PMID:24402418

  7. A nonlinear optoelectronic filter for electronic signal processing

    PubMed Central

    Loh, William; Yegnanarayanan, Siva; Ram, Rajeev J.; Juodawlkis, Paul W.

    2014-01-01

    The conversion of electrical signals into modulated optical waves and back into electrical signals provides the capacity for low-loss radio-frequency (RF) signal transfer over optical fiber. Here, we show that the unique properties of this microwave-photonic link also enable the manipulation of RF signals beyond what is possible in conventional systems. We achieve these capabilities by realizing a novel nonlinear filter, which acts to suppress a stronger RF signal in the presence of a weaker signal independent of their separation in frequency. Using this filter, we demonstrate a relative suppression of 56 dB for a stronger signal having a 1-GHz center frequency, uncovering the presence of otherwise undetectable weaker signals located as close as 3.5 Hz away. The capabilities of the optoelectronic filter break the conventional limits of signal detection, opening up new possibilities for radar and communication systems, and for the field of precision frequency metrology. PMID:24402418

  8. Propagation of ultra-short solitons in stochastic Maxwell's equations

    SciTech Connect

    Kurt, Levent; Schäfer, Tobias

    2014-01-15

    We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

  9. Complex Population Dynamics in Mussels Arising from Density-Linked Stochasticity

    PubMed Central

    Wootton, J. Timothy; Forester, James D.

    2013-01-01

    Population fluctuations are generally attributed to the deterministic consequences of strong non-linear interactions among organisms, or the effects of random stochastic environmental variation superimposed upon the deterministic skeleton describing population change. Analysis of the population dynamics of the mussel Mytilus californianus taken in 16 plots over 18-years found no evidence that these processes explained observed strong fluctuations. Instead, population fluctuations arose because environmental stochasticity varied with abundance, which we term density-linked stochasticity. This phenomenon arises from biologically relevant mechanisms: recruitment variation and transmission of disturbance among neighboring individuals. Density-linked stochasticity is probably present frequently in populations, as it arises naturally from several general ecological processes, including stage structure variation with density, ontogenetic niche shifts, and local transmission of stochastic perturbations. More thoroughly characterizing and interpreting deviations from the mean behavior of a system will lead to better ecological prediction and improved insight into the important processes affecting populations and ecosystems. PMID:24086617

  10. Nonlinear silicon-on-insulator waveguides for all-optical signal processing

    NASA Astrophysics Data System (ADS)

    Koos, C.; Jacome, L.; Poulton, C.; Leuthold, J.; Freude, W.

    2007-05-01

    Values up to γ=7×106/(Wkm) for the nonlinear parameter are feasible if silicon-on-insulator based strip and slot waveguides are properly designed. This is more than three orders of magnitude larger than for state-of-the-art highly nonlinear fibers, and it enables ultrafast all-optical signal processing with nonresonant compact devices. At λ=1.55μm we provide universal design curves for strip and slot waveguides which are covered with different linear and nonlinear materials, and we calculate the resulting maximum γ.

  11. From spin noise to systematics: stochastic processes in the first International Pulsar Timing Array data release

    NASA Astrophysics Data System (ADS)

    Lentati, L.; Shannon, R. M.; Coles, W. A.; Verbiest, J. P. W.; van Haasteren, R.; Ellis, J. A.; Caballero, R. N.; Manchester, R. N.; Arzoumanian, Z.; Babak, S.; Bassa, C. G.; Bhat, N. D. R.; Brem, P.; Burgay, M.; Burke-Spolaor, S.; Champion, D.; Chatterjee, S.; Cognard, I.; Cordes, J. M.; Dai, S.; Demorest, P.; Desvignes, G.; Dolch, T.; Ferdman, R. D.; Fonseca, E.; Gair, J. R.; Gonzalez, M. E.; Graikou, E.; Guillemot, L.; Hessels, J. W. T.; Hobbs, G.; Janssen, G. H.; Jones, G.; Karuppusamy, R.; Keith, M.; Kerr, M.; Kramer, M.; Lam, M. T.; Lasky, P. D.; Lassus, A.; Lazarus, P.; Lazio, T. J. W.; Lee, K. J.; Levin, L.; Liu, K.; Lynch, R. S.; Madison, D. R.; McKee, J.; McLaughlin, M.; McWilliams, S. T.; Mingarelli, C. M. F.; Nice, D. J.; Osłowski, S.; Pennucci, T. T.; Perera, B. B. P.; Perrodin, D.; Petiteau, A.; Possenti, A.; Ransom, S. M.; Reardon, D.; Rosado, P. A.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Siemens, X.; Smits, R.; Stairs, I.; Stappers, B.; Stinebring, D. R.; Stovall, K.; Swiggum, J.; Taylor, S. R.; Theureau, G.; Tiburzi, C.; Toomey, L.; Vallisneri, M.; van Straten, W.; Vecchio, A.; Wang, J.-B.; Wang, Y.; You, X. P.; Zhu, W. W.; Zhu, X.-J.

    2016-05-01

    We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual pulsar timing array (PTA) data sets. For example, we show that PSR J1643-1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionized interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin-noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsar's sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437-4715 data set improves the upper limit on a fiducial GW background by ˜60 per cent compared to a model that includes DM variations and spin-noise only.

  12. Quantitative methods for stochastic high frequency spatio-temporal and non-linear analysis: Assessing health effects of exposure to extreme ambient temperature

    NASA Astrophysics Data System (ADS)

    Liss, Alexander

    Extreme weather events, such as heat waves and cold spells, cause substantial excess mortality and morbidity in the vulnerable elderly population, and cost billions of dollars. The accurate and reliable assessment of adverse effects of extreme weather events on human health is crucial for environmental scientists, economists, and public health officials to ensure proper protection of vulnerable populations and efficient allocation of scarce resources. However, the methodology for the analysis of large national databases is yet to be developed. The overarching objective of this dissertation is to examine the effect of extreme weather on the elderly population of the Conterminous US (ConUS) with respect to seasonality in temperature in different climatic regions by utilizing heterogeneous high frequency and spatio-temporal resolution data. To achieve these goals the author: 1) incorporated dissimilar stochastic high frequency big data streams and distinct data types into the integrated data base for use in analytical and decision support frameworks; 2) created an automated climate regionalization system based on remote sensing and machine learning to define climate regions for the Conterminous US; 3) systematically surveyed the current state of the art and identified existing gaps in the scientific knowledge; 4) assessed the dose-response relationship of exposure to temperature extremes on human health in relatively homogeneous climate regions using different statistical models, such as parametric and non-parametric, contemporaneous and asynchronous, applied to the same data; 5) assessed seasonal peak timing and synchronization delay of the exposure and the disease within the framework of contemporaneous high frequency harmonic time series analysis and modification of the effect by the regional climate; 6) modeled using hyperbolic functional form non-linear properties of the effect of exposure to extreme temperature on human health. The proposed climate

  13. Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes

    NASA Astrophysics Data System (ADS)

    Kannan, Rohit; Tangirala, Arun K.

    2014-06-01

    Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.

  14. Emergence of Heavy-Tailed Distributions in a Random Multiplicative Model Driven by a Gaussian Stochastic Process

    NASA Astrophysics Data System (ADS)

    Pirjol, Dan

    2014-02-01

    We consider a random multiplicative stochastic process with multipliers given by the exponential of a Brownian motion. The positive integer moments of the distribution function can be computed exactly, and can be represented as the grand partition function of an equivalent lattice gas with attractive 2-body interactions. The numerical results for the positive integer moments display a sharp transition at a critical value of the model parameters, which corresponds to a phase transition in the equivalent lattice gas model. The shape of the terminal distribution changes suddenly at the critical point to a heavy-tailed distribution. The transition can be related to the position of the complex zeros of the grand partition function of the lattice gas, in analogy with the Lee, Yang picture of phase transitions in statistical mechanics. We study the properties of the equivalent lattice gas in the thermodynamical limit, which corresponds to the continuous time limit of the random multiplicative model, and derive the asymptotics of the approach to the continuous time limit. The results can be generalized to a wider class of random multiplicative processes, driven by the exponential of a Gaussian stochastic process.

  15. Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions

    NASA Technical Reports Server (NTRS)

    Bjorklund, G. C.

    1975-01-01

    Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.

  16. Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.

    PubMed

    Brett, Tobias; Galla, Tobias

    2013-06-21

    We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.

  17. Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities

    NASA Astrophysics Data System (ADS)

    Moradi, Hamed; Movahhedy, Mohammad R.; Vossoughi, Gholamreza

    2012-07-01

    In this paper, internal resonance and nonlinear dynamics of regenerative chatter in milling process is investigated. An extended dynamic model of the peripheral milling process including both structural and cutting force nonlinearities is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. In the presence of the large vibration amplitudes, the loss of contact effect is included in this model. Using the multiple-scales approach, analytical approximate response of the delayed nonlinear system is obtained. Considering the internal resonance dynamics (i.e. mode coupling), the energy transfer between the coupled x-y modes is studied. The results show that during regenerative chatter under specific cutting conditions, one mode can decay. Furthermore, it is possible to adjust the rate at which the x-mode (or y-mode) decays by implementation of the internal resonance. Therefore, under both internal resonance and regenerative chatter conditions, it is possible to suppress the undesirable vibration of one mode (direction) in which accurate surface finish is required. Under the steady-state motion, jump phenomenon is investigated for the process with regenerative chatter under various cutting conditions. Moreover, the effects of structural and cutting force nonlinearities on the stability lobes diagram of the process are investigated.

  18. Stochastic Models of Human Growth.

    ERIC Educational Resources Information Center

    Goodrich, Robert L.

    Stochastic difference equations of the Box-Jenkins form provide an adequate family of models on which to base the stochastic theory of human growth processes, but conventional time series identification methods do not apply to available data sets. A method to identify structure and parameters of stochastic difference equation models of human…

  19. Stochastic optical active rheology

    NASA Astrophysics Data System (ADS)

    Lee, Hyungsuk; Shin, Yongdae; Kim, Sun Taek; Reinherz, Ellis L.; Lang, Matthew J.

    2012-07-01

    We demonstrate a stochastic based method for performing active rheology using optical tweezers. By monitoring the displacement of an embedded particle in response to stochastic optical forces, a rapid estimate of the frequency dependent shear moduli of a sample is achieved in the range of 10-1-103 Hz. We utilize the method to probe linear viscoelastic properties of hydrogels at varied cross-linker concentrations. Combined with fluorescence imaging, our method demonstrates non-linear changes of bond strength between T cell receptors and an antigenic peptide due to force-induced cell activation.

  20. Robust H infinity-stabilization design in gene networks under stochastic molecular noises: fuzzy-interpolation approach.

    PubMed

    Chen, Bor-Sen; Chang, Yu-Te; Wang, Yu-Chao

    2008-02-01

    Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering in gene networks is crucial to understand the signal processing in gene networks and to design noise-tolerant gene circuits for synthetic biology. A nonlinear stochastic dynamic model is proposed in describing a gene network under intrinsic molecular fluctuations and extrinsic molecular noises. The stochastic molecular-noise-processing scheme of gene regulatory networks for attenuating these molecular noises is investigated from the nonlinear robust stabilization and filtering perspective. In order to improve the robust stability and noise filtering, a robust gene circuit design for gene networks is proposed based on the nonlinear robust H infinity stochastic stabilization and filtering scheme, which needs to solve a nonlinear Hamilton-Jacobi inequality. However, in order to avoid solving these complicated nonlinear stabilization and filtering problems, a fuzzy approximation method is employed to interpolate several linear stochastic gene networks at different operation points via fuzzy bases to approximate the nonlinear stochastic gene network. In this situation, the method of linear matrix inequality technique could be employed to simplify the gene circuit design problems to improve robust stability and molecular-noise-filtering ability of gene networks to overcome intrinsic molecular fluctuations and extrinsic molecular noises. PMID:18270080

  1. Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals

    NASA Astrophysics Data System (ADS)

    Morimoto, Takahiro; Nagaosa, Naoto

    2016-07-01

    We study excitonic processes second order in the electric fields in noncentrosymmetric crystals. We derive formulas for shift current and second harmonic generation produced by exciton creation, by using the Floquet formalism combined with the Keldysh Green's function method. It is shown that (i) the steady dc shift current flows by exciton creation without dissociation into free carriers and (ii) second harmonic generation is enhanced at the exciton resonance. The obtained formulas clarify topological aspects of these second order excitonic processes which are described by Berry connections of the relevant valence and conduction bands.

  2. On the noise-enhancing ability of stochastic Hodgkin-Huxley neuron systems.

    PubMed

    Chen, Bor-Sen; Li, Cheng-Wei

    2010-07-01

    Recently noise has been shown to be useful in enhancing neuron sensitivity by stochastic resonance. In this study, in order to measure the noise-enhancing factor (NEF), a nonlinear stochastic model is introduced for the Hodgkin-Huxley (HH) neuron system with synaptic noise input stimulation and channel noises in the sodium and potassium channels. The enhancing factor of the HH neuron system is measured from the point of view of the noise-exploiting level of nonlinear stochastic H(infinity) signal processing. Since the nonlinear stochastic-enhancing measure problem of HH neuron systems requires a solution for the difficulty presented by the Hamilton Jacobi inequality (HJI), a fuzzy interpolation of locally linearized systems is employed to simplify the nonlinear noise-enhancing problems by solving only a set of linear matrix inequalities. The NEF of the HH neuron system is found to be related to the locations of eigenvalues of linearized HH neuron systems and can be estimated through the H(infinity) signal processing method. Based on a stochastic fuzzy linearized HH neuron system, we found that channel noises are enhanced by the active eigenvalues of ionic channels while synaptic noises are attenuated by the passive eigenvalues of synaptic process. PMID:20235824

  3. The importance of stochastic signaling processes in the induction of long-term synaptic plasticity.

    PubMed

    De Schutter, Erik

    2013-11-01

    A stochastic model of the signaling network responsible for the induction of long-term depression (LTD) at the parallel fiber to Purkinje cell synapse is described. The model includes a PKC-ERK-cPLA2 positive feedback loop and mechanisms of AMPA receptor trafficking. It was tuned to replicate calcium uncaging experiments that cause LTD. The ultrasensitive activation of ERK makes the signaling network activity bistable, causing either LTD or not. Therefore, in single synapses only two discrete stable states (LTD and non-LTD) can be expressed. The stochastic properties of the signaling network causes threshold dithering and probabilistic expression of LTD, which allows at the macroscopic level for many different and stable mean magnitudes of depression. When the volume of a single spine is simulated no thresholds for the calcium input signal are present. Such thresholds appear only when the volume of simulation is increased by a factor 100 or more and the model output is then bistable. Similarly, deterministic solutions of the same model show only bistable behavior. LTD induction requires activation of the PKC-ERK-cPLA2 positive feedback loop but this activity is not constant: the activities of ERK and of cPLA2 fluctuate strongly. This is much less the case for PKC which is more constantly activated and thereby promotes a stable output of the pathway. PMID:23267752

  4. A Stochastic Framework For Sediment Concentration Estimation By Accounting Random Arrival Processes Of Incoming Particles Into Receiving Waters

    NASA Astrophysics Data System (ADS)

    Tsai, C.; Hung, R. J.

    2015-12-01

    This study attempts to apply queueing theory to develop a stochastic framework that could account for the random-sized batch arrivals of incoming sediment particles into receiving waters. Sediment particles, control volume, mechanics of sediment transport (such as mechanics of suspension, deposition and resuspension) are treated as the customers, service facility and the server respectively in queueing theory. In the framework, the stochastic diffusion particle tracking model (SD-PTM) and resuspension of particles are included to simulate the random transport trajectories of suspended particles. The most distinguished characteristic of queueing theory is that customers come to the service facility in a random manner. In analogy to sediment transport, this characteristic is adopted to model the random-sized batch arrival process of sediment particles including the random occurrences and random magnitude of incoming sediment particles. The random occurrences of arrivals are simulated by Poisson process while the number of sediment particles in each arrival can be simulated by a binominal distribution. Simulations of random arrivals and random magnitude are proposed individually to compare with the random-sized batch arrival simulations. Simulation results are a probabilistic description for discrete sediment transport through ensemble statistics (i.e. ensemble means and ensemble variances) of sediment concentrations and transport rates. Results reveal the different mechanisms of incoming particles will result in differences in the ensemble variances of concentrations and transport rates under the same mean incoming rate of sediment particles.

  5. Nonlinear processes upon two-photon interband picosecond excitation of PbWO4 crystal

    NASA Astrophysics Data System (ADS)

    Lukanin, V. I.; Karasik, A. Ya

    2016-09-01

    A new experimental method is proposed to study the dynamics of nonlinear processes occurring upon two-photon interband picosecond excitation of a lead tungstate crystal and upon its excitation by cw probe radiation in a temporal range from several nanoseconds to several seconds. The method is applied to the case of crystal excitation by a sequence of 25 high-power picosecond pulses with a wavelength of 523.5 nm and 633-nm cw probe radiation. Measuring the probe beam transmittance during crystal excitation, one can investigate the influence of two-photon interband absorption and the thermal nonlinearity of the refractive index on the dynamics of nonlinear processes in a wide range of times (from several nanoseconds to several seconds). The time resolution of the measuring system makes it possible to distinguish fast and slow nonlinear processes of electronic or thermal nature, including the generation of a thermal lens and thermal diffusion. An alternative method is proposed to study the dynamics of induced absorption transformation and, therefore, the dynamics of the development of nonlinear rocesses upon degenerate two-photon excitation of the crystal in the absence of external probe radiation.

  6. Robust algorithms for solving stochastic partial differential equations

    SciTech Connect

    Werner, M.J.; Drummond, P.D.

    1997-04-01

    A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in X{sup 2} parametric waveguides. This example uses non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used will be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. 27 refs., 4 figs.

  7. Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.

    PubMed

    Borgogno, Fabio; D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

    2012-01-21

    Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers.

  8. The effect of process delay on dynamical behaviors in a self-feedback nonlinear oscillator

    NASA Astrophysics Data System (ADS)

    Yao, Chenggui; Ma, Jun; Li, Chuan; He, Zhiwei

    2016-10-01

    The delayed feedback loops play a crucial role in the stability of dynamical systems. The effect of process delay in feedback is studied numerically and theoretically in the delayed feedback nonlinear systems including the neural model, periodic system and chaotic oscillator. The process delay is of key importance in determining the evolution of systems, and the rich dynamical phenomena are observed. By introducing a process delay, we find that it can induce bursting electric activities in the neural model. We demonstrate that this novel regime of amplitude death also exists in the parameter space of feedback strength and process delay for the periodic system and chaotic oscillator. Our results extend the effect of process delay in the paper of Zou et al.(2013) where the process delay can eliminate the amplitude death of the coupled nonlinear systems.

  9. Simultaneous spatial and temporal focusing: a route towards confined nonlinear materials processing

    NASA Astrophysics Data System (ADS)

    Kammel, Robert; Bergner, Klaus; Thomas, Jens; Ackermann, Roland; Skupin, Stefan; Nolte, Stefan

    2016-03-01

    Ultrashort pulse lasers enable reliable and versatile high precision ablation and surface processing of various materials such as metals, polymers and semiconductors. However, when modifications deep inside the bulk of transparent media are required, nonlinear pulse material interactions can decrease the precision, since weak focusing and the long propagation of the intense pulses within the nonlinear media may induce Kerr self-focusing, filamentation and white light generation. In order to improve the precision of those modifications, simultaneous spatial and temporal focusing (SSTF) allows to reduce detrimental nonlinear interactions, because the ultrashort pulse duration is only obtained at the focus, while outside of the focal region the continuously increasing pulse duration strongly reduces the pulse intensity. In this paper, we review the fundamental concepts of this technology and provide an overview of its applications for purposes of multiphoton microscopy and laser materials processing. Moreover, numerical simulations on the nonlinear pulse propagation within transparent media illustrate the linear and nonlinear pulse propagation, highlighting the differences between conventional focusing and SSTF. Finally, fs-laser induced modifications in gelatine are presented to compare nonlinear side-effects caused by conventional focusing and SSTF. With conventional focusing the complex interplay of self-focusing and filamentation induces strongly inhomogeneous, elongated disruptions. In contrast, disruptions induced by SSTF are homogeneously located at the focal plane and reduced in length by a factor >2, which is in excellent agreement with the numerical simulations of the nonlinear pulse propagation and might favor SSTF for demanding applications such as intraocular fs-laser surgery.

  10. Nonlinear signal processing of electroencephalograms for automated sleep monitoring

    NASA Astrophysics Data System (ADS)

    Wilson, D.; Rowlands, D. D.; James, Daniel A.; Cutmore, T.

    2005-02-01

    An automated classification technique is desirable to identify the different stages of sleep. In this paper a technique for differentiating the characteristics of each sleep phase has been developed. This is an ideal pre-processor stage for classifying systems such as neural networks. A wavelet based continuous Morlet transform was developed to analyse the EEG signal in both the time and frequency domain. Test results using two 100 epoch EEG test data sets from pre-recorded EEG data are presented. Key rhythms in the EEG signal were identified and classified using the continuous wavelet transform. The wavelet results indicated each sleep phase contained different rhythms and artefacts (noise from muscle movement in the EEG); providing proof that an EEG can be classified accordingly. The coefficients founded by the wavelet transform have been emphasised by statistical techniques. Hypothesis testing was used to highlight major differences between adjacent sleep stages. Various signal processing methods such as power spectrum density and the discrete wavelet transform have been used to emphasise particular characteristics in an EEG. By implementing signal processing methods on an EEG data set specific rules for each sleep stage have been developed suitable for a neural network classification solution.

  11. EGS Richardson AGU Chapman NVAG3 Conference: Nonlinear Variability in Geophysics: scaling and multifractal processes

    NASA Astrophysics Data System (ADS)

    Schertzer, D.; Lovejoy, S.

    1. The conference The third conference on "Nonlinear VAriability in Geophysics: scaling and multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993. NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first specialist conference jointly sponsored by the two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988; Schertzer and Lovejoy, 1991), five consecutive annual sessions at EGS general assemblies and two consecutive spring AGU meeting sessions. As with the other conferences and workshops mentioned above, the aim was to develop confrontation between theories and experiments on scaling/multifractal behaviour of geophysical fields. Subjects covered included climate, clouds, earthquakes, atmospheric and ocean dynamics, tectonics, precipitation, hydrology, the solar cycle and volcanoes. Areas of focus included new methods of data analysis (especially those used for the reliable estimation of multifractal and scaling exponents), as well as their application to rapidly growing data bases from in situ networks and remote sensing. The corresponding modelling, prediction and estimation techniques were also emphasized as were the current debates about stochastic and deterministic dynamics, fractal geometry and multifractals, self-organized criticality and multifractal fields, each of which was the subject of a specific general discussion. The conference started with a one day short course of multifractals featuring four lectures on a) Fundamentals of multifractals: dimension, codimensions, codimension formalism, b) Multifractal estimation techniques: (PDMS, DTM), c) Numerical simulations, Generalized Scale Invariance analysis, d) Advanced multifractals, singular statistics, phase transitions, self-organized criticality and Lie cascades (given by D. Schertzer and S. Lovejoy, detailed course notes were sent to participants shortly after the conference). This

  12. Random musings on stochastics (Lorenz Lecture)

    NASA Astrophysics Data System (ADS)

    Koutsoyiannis, D.

    2014-12-01

    In 1960 Lorenz identified the chaotic nature of atmospheric dynamics, thus highlighting the importance of the discovery of chaos by Poincare, 70 years earlier, in the motion of three bodies. Chaos in the macroscopic world offered a natural way to explain unpredictability, that is, randomness. Concurrently with Poincare's discovery, Boltzmann introduced statistical physics, while soon after Borel and Lebesgue laid the foundation of measure theory, later (in 1930s) used by Kolmogorov as the formal foundation of probability theory. Subsequently, Kolmogorov and Khinchin introduced the concepts of stochastic processes and stationarity, and advanced the concept of ergodicity. All these areas are now collectively described by the term "stochastics", which includes probability theory, stochastic processes and statistics. As paradoxical as it may seem, stochastics offers the tools to deal with chaos, even if it results from deterministic dynamics. As chaos entails uncertainty, it is more informative and effective to replace the study of exact system trajectories with that of probability densities. Also, as the exact laws of complex systems can hardly be deduced by synthesis of the detailed interactions of system components, these laws should inevitably be inferred by induction, based on observational data and using statistics. The arithmetic of stochastics is quite different from that of regular numbers. Accordingly, it needs the development of intuition and interpretations which differ from those built upon deterministic considerations. Using stochastic tools in a deterministic context may result in mistaken conclusions. In an attempt to contribute to a more correct interpretation and use of stochastic concepts in typical tasks of nonlinear systems, several examples are studied, which aim (a) to clarify the difference in the meaning of linearity in deterministic and stochastic context; (b) to contribute to a more attentive use of stochastic concepts (entropy, statistical

  13. Stochastic modelling of landfill processes incorporating waste heterogeneity and data uncertainty.

    PubMed

    Zacharof, A I; Butler, A P

    2004-01-01

    A landfill is a very complex heterogeneous environment and as such it presents many modelling challenges. Attempts to develop models that reproduce these complexities generally involve the use of large numbers of spatially dependent parameters that cannot be properly characterised in the face of data uncertainty. An alternative method is presented, which couples a simplified microbial degradation model with a stochastic hydrological and contaminant transport model. This provides a framework for incorporating the complex effects of spatial heterogeneity within the landfill in a simplified manner, along with other key variables. A methodology for handling data uncertainty is also integrated into the model structure. Illustrative examples of the model's output are presented to demonstrate effects of data uncertainty on leachate composition and gas volume prediction.

  14. Stochasticity enhances the gaining of bet-hedging strategies in contact-process-like dynamics.

    PubMed

    Hidalgo, Jorge; Pigolotti, Simone; Muñoz, Miguel A

    2015-03-01

    In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as "bet-hedging." Long-term survival probabilities and population sizes can be much enhanced by exploiting such hybrid strategies. Here, we study the simplest possible birth-death stochastic model in which individuals can choose among a poor but safe strategy, a better but risky alternative, or a combination of both. We show analytically and computationally that the benefits derived from bet-hedging strategies are much stronger for higher environmental variabilities (large external noise) and/or for small spatial dimensions (large intrinsic noise). These circumstances are typically encountered by living systems, thus providing us with a possible justification for the ubiquitousness of bet-hedging in nature.

  15. Solution of the stochastic generalized shallow-water wave equation using RVT technique

    NASA Astrophysics Data System (ADS)

    Hussein, Abdallah; Selim, Mustafa M.

    2015-12-01

    In this paper, some exact solutions of the stochastic generalized nonlinear shallow-water wave (SGNSWW) equation are obtained. This equation is an important equation in fluid mechanics field. Opposite to what is usually assumed in the literature, the coefficients of the nonlinear terms in this stochastic nonlinear partial differential equation (SNLPDE) are considered to be random quantities. The random variable transformation (RVT) technique is combined with the modified extended-tanh function method (METFM) to get the stochastic solutions represented by the probability density functions (PDFs) of the solution processes in terms of the PDFs of the random coefficients. These solutions are illustrated graphically along the spacial and time dimensions at a certain wave speed.

  16. Non-linear, adaptive array processing for acoustic interference suppression.

    PubMed

    Hoppe, Elizabeth; Roan, Michael

    2009-06-01

    A method is introduced where blind source separation of acoustical sources is combined with spatial processing to remove non-Gaussian, broadband interferers from space-time displays such as bearing track recorder displays. This differs from most standard techniques such as generalized sidelobe cancellers in that the separation of signals is not done spatially. The algorithm performance is compared to adaptive beamforming techniques such as minimum variance distortionless response beamforming. Simulations and experiments using two acoustic sources were used to verify the performance of the algorithm. Simulations were also used to determine the effectiveness of the algorithm under various signal to interference, signal to noise, and array geometry conditions. A voice activity detection algorithm was used to benchmark the performance of the source isolation.

  17. Stochastic Thermal Convection

    NASA Astrophysics Data System (ADS)

    Venturi, Daniele

    2005-11-01

    Stochastic bifurcations and stability of natural convective flows in 2d and 3d enclosures are investigated by the multi-element generalized polynomial chaos (ME-gPC) method (Xiu and Karniadakis, SISC, vol. 24, 2002). The Boussinesq approximation for the variation of physical properties is assumed. The stability analysis is first carried out in a deterministic sense, to determine steady state solutions and primary and secondary bifurcations. Stochastic simulations are then conducted around discontinuities and transitional regimes. It is found that these highly non-linear phenomena can be efficiently captured by the ME-gPC method. Finally, the main findings of the stochastic analysis and their implications for heat transfer will be discussed.

  18. High-order optical processes in intense laser field: Towards nonperturbative nonlinear optics

    NASA Astrophysics Data System (ADS)

    Strelkov, V. V.

    2016-05-01

    We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schrödinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields, we derive and analytically solve propagation equations describing high-order (HO) wave mixing, HO parametric amplification, and HO stimulated scattering. These processes provide a way of efficient coherent xuv generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the superexponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.

  19. Second-order cascading in third-order nonlinear optical processes

    NASA Astrophysics Data System (ADS)

    Meredith, Gerald R.

    1982-12-01

    Because cascaded second-order processes make substantial qualitative and quanitative differences to the results of third-order nonlinear optical experiments, a formalism for their treatment is presented. The symmetry dictates concerning the occurrence and relationships of magnitudes of cascading are tabulated for the higher symmetry crystal classes. Angular momentum considerations are applied to the situations allowing circularly polarized light waves.

  20. Compound Cue Processing within the Fast and Frugal Heuristics Approach in Nonlinearly Separable Environments

    ERIC Educational Resources Information Center

    Garcia-Retamero, Rocio; Hoffrage, Ulrich; Dieckmann, Anja; Ramos, Manuel

    2007-01-01

    Three experiments investigated whether participants used Take The Best (TTB) Configural, a fast and frugal heuristic that processes configurations of cues when making inferences concerning which of two alternatives has a higher criterion value. Participants were presented with a compound cue that was nonlinearly separable from its elements. The…

  1. Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

    NASA Astrophysics Data System (ADS)

    Liu, Yunqi; Gong, Yungui; Wang, Bin

    2016-02-01

    We study the non-equilibrium condensation process in a holographic superconductor with nonlinear corrections to the U (1) gauge field. We start with an asymptotic Anti-de-Sitter (AdS) black hole against a complex scalar perturbation at the initial time, and solve the dynamics of the gravitational systems in the bulk. When the black hole temperature T is smaller than a critical value T c , the scalar perturbation grows exponentially till saturation, the final state of spacetime approaches to a hairy black hole. In the bulk theory, we find the clue of the influence of nonlinear corrections in the gauge filed on the process of the scalar field condensation. We show that the bulk dynamics in the non-equilibrium process is completely consistent with the observations on the boundary order parameter. Furthermore we examine the time evolution of horizons in the bulk non-equilibrium transformation process from the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent and event horizons show that the original AdS black hole configuration requires more time to finish the transformation to become a hairy black hole if there is nonlinear correction to the electromagnetic field. We generalize our non-equilibrium discussions to the holographic entanglement entropy and find that the holographic entanglement entropy can give us further understanding of the influence of the nonlinearity in the gauge field on the scalar condensation.

  2. Multilevel Modeling of Two Cyclical Processes: Extending Differential Structural Equation Modeling to Nonlinear Coupled Systems

    ERIC Educational Resources Information Center

    Butner, Jonathan; Amazeen, Polemnia G.; Mulvey, Genna M.

    2005-01-01

    The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Graham's (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination…

  3. Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models

    NASA Astrophysics Data System (ADS)

    Wei, Song; Chen, Wen; Hon, Y. C.

    2016-11-01

    This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.

  4. The Creative Chaos: Speculations on the Connection Between Non-Linear Dynamics and the Creative Process

    NASA Astrophysics Data System (ADS)

    Zausner, Tobi

    Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.

  5. Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

    NASA Technical Reports Server (NTRS)

    Mangalgiri, P. D.; Prabhakaran, R.

    1986-01-01

    An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

  6. Heterogeneous recurrence representation and quantification of dynamic transitions in continuous nonlinear processes

    NASA Astrophysics Data System (ADS)

    Chen, Yun; Yang, Hui

    2016-06-01

    Many real-world systems are evolving over time and exhibit dynamical behaviors. In order to cope with system complexity, sensing devices are commonly deployed to monitor system dynamics. Online sensing brings the proliferation of big data that are nonlinear and nonstationary. Although there is rich information on nonlinear dynamics, significant challenges remain in realizing the full potential of sensing data for system control. This paper presents a new approach of heterogeneous recurrence analysis for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named as Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multi-dimensional continuous state space. Further, we design a new fractal representation of state transitions among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we develop a multivariate detection method for on-line monitoring and predictive control of process recurrences. Case studies show that the proposed approach not only captures heterogeneous recurrence patterns in the transformed space, but also provides effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear processes.

  7. Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis.

    PubMed

    Yulmetyev, R; Gafarov, F; Hänggi, P; Nigmatullin, R; Kayumov, S

    2001-12-01

    The basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature. One example of such kinds of signals is presented by seismograms containing recordings of earthquakes (EQ's) and technogenic explosions (TE's). EQ's are among the most dramatic phenomena in nature. We propose here a discrete stochastic model for possible solution of a problem of strong EQ forecasting and differentiation of TE's from the weak EQ's. Theoretical analysis is performed by two independent methods: by using statistical theory of discrete non-Markov stochastic processes [Phys. Rev. E 62, 6178 (2000)] and the local Hurst exponent. The following Earth states have been considered among them: before (Ib) and during (I) strong EQ, during weak EQ (II) and during TE (III), and in a calm state of Earth's core (IV). The estimation of states I, II, and III has been made on the particular examples of Turkey (1999) EQ's, state IV has been taken as an example of Earth's state before underground TE. Time recordings of seismic signals of the first four dynamic orthogonal collective variables, six various planes of phase portrait of four-dimensional phase space of orthogonal variables and the local Hurst exponent have been calculated for the dynamic analysis of states of systems I-IV. The analysis of statistical properties of seismic time series I-IV has been realized with the help of a set of discrete time-dependent functions (time correlation function and first three memory functions), their power spectra, and the first three points in the statistical spectrum of non-Markovity parameters. In all systems studied we have found a bizarre combination of the following spectral characteristics: the fractal frequency spectra adjustable by phenomena of usual and restricted self-organized criticality, spectra of white and color noises and unusual alternation of Markov and non-Markov effects of long-range memory

  8. Kinetics of single cells: observation and modeling of a stochastic process.

    PubMed

    Pin, Carmen; Baranyi, József

    2006-03-01

    The successive generation times for single cells of Escherichia coli K-12 were measured as described by A. Elfwing, Y. LeMarc, J. Baranyi, and A. Ballagi (Appl. Environ. Microbiol. 70:675-678, 2004), and the histograms they generated were used as empirical distributions to simulate growth of the population as the result of the multiplication of its single cells. This way, a stochastic birth model in which the underlying distributions were measured experimentally was simulated. To validate the model, analogous bacterial growth curves were generated by the use of different inoculum levels. The agreement with the simulation was very good, proving that the growth of the population can be predicted accurately if the distribution of the first few division times for the single cells within that population is known. Two questions were investigated by the simulation. (i) To what extent can we say that the distribution of the detection time, i.e., the time by which a single-cell-generated subpopulation reaches a detectable level, can be identified with that of the lag time of the original single cell? (ii) For low inocula, how does the inoculum size affect the lag time of the population?

  9. Time reversibility and nonequilibrium thermodynamics of second-order stochastic processes

    NASA Astrophysics Data System (ADS)

    Ge, Hao

    2014-02-01

    Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time reversibility over the phase space is equivalent to the antisymmetry of spatial flux and the symmetry of velocity flux. Then we show that the condition of time reversibility alone cannot always guarantee the Maxwell-Boltzmann distribution. Comparing the two conditions together, we find that the frictional force naturally emerges as the unique odd term of the total force at thermodynamic equilibrium, and is followed by the Einstein relation. The two conditions respectively correspond to two previously reported different entropy production rates. In the case where the external force is only position dependent, the two entropy production rates become one. We prove that such an entropy production rate can be decomposed into two non-negative terms, expressed respectively by the conditional mean and variance of the thermodynamic force associated with the irreversible velocity flux at any given spatial coordinate. In the small inertia limit, the former term becomes the entropy production rate of the corresponding overdamped dynamics, while the anomalous entropy production rate originates from the latter term. Furthermore, regarding the connection between the first law and second law, we find that in the steady state of such a limit, the anomalous entropy production rate is also the leading order of the Boltzmann-factor weighted difference between the spatial heat dissipation densities of the underdamped and overdamped dynamics, while their unweighted difference always tends to vanish.

  10. Optimisation of simulations of stochastic processes by removal of opposing reactions.

    PubMed

    Spill, Fabian; Maini, Philip K; Byrne, Helen M

    2016-02-28

    Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model. PMID:26931679

  11. Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

    SciTech Connect

    Zhu, Zhiwen; Zhang, Qingxin Xu, Jia

    2014-05-07

    Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.

  12. Nonlinear optical processing with Fabry-Perot interferometers containing phase recording media

    NASA Technical Reports Server (NTRS)

    Bartholomew, B. J.; Lee, S. H.

    1980-01-01

    New techniques in nonlinear optical processing are explored, based on the operation of intensity level selection as performed by a Fabry-Perot interferometer containing a phase object. The image being processed is recorded on a medium between the mirrors as a spatially varying phase shift less than pi. The interferometer only transmits light through those portions of the object that corresponds to a single value of the phase and hence to a single intensity level in the input. More complicated operations such as thresholding and analog-to-digital conversion are performed by modulating the light source as the different levels are selected. Photoresist and lithium niobate have been used as phase objects, and experimental data for both are presented. Three kinds of Fabry-Perot interferometers have been used to demonstrate nonlinear processing using coherent and incoherent light. Color images have been produced with black and white inputs and white light illumination.

  13. Nonlinear data processing method for the signal enhancement of GPR data

    NASA Astrophysics Data System (ADS)

    Chen, Chih-Sung; Jeng, Yih

    2011-09-01

    An alternative data processing procedure is proposed in this paper for the purpose of enhancing the signal/noise (S/N) ratio of ground penetrating radar (GPR) data. The processing methodology is achieved by performing the logarithmic transform in conjunction with the ensemble empirical mode decomposition (EEMD), a new nonlinear data analysis method in signal processing. The synthetic model study and field example indicate that the logarithmic transform is effective in alleviating the attenuation problem. Additionally, the spectrogram obtained from Hilbert-Huang transform (HHT) shows that the decomposition sensitivity of the EEMD method is greatly improved with the aid of the logarithmic transform. This new method allows us to extract the signal components from noisy GPR data efficiently. The success of this study suggests a possible nonlinear analysis application in future GPR investigation, particularly in the filter design and gain correction.

  14. Some applications of nonlinear diffusion to processing of dynamic evolution images

    SciTech Connect

    Goltsov, Alexey N.; Nikishov, Sergey A.

    1997-05-15

    Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung.

  15. Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process.

    PubMed

    Lee, Joong-Won; Hong, Yoon-Seok Timothy; Suh, Changwon; Shin, Hang-Sik

    2012-03-01

    Online estimation of unknown state variables is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The extended Kalman filter (EKF) algorithm has been widely applied for wastewater treatment processes. However, the series approximations in the EKF algorithm are not valid, because biological wastewater treatment processes are highly nonlinear with a time-varying characteristic. This work proposes an alternative online estimation approach using the sequential Monte Carlo (SMC) methods for recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. SMC is an algorithm that makes it possible to recursively construct the posterior probability density of the state variables, with respect to all available measurements, through a random exploration of the states by entities called 'particle'. In this work, the simplified and modified Activated Sludge Model No. 3 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic state-space model applied to the SMC method. The performance of the SMC method for online state estimation applied to a biological sequencing batch reactor with online and offline measured data is encouraging. The results indicate that the SMC method could emerge as a powerful tool for solving online state and parameter estimation problems without any model linearization or restrictive assumptions pertaining to the type of nonlinear models for biological wastewater treatment processes. PMID:21792564

  16. Nonlinear GARCH model and 1 / f noise

    NASA Astrophysics Data System (ADS)

    Kononovicius, A.; Ruseckas, J.

    2015-06-01

    Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

  17. Stochastic games

    PubMed Central

    Solan, Eilon; Vieille, Nicolas

    2015-01-01

    In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution. PMID:26556883

  18. Mathematics Education. Selected Papers from the Conference on Stochastic Processes and Their Applications. (15th, Nagoya, Japan, July 2-5, 1985).

    ERIC Educational Resources Information Center

    Hida, Takeyuki; Shimizu, Akinobu

    This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical…

  19. The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes

    NASA Astrophysics Data System (ADS)

    Bouchaud, Jean-Philippe; Sornette, Didier

    1994-06-01

    The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processes, such as ARCH, jump or Lévy processes. We also address thé case of correlated Gaussian processes, which is shown to be a good description of three différent market indices (MATIF, CAC40, FTSE100). Our main result is thé introduction of thé concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no longer the case for more general stochastic processes. The value of the residual risk is obtained and suggests the concept of risk-corrected option prices. In the presence of very large deviations such as in Lévy processes, new criteria for rational fixing of the option prices are discussed. We also apply our method to other types of options, `Asian', `American', and discuss new possibilities (`doubledecker'...). The inclusion of transaction costs leads to the appearance of a natural characteristic trading time scale. L'aptitude à quantifier le coût du risque et à définir une stratégie optimale de gestion de portefeuille dans un marché aléatoire constitue la base de la théorie moderne de la finance. Nous considérons d'abord le problème le plus simple de ce type, à savoir celui de l'option d'achat `européenne', qui a été résolu par Black et Scholes à l'aide du calcul stochastique d'Ito appliqué aux marchés modélisés par un processus Log

  20. Stochastic superparameterization in quasigeostrophic turbulence

    SciTech Connect

    Grooms, Ian; Majda, Andrew J.

    2014-08-15

    In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and