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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. Heat Shock Response in CHO Mammalian Cells Is Controlled by a Nonlinear Stochastic Process

    PubMed Central

    Lipan, Ovidiu; Navenot, Jean-Marc; Wang, Zixuan; Huang, Lei; Peiper, Stephen C

    2007-01-01

    In many biological systems, the interactions that describe the coupling between different units in a genetic network are nonlinear and stochastic. We study the interplay between stochasticity and nonlinearity using the responses of Chinese hamster ovary (CHO) mammalian cells to different temperature shocks. The experimental data show that the mean value response of a cell population can be described by a mathematical expression (empirical law) which is valid for a large range of heat shock conditions. A nonlinear stochastic theoretical model was developed that explains the empirical law for the mean response. Moreover, the theoretical model predicts a specific biological probability distribution of responses for a cell population. The prediction was experimentally confirmed by measurements at the single-cell level. The computational approach can be used to study other nonlinear stochastic biological phenomena. PMID:17922567

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

    NASA Astrophysics Data System (ADS)

    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.

  4. 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. PMID:26565359

  5. Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes.

    PubMed

    Galtier, Mathieu N; Marini, Camille; Wainrib, Gilles; Jaeger, Herbert

    2014-08-01

    A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Niño phenomenon studied in climate research. PMID:24815743

  6. 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.

  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. Generalized spectral decomposition for stochastic nonlinear problems

    SciTech Connect

    Nouy, Anthony Le Maitre, Olivier P.

    2009-01-10

    We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.

  9. Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

    SciTech Connect

    Kadtke, J.B.; Bulsara, A.

    1997-12-01

    These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

  10. 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].

  11. 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.

  12. Stochastic differential equations for non-linear hydrodynamics

    NASA Astrophysics Data System (ADS)

    Español, Pep

    1998-02-01

    We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stres tensor and random heat flux as in the Landau and Lifshitz theory. However, the equations are non-linear and the random forces are non-Gaussian. We provide explicit expressions for these random quantities in terms of the well-defined increments of the Wienner process.

  13. Variational approach to stochastic nonlinear problems

    SciTech Connect

    Phythian, R.; Curtis, W.D.

    1986-03-01

    A variational principle is formulated which enables the mean value and higher moments of the solution of a stochastic nonlinear differential equation to be expressed as stationary values of certain quantities. Approximations are generated by using suitable trial functions in this variational principle and some of these are investigated numerically for the case of a Bernoulli oscillator driven by white noise. Comparison with exact data available for this system show that the variational approach to such problems can be quite effective.

  14. Fully nonlinear dynamics of stochastic thin-film dewetting.

    PubMed

    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. PMID:26764623

  15. 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.

  16. 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.

  17. Stochastic Processes in Electrochemistry.

    PubMed

    Singh, Pradyumna S; Lemay, Serge G

    2016-05-17

    Stochastic behavior becomes an increasingly dominant characteristic of electrochemical systems as we probe them on the smallest scales. Advances in the tools and techniques of nanoelectrochemistry dictate that stochastic phenomena will become more widely manifest in the future. In this Perspective, we outline the conceptual tools that are required to analyze and understand this behavior. We draw on examples from several specific electrochemical systems where important information is encoded in, and can be derived from, apparently random signals. This Perspective attempts to serve as an accessible introduction to understanding stochastic phenomena in electrochemical systems and outlines why they cannot be understood with conventional macroscopic descriptions. PMID:27120701

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

    PubMed

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

    2016-03-01

    The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. PMID:26707373

  19. 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

  20. 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.

  1. Haotic, Fractal, and Nonlinear Signal Processing. Proceedings

    SciTech Connect

    Katz, R.A.

    1996-10-01

    These proceedings include papers presented at the Third Technical Conference on Nonlinear Dynamics and Full{minus}Spectrum Processing held in Mystic, Connecticut. The Conference focus was on the latest advances in chaotic, fractal and nonlinear signal processing methods. Topics of discussion covered in the Conference include: mathematical frontiers; predictability and control of chaos, detection and classification with applications in acoustics; advanced applied signal processing methods(linear and nonlinear); stochastic resonance; machinery diagnostics; turbulence; geophysics; medicine; and recent novel approaches to modeling nonlinear systems. There were 58 papers in the conference and all have been abstracted for the Energy Science and Technology database. (AIP)

  2. 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.

  3. 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.

  4. 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.

  5. Accelerated stochastic diffusion processes

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr

    1990-07-01

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

  6. 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.

  7. Nonlinear Markov processes

    NASA Astrophysics Data System (ADS)

    Frank, T. D.

    2008-06-01

    Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.

  8. 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. PMID:26585899

  9. A Stochastic Diffusion Process for the Dirichlet Distribution

    DOE PAGESBeta

    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

  10. 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.

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

    NASA Technical Reports Server (NTRS)

    Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.

    2004-01-01

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

  12. Stochasticity in numerical solutions of the nonlinear Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Shen, Mei-Mei; Nicholson, D. R.

    1987-01-01

    The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

  13. On Input-to-State Stability of Switched Stochastic Nonlinear Systems Under Extended Asynchronous Switching.

    PubMed

    Kang, Yu; Zhai, Di-Hua; Liu, Guo-Ping; Zhao, Yun-Bo

    2016-05-01

    An extended asynchronous switching model is investigated for a class of switched stochastic nonlinear retarded systems in the presence of both detection delay and false alarm, where the extended asynchronous switching is described by two independent and exponentially distributed stochastic processes, and further simplified as Markovian. Based on the Razumikhin-type theorem incorporated with average dwell-time approach, the sufficient criteria for global asymptotic stability in probability and stochastic input-to-state stability are given, whose importance and effectiveness are finally verified by numerical examples. PMID:26068932

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

    NASA Technical Reports Server (NTRS)

    Bayard, David S.

    1988-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Jennings, Elise; Jennings, David

    2015-06-01

    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 = nabla \\cdot 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 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) for k < 0.1 h Mpc-1. 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. 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.

  16. 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.

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

    DOE PAGESBeta

    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

  18. 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.

  19. 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.

  20. Stochastic slowdown in evolutionary processes.

    PubMed

    Altrock, Philipp M; Gokhale, Chaitanya S; Traulsen, Arne

    2010-07-01

    We examine birth-death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but nonvanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes. PMID:20866666

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

    NASA Technical Reports Server (NTRS)

    Cantrell, J. H.

    1985-01-01

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

  2. Nonlinear 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.

  3. 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.

  4. 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.

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

    NASA Technical Reports Server (NTRS)

    Williams Colin P.

    1999-01-01

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

  6. 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.

  7. Stochastic resonance in a nonlinear mechanical vibration isolation system

    NASA Astrophysics Data System (ADS)

    Lu, Zeqi; Chen, Li-Qun; Brennan, Michael J.; Yang, Tiejun; Ding, Hu; Liu, Zhigang

    2016-05-01

    This paper concerns the effect that a stochastic resonance can have on a vibration isolation system. Rather than reducing the transmitted force, it is shown that it is possible to significantly mask the component of the force transmitted though the isolator, when the system is excited harmonically. This can be achieved by adding a very low intensity of random noise to the harmonic excitation force. The nonlinear mechanical vibration isolation system used in the study consists of a vertical linear spring in parallel with two horizontal springs, which are configured so that the potential energy of the system has a double-well. Prior to the analytical and numerical study, an experiment to demonstrate stochastic resonance in a mechanical system is described.

  8. Stochastic Resonance and Information Processing

    NASA Astrophysics Data System (ADS)

    Nicolis, C.

    2014-12-01

    A dynamical system giving rise to multiple steady states and subjected to noise and a periodic forcing is analyzed from the standpoint of information theory. It is shown that stochastic resonance has a clearcut signature on information entropy, information transfer and other related quantities characterizing information transduction within the system.

  9. 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.

  10. Sequential decision analysis for nonstationary stochastic processes

    NASA Technical Reports Server (NTRS)

    Schaefer, B.

    1974-01-01

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

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

    PubMed

    Chen, Yi; Hunter, Ian W

    2013-04-01

    Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy. PMID:23264003

  12. 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.

  13. Reducing sample variance: halo biasing, non-linearity and stochasticity

    NASA Astrophysics Data System (ADS)

    Gil-Marín, Héctor; Wagner, Christian; Verde, Licia; Jimenez, Raul; Heavens, Alan F.

    2010-09-01

    Comparing clustering of differently biased tracers of the dark matter distribution offers the opportunity to reduce the sample or cosmic variance error in the measurement of certain cosmological parameters. We develop a formalism that includes bias non-linearities and stochasticity. Our formalism is general enough that it can be used to optimize survey design and tracers selection and optimally split (or combine) tracers to minimize the error on the cosmologically interesting quantities. Our approach generalizes the one presented by McDonald & Seljak of circumventing sample variance in the measurement of f ≡ d lnD/d lna. We analyse how the bias, the noise, the non-linearity and stochasticity affect the measurements of Df and explore in which signal-to-noise regime it is significantly advantageous to split a galaxy sample in two differently biased tracers. We use N-body simulations to find realistic values for the parameters describing the bias properties of dark matter haloes of different masses and their number density. We find that, even if dark matter haloes could be used as tracers and selected in an idealized way, for realistic haloes, the sample variance limit can be reduced only by up to a factor σ2tr/σ1tr ~= 0.6. This would still correspond to the gain from a three times larger survey volume if the two tracers were not to be split. Before any practical application one should bear in mind that these findings apply to dark matter haloes as tracers, while realistic surveys would select galaxies: the galaxy-host halo relation is likely to introduce extra stochasticity, which may reduce the gain further.

  14. Stochastic resonance during a polymer translocation process

    NASA Astrophysics Data System (ADS)

    Mondal, Debasish; Muthukumar, Murugappan

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

  15. 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.

  16. Digital switching noise as a stochastic process

    NASA Astrophysics Data System (ADS)

    Boselli, Giorgio; Trucco, Gabriella; Liberali, Valentino

    2007-06-01

    Switching activity of logic gates in a digital system is a deterministic process, depending on both circuit parameters and input signals. However, the huge number of logic blocks in a digital system makes digital switching a cognitively stochastic process. Switching activity is the source of the so-called "digital noise", which can be analyzed using a stochastic approach. For an asynchronous digital network, we can model digital switching currents as a shot noise process, deriving both its amplitude distribution and its power spectral density. From spectral distribution of digital currents, we can also calculate the spectral distribution and the power of disturbances injected into the on-chip power supply lines.

  17. 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

  18. A Note on Boolean Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Fidaleo, Francesco

    2015-03-01

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

  19. Stochastic processes in muon ionization cooling

    NASA Astrophysics Data System (ADS)

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

    2004-02-01

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

  20. 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.

  1. Analysis of time series from stochastic processes

    PubMed

    Gradisek; Siegert; Friedrich; Grabec

    2000-09-01

    Analysis of time series from stochastic processes governed by a Langevin equation is discussed. Several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the Fokker-Planck equation. The coefficients are estimated directly from a time series. The applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting. PMID:11088809

  2. 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.

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Kunwar, Ambarish; Mogilner, Alexander

    2010-03-01

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

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

    PubMed 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

  6. 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.

  7. On strongly GA-convex functions and stochastic processes

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  8. Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Feng, Ju; Zhu, Weiqiu; Ying, Zuguang

    2010-01-01

    The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

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

    NASA Astrophysics Data System (ADS)

    Geist, E. L.

    2014-12-01

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

  10. 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.

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

    NASA Astrophysics Data System (ADS)

    Rowe, Michael; Afghan, Muhammad; Neiman, Alexander

    2004-03-01

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

  12. Decomposing generalized measurements into continuous stochastic processes

    SciTech Connect

    Varbanov, Martin; Brun, Todd A.

    2007-09-15

    One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with n outcomes, this information is captured by a real n-vector on an n-simplex, which obeys a simple classical stochastic evolution.

  13. 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.

  14. 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.

  15. 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

  16. Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

    NASA Astrophysics Data System (ADS)

    Vrecica, Teodor; Toledo, Yaron

    2015-04-01

    One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly

  17. Stochastic EM algorithm for nonlinear state estimation with model uncertainties

    NASA Astrophysics Data System (ADS)

    Zia, Amin; Kirubarajan, Thiagalingam; Reilly, James P.; Shirani, Shahram

    2004-01-01

    In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identification for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard

  18. Stochastic EM algorithm for nonlinear state estimation with model uncertainties

    NASA Astrophysics Data System (ADS)

    Zia, Amin; Kirubarajan, Thiagalingam; Reilly, James P.; Shirani, Shahram

    2003-12-01

    In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identification for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard

  19. 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. PMID:24718584

  20. 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.

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

    SciTech Connect

    Li, Xuefeng; Cao, Guangzhan; Liu, Hongjun

    2014-04-15

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

  2. Cognitive processing for nonlinear radar

    NASA Astrophysics Data System (ADS)

    Martone, Anthony; Ranney, Kenneth; Hedden, Abigail; Mazzaro, Gregory; McNamara, David

    2013-05-01

    An increasingly cluttered electromagnetic environment (EME) is a growing problem for radar systems. This problem is becoming critical as the available frequency spectrum shrinks due to growing wireless communication device usage and changing regulations. A possible solution to these problems is cognitive radar, where the cognitive radar learns from the environment and intelligently modifies the transmit waveform. In this paper, a cognitive nonlinear radar processing framework is introduced where the main components of this framework consist of spectrum sensing processing, target detection and classification, and decision making. The emphasis of this paper is to introduce a spectrum sensing processing technique that identifies a transmit-receive frequency pair for nonlinear radar. It will be shown that the proposed technique successfully identifies a transmit-receive frequency pair for nonlinear radar from data collected from the EME.

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2015-05-01

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

  5. 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.

  6. Neuronal Spike Trains and Stochastic Point Processes

    PubMed Central

    Perkel, Donald H.; Gerstein, George L.; Moore, George P.

    1967-01-01

    In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains. PMID:4292791

  7. 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

  8. 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

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

    PubMed

    Zhu, Wei-qiu; Ying, Zu-guang

    2004-11-01

    A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy. PMID:15495321

  10. A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Ying, Z. G.; Zhu, W. Q.

    2008-02-01

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

  11. 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.

  12. 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.

  13. 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.

  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. 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.

  16. 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.

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

    NASA Astrophysics Data System (ADS)

    Ryashko, Lev

    2015-11-01

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

  18. Renormalization group and instantons in stochastic nonlinear dynamics. From self-organized criticality to thermonuclear reactors

    NASA Astrophysics Data System (ADS)

    Volchenkov, D.

    2009-03-01

    Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications.

  19. Enhanced vibrational energy harvesting using nonlinear stochastic resonance

    NASA Astrophysics Data System (ADS)

    McInnes, C. R.; Gorman, D. G.; Cartmell, M. P.

    2008-12-01

    Stochastic resonance has seen wide application in the physical sciences as a tool to understand weak signal amplification by noise. However, this apparently counter-intuitive phenomenon does not appear to have been exploited as a tool to enhance vibrational energy harvesting. In this note we demonstrate that by adding periodic forcing to a vibrationally excited energy harvesting mechanism, the power available from the device is apparently enhanced over a mechanism without periodic forcing. In order to illustrate this novel effect, a conceptually simple, but plausible model of such a device is proposed to explore the use of stochastic resonance to enhance vibrational energy harvesting.

  20. 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.

  1. 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.

  2. 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.

  3. Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method

    NASA Astrophysics Data System (ADS)

    Er, GuoKang; Iu, VaiPan

    2011-09-01

    The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  5. 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.

  6. Robustness and computational aspects of nonlinear stochastic estimators and regulators. [extended Kalman filters in control

    NASA Technical Reports Server (NTRS)

    Safonov, M. G.; Athans, M.

    1977-01-01

    Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.

  7. 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.

  8. 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.

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

    PubMed Central

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2014-01-01

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

  10. 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.

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

    SciTech Connect

    Liang, Fei; Department of Mathematics, Xi An University of Science and Technology, Xi An 710054 ; 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.

  12. Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence

    NASA Astrophysics Data System (ADS)

    Liu, Qun; Chen, Qingmei

    2015-06-01

    In this paper, the deterministic and stochastic SIRS epidemic models with nonlinear incidence are introduced and investigated. For deterministic system, the basic reproductive number R0 is obtained. Furthermore, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and if R0 > 1, then there is a unique endemic equilibrium which is globally asymptotically stable. For stochastic system, to begin with, we verify that there is a unique global positive solution starting from the positive initial value. Then when R0 > 1, we prove that stochastic perturbations may lead the disease to extinction in scenarios where the deterministic system is persistent. When R0 ≤ 1, a result on fluctuation of the solution around the disease-free equilibrium of deterministic model is obtained under appropriate conditions. At last, if the intensity of the white noise is sufficiently small and R0 > 1, then there is a unique stationary distribution to stochastic system.

  13. 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

  14. Stochastic resonance during a polymer translocation process.

    PubMed

    Mondal, Debasish; Muthukumar, M

    2016-04-14

    We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly. PMID:27083746

  15. 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.

  16. Soil Erosion as a stochastic process

    NASA Astrophysics Data System (ADS)

    Casper, Markus C.

    2015-04-01

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

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

    SciTech Connect

    Kushner, Harold J.

    2012-08-15

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

  18. 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.

  19. 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

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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

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

    NASA Astrophysics Data System (ADS)

    Bashkirtseva, Irina; Ryashko, Lev

    2016-04-01

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

  6. 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.

  7. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  9. The probabilistic solution of stochastic oscillators with even nonlinearity under poisson excitation

    NASA Astrophysics Data System (ADS)

    Guo, Siu-Siu; Er, Guo-Kang

    2012-06-01

    The probabilistic solutions of nonlinear stochastic oscillators with even nonlinearity driven by Poisson white noise are investigated in this paper. The stationary probability density function (PDF) of the oscillator responses governed by the reduced Fokker-Planck-Kolmogorov equation is obtained with exponentialpolynomial closure (EPC) method. Different types of nonlinear oscillators are considered. Monte Carlo simulation is conducted to examine the effectiveness and accuracy of the EPC method in this case. It is found that the PDF solutions obtained with EPC agree well with those obtained with Monte Carlo simulation, especially in the tail regions of the PDFs of oscillator responses. Numerical analysis shows that the mean of displacement is nonzero and the PDF of displacement is nonsymmetric about its mean when there is even nonlinearity in displacement in the oscillator. Numerical analysis further shows that the mean of velocity always equals zero and the PDF of velocity is symmetrically distributed about its mean.

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-01-01

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

  12. 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.

  13. Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

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

    2011-02-01

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

  14. 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.

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

    NASA Technical Reports Server (NTRS)

    Fang, J.

    1994-01-01

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

  16. 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

  17. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

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

  19. Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

    NASA Astrophysics Data System (ADS)

    Popov, N. N.; Radchenko, V. P.

    2007-03-01

    An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained.

  20. Array enhanced stochastic resonance: Implications for signal processing

    SciTech Connect

    Inchiosa, M.E.; Bulsara, A.R.; Lindner, J.F.; Meadows, B.K.; Ditto, W.L.

    1996-06-01

    In computer simulations, we enhance the response of a {open_quote}{open_quote}stochastic resonator{close_quote}{close_quote} by coupling it into an array of identical resonators. We relate this array enhanced stochastic resonance (AESR) to the global spatiotemporal dynamics of the array and show how noise and coupling cooperate to organize spatial order, temporal periodicity, and peak output signal-to-noise ratio. We consider the application of AESR to signal processing. {copyright} {ital 1996 American Institute of Physics.}

  1. 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.

  2. Automatic Classification of Cellular Expression by Nonlinear Stochastic Embedding (ACCENSE).

    PubMed

    Shekhar, Karthik; Brodin, Petter; Davis, Mark M; Chakraborty, Arup K

    2014-01-01

    Mass cytometry enables an unprecedented number of parameters to be measured in individual cells at a high throughput, but the large dimensionality of the resulting data severely limits approaches relying on manual "gating." Clustering cells based on phenotypic similarity comes at a loss of single-cell resolution and often the number of subpopulations is unknown a priori. Here we describe ACCENSE, a tool that combines nonlinear dimensionality reduction with density-based partitioning, and displays multivariate cellular phenotypes on a 2D plot. We apply ACCENSE to 35-parameter mass cytometry data from CD8(+) T cells derived from specific pathogen-free and germ-free mice, and stratify cells into phenotypic subpopulations. Our results show significant heterogeneity within the known CD8(+) T-cell subpopulations, and of particular note is that we find a large novel subpopulation in both specific pathogen-free and germ-free mice that has not been described previously. This subpopulation possesses a phenotypic signature that is distinct from conventional naive and memory subpopulations when analyzed by ACCENSE, but is not distinguishable on a biaxial plot of standard markers. We are able to automatically identify cellular subpopulations based on all proteins analyzed, thus aiding the full utilization of powerful new single-cell technologies such as mass cytometry. PMID:24344260

  3. Automatic Classification of Cellular Expression by Nonlinear Stochastic Embedding (ACCENSE)

    PubMed Central

    Shekhar, Karthik; Brodin, Petter; Davis, Mark M.; Chakraborty, Arup K.

    2014-01-01

    Mass cytometry enables an unprecedented number of parameters to be measured in individual cells at a high throughput, but the large dimensionality of the resulting data severely limits approaches relying on manual “gating.” Clustering cells based on phenotypic similarity comes at a loss of single-cell resolution and often the number of subpopulations is unknown a priori. Here we describe ACCENSE, a tool that combines nonlinear dimensionality reduction with density-based partitioning, and displays multivariate cellular phenotypes on a 2D plot. We apply ACCENSE to 35-parameter mass cytometry data from CD8+ T cells derived from specific pathogen-free and germ-free mice, and stratify cells into phenotypic subpopulations. Our results show significant heterogeneity within the known CD8+ T-cell subpopulations, and of particular note is that we find a large novel subpopulation in both specific pathogen-free and germ-free mice that has not been described previously. This subpopulation possesses a phenotypic signature that is distinct from conventional naive and memory subpopulations when analyzed by ACCENSE, but is not distinguishable on a biaxial plot of standard markers. We are able to automatically identify cellular subpopulations based on all proteins analyzed, thus aiding the full utilization of powerful new single-cell technologies such as mass cytometry. PMID:24344260

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

    PubMed

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

    2002-01-01

    When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm. PMID:11965260

  5. Identifying different types of stochastic processes with the same spectra

    NASA Astrophysics Data System (ADS)

    Kim, Jong U.; Kish, Laszlo B.; Schmera, Gabor

    2005-05-01

    We propose a new way of pattern recognition which can distinguish different stochastic processes even if they have the same power density spectrum. Known crosscorrelation techniques recognize only the same realizations of a stochastic process in the two signal channels. However, crosscorrelation techniques do not work for recognizing independent realizations of the same stochastic process because their crosscorrelation function and cross spectrum are zero. A method able to do that would have the potential to revolutionize identification and pattern recognition, techniques, including sensing and security applications. The new method we are proposing is able to identify independent realizations of the same process, and at the same time, does not give false alarm for different processes which are very similar in nature. We demonstrate the method by using different realizations of two different types of random telegram signals, which are indistinguishable with respect to power density spectra (PDS). We call this method bispectrum correlation coefficient (BCC) technique.

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  7. 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

  8. Stochastic Equation of Fragmentation and Branching Processes Related to Avalanches

    NASA Astrophysics Data System (ADS)

    Beznea, Lucian; Deaconu, Madalina; Lupaşcu, Oana

    2016-02-01

    We give a stochastic model for the fragmentation phase of an avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by Bertoin. A fractal property of this process is emphasized. We also establish a specific stochastic differential equation of fragmentation. It turns out that specific branching Markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments. The results are obtained by combining analytic and probabilistic potential theoretical tools.

  9. Stochastic and Deterministic Assembly Processes in Subsurface Microbial Communities

    SciTech Connect

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

    2012-03-29

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

  10. Branching process in a stochastic extremal model

    NASA Astrophysics Data System (ADS)

    Manna, S. S.

    2009-08-01

    We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the number M of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions d=1 and 2. However on the scale-free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean-field like. Finally ⟨M⟩ has been made even smaller than two by probabilistically updating the mutation zone, which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.

  11. Branching process in a stochastic extremal model.

    PubMed

    Manna, S S

    2009-08-01

    We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the number M of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions d=1 and 2. However on the scale-free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean-field like. Finally M has been made even smaller than two by probabilistically updating the mutation zone, which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state. PMID:19792102

  12. 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.

  13. 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.

  14. Stochastic nature of domain nucleation process in magnetization reversal

    SciTech Connect

    Im, Mi-Young; Lee, S.-H.; Kim, D.-H.; Fischer, Peter; Shin, S.-C.

    2007-06-01

    Whether domain configurations that occur during magnetization reversal processes on a nanoscale are deterministic or nondeterministic is both fundamentally of great interest and technologically of utmost relevance[1]. However, due to the limited spatial resolution of the microscopic measurement techniques employed so far, no direct observation on the stochastic behavior of local domain nucleation during magnetization reversal in real space at the nanometer scale has yet been reported. In this work, we have investigated a stochastic nature of domain nucleation process during magnetization reversal by utilizing magnetic soft X-ray transmission microscopy with high spatial resolution of 15 nm [2]. The sample used in our study is CoCrPt alloy film,which is the promising candidate for high-density perpendicular magnetic recording media. Typical domain configurations of (Co{sub 83}Cr{sub 17}){sub 87}Pt{sub 13} taken at an applied magnetic field of 383 Oe during three successive hysteretic cycles are illustrated in Fig. 1. Interestingly enough, one clearly notes that the domain nucleation process of CoCrPt alloy film is not deterministic, but stochastic for repeated hysteretic cycles. The stochastic nature was quantitatively confirmed by correlation coefficient, where the correlation coefficients increase as magnetization reversal was progressed. Nanomagnetic simulations considering thermal fluctuations of the magnetic moments of the grains explains the stochastic nature of the domain nucleation behavior observed in CoCrPt alloy film.

  15. Models for interrupted monitoring of a stochastic process

    NASA Technical Reports Server (NTRS)

    Palmer, E.

    1977-01-01

    As computers are added to the cockpit, the pilot's job is changing from of manually flying the aircraft, to one of supervising computers which are doing navigation, guidance and energy management calculations as well as automatically flying the aircraft. In this supervisorial role the pilot must divide his attention between monitoring the aircraft's performance and giving commands to the computer. Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies.

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

    NASA Astrophysics Data System (ADS)

    Song, Jun; Niu, Yugang; Jia, Tinggang

    2016-09-01

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

  17. 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.

  18. 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.

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

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

  20. Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems

    NASA Astrophysics Data System (ADS)

    Li, Tao; Chen, Jian-bing; Li, Jie

    2016-03-01

    The point group identification (PGI) algorithm is proposed to determine the representative point sets in response analysis of nonlinear stochastic dynamic systems. The PGI algorithm is employed to identify point groups and their feature points in an initial point set by combining subspace clustering analysis and the graph theory. Further, the representative point set of the random-variate space is determined according to the minimum generalized F-discrepancy. The dynamic responses obtained by incorporating the algorithm PGI into the probability density evolution method (PDEM) are compared with those by the Monte Carlo simulation method. The investigations indicate that the proposed method can reduce the number of the representative points, lower the generalized F-discrepancy of the representative point set, and also ensure the accuracy of stochastic structural dynamic analysis.

  1. 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.

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

    PubMed

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

    2016-02-01

    In this paper, a fuzzy adaptive approach for stochastic strict-feedback nonlinear systems with quantized input signal is developed. Compared with the existing research on quantized input problem, the existing works focus on quantized stabilization, while this paper considers the quantized tracking problem, which recovers stabilization as a special case. In addition, uncertain nonlinearity and the unknown stochastic disturbances are simultaneously considered in the quantized feedback control systems. By putting forward a new nonlinear decomposition of the quantized input, the relationship between the control signal and the quantized signal is established, as a result, the major technique difficulty arising from the piece-wise quantized input is overcome. Based on fuzzy logic systems' universal approximation capability, a novel fuzzy adaptive tracking controller is constructed via backstepping technique. The proposed controller guarantees that the tracking error converges to a neighborhood of the origin in the sense of probability and all the signals in the closed-loop system remain bounded in probability. Finally, an example illustrates the effectiveness of the proposed control approach. PMID:25751885

  3. Extending Newtonian Dynamics to Include Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2009-01-01

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

  4. A Stochastic Cellular Automaton Model of Non-linear Diffusion and Diffusion with Reaction

    NASA Astrophysics Data System (ADS)

    Brieger, Leesa M.; Bonomi, Ernesto

    1991-06-01

    This article presents a stochastic cellular automaton model of diffusion and diffusion with reaction. The master equations for the model are examined, and we assess the difference between the implementation in which a single particle at a time moves (asynchronous dynamics) and one implementation in which all particles move simultaneously (synchronous dynamics). Biasing locally each particle's random walk, we alter the diffusion coefficients of the system. By appropriately choosing the biasing function, we can impose a desired non-linear diffusive behaviour in the model. We present an application of this model, adapted to include two diffusing species, two static species, and a chemical reaction in a prototypical simulation of carbonation in concrete.

  5. 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

  6. 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

  7. Stochastic processes with orthogonal polynomial eigenfunctions

    NASA Astrophysics Data System (ADS)

    Griffiths, Bob

    2009-12-01

    Markov processes which are reversible with either Gamma, Normal, Poisson or Negative Binomial stationary distributions in the Meixner class and have orthogonal polynomial eigenfunctions are characterized as being processes subordinated to well-known diffusion processes for the Gamma and Normal, and birth and death processes for the Poisson and Negative Binomial. A characterization of Markov processes with Beta stationary distributions and Jacobi polynomial eigenvalues is also discussed.

  8. Abductive learning of quantized stochastic processes with probabilistic finite automata.

    PubMed

    Chattopadhyay, Ishanu; Lipson, Hod

    2013-02-13

    We present an unsupervised learning algorithm (GenESeSS) to infer the causal structure of quantized stochastic processes, defined as stochastic dynamical systems evolving over discrete time, and producing quantized observations. Assuming ergodicity and stationarity, GenESeSS infers probabilistic finite state automata models from a sufficiently long observed trace. Our approach is abductive; attempting to infer a simple hypothesis, consistent with observations and modelling framework that essentially fixes the hypothesis class. The probabilistic automata we infer have no initial and terminal states, have no structural restrictions and are shown to be probably approximately correct-learnable. Additionally, we establish rigorous performance guarantees and data requirements, and show that GenESeSS correctly infers long-range dependencies. Modelling and prediction examples on simulated and real data establish relevance to automated inference of causal stochastic structures underlying complex physical phenomena. PMID:23277601

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

    PubMed Central

    Hornos, José Eduardo M.; Reinitz, John

    2015-01-01

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

  10. 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.

  11. 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.

  12. 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.

  13. Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

    NASA Astrophysics Data System (ADS)

    Torkamani, Shahab; Butcher, Eric A.

    2013-07-01

    The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

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

    DOE PAGESBeta

    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

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

    2016-04-01

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

  1. 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.

  2. 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

  3. 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

  4. Nonlinear stochastic model for the analysis of energy investment in the manufacturing sector of the United States

    SciTech Connect

    Pena-Taveras, M.S.

    1986-01-01

    The fast depletion of the non-renewable energy resources and the need to introduce new technologies into the manufacturing sector of the US economy require a better understanding of investment patterns for equipment and operational energy. In view of the above, and to provide a useful tool to the decision maker, a nonlinear, stochastic model is developed using the concepts of the Schumpeter Clock Model. The proposed model is validated using economic data for the period 1961-1980. It appears that the proposed model is a useful tool in the decision making process, where the manager, to maximize profit, must make choices between investing in equipment and the purchase of fuels and electricity.

  5. 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,

  6. 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.

  7. Penaeus orientolis prawn freshness rapid determination method based on electronic nose and non-linear stochastic resonance technique

    PubMed Central

    Wei, Liu; Yuanyuan, Han; Yanping, Cai; Jiaojiao, Jin; Guohua, Hui

    2015-01-01

    In this paper, Penaeus orientolis prawn freshness rapid determination method using electronic nose (e-nose) and non-linear data processing technique is studied. E-nose responses to prawns stored at 4°C are measured. Meanwhile, physical/chemical indexes (firmness, pH, total volatile basic nitrogen (TVB-N), total viable count (TVC), and human sensory evaluation) are examined to provide freshness references for e-nose analysis. E-nose measurement data is analyzed by principal component analysis (PCA), stochastic resonance (SR), and double-layered cascaded serial stochastic resonance (DCSSR). PCA partially discriminates prawns under different storage time. SR and DCSSR signal-to-noise ratio (SNR) spectrum eigen values discriminate prawns successfully. Multi-variables regressions (MVR) are conducted between physical/chemical indexes and SR/DCSSR output SNR minimal (SNR-Min) values. Results indicate that SNR-Min values present more significant linearity relation with physical/chemical indexes. Prawn freshness forecasting model is developed via Harris fitting regression on DCSSR SNR-Min values. Validating experiments demonstrate that forecasting accuracy of this model is 94.29%. PMID:25551520

  8. 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.

  9. Probabilistic solutions of some multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise

    NASA Astrophysics Data System (ADS)

    Er, Guo-Kang

    2014-04-01

    In this paper, the state-space-split method is extended for the dimension reduction of some high-dimensional Fokker-Planck-Kolmogorov equations or the nonlinear stochastic dynamical systems in high dimensions subject to external excitation which is the filtered Gaussian white noise governed by the second order stochastic differential equation. The selection of sub state variables and then the dimension-reduction procedure for a class of nonlinear stochastic dynamical systems is given when the external excitation is the filtered Gaussian white noise. The stretched Euler-Bernoulli beam with hinge support at two ends, point-spring supports, and excited by uniformly distributed load being filtered Gaussian white noise governed by the second-order stochastic differential equation is analyzed and numerical results are presented. The results obtained with the presented procedure are compared with those obtained with the Monte Carlo simulation and equivalent linearization method to show the effectiveness and advantage of the state-space-split method and exponential polynomial closure method in analyzing the stationary probabilistic solutions of the multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise.

  10. 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.

  11. 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.

  12. Random migration processes between two stochastic epidemic centers.

    PubMed

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

    2016-04-01

    We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. PMID:26877075

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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…

  1. Nonequilibrium dynamics of stochastic point processes with refractoriness

    SciTech Connect

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

    2010-08-15

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

  2. 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.

  3. A two-parameter stochastic process for Dansgaard-Oeschger events

    NASA Astrophysics Data System (ADS)

    Braun, H.; Ditlevsen, P.; Kurths, J.; Mudelsee, M.

    2011-09-01

    Various climatic processes are thought to evolve as rapid, shift-like events, which points at the presence of nonlinear dynamics. Time series analysis of nonlinear processes, however, is not trivial, for example, because of the difficulty in coming up with a realistic random process as a viable null hypothesis. In this methodology paper we construct a basic two-parameter process of shift-like excursions in an excitable system with a threshold. We demonstrate that this stochastic process, in comparison with a specific one-parameter process, can better reproduce main features of the waiting time histogram of abrupt glacial climate events, the Dansgaard-Oeschger events, as seen in two paleoclimatic proxy records, the North Greenland Ice core Project (NGRIP) ice core and the Sofular stalagmite δ18O records. We use the two-parameter process to test some arguments that were proposed in the ongoing discussion of a possible solar role in triggering Dansgaard-Oeschger events. Using our approach, we suggest for future studies to generate time series of random events which can serve as a more plausible null hypothesis for Monte Carlo based statistical tests on the regularity of shift-like processes such as Dansgaard-Oeschger events.

  4. Wavelet-Variance-Based Estimation for Composite Stochastic Processes.

    PubMed

    Guerrier, Stéphane; Skaloud, Jan; Stebler, Yannick; Victoria-Feser, Maria-Pia

    2013-09-01

    This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-based WV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic error's parameters of the sum of three first order Gauss-Markov processes by means of a sample of over 800,000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online. PMID:24174689

  5. Wavelet-Variance-Based Estimation for Composite Stochastic Processes

    PubMed Central

    Guerrier, Stéphane; Skaloud, Jan; Stebler, Yannick; Victoria-Feser, Maria-Pia

    2013-01-01

    This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-based WV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic error's parameters of the sum of three first order Gauss-Markov processes by means of a sample of over 800,000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online. PMID:24174689

  6. 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.

  7. 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. PMID:24012389

  8. 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.

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

    PubMed

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

    2016-03-01

    Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero. PMID:26940822

  10. 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

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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

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

    PubMed Central

    Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

    2016-01-01

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

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

    PubMed

    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

  18. Construction of the first-order stochastic nonlinear differential equations in the modeling of stimulated scattering of optical fields

    NASA Astrophysics Data System (ADS)

    Babin, Vasile D.; Grigore, Maria; Cojocaru, Laurentiu; Ersen, Simion; Moldovan, Adrian

    1998-07-01

    In this work we use a technique inspired by the inverse problem in the scattering theory, that is, the calculation of partial derivatives along the characteristic directions of the D'Alembert solution of the wave equation (Maxwell and Euler). In this way, we construct a system of stochastic non-linear differential equations. The analysis of this system, using algebraic invariants, gives more information in comparison with that given by Ghelfand-Levitan-Marcenko, in the inverse problem in the scattering theory.

  19. 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.

  20. 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.

  1. 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.

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

    SciTech Connect

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

    1994-07-01

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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    Geist, Eric L.

    2016-02-01

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

  13. 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.

  14. 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.

  15. Characterizing Nonlinear Heartbeat Dynamics within a Point Process Framework

    PubMed Central

    Chen, Z; Brown, EN; Barbieri, R

    2009-01-01

    Heartbeat intervals are known to have nonlinear and non-stationary dynamics. In this paper, we propose a nonlinear Volterra-Wiener expansion modeling of human heartbeat dynamics within a point process framework. Inclusion of second-order nonlinearity allows us to estimate dynamic bispectrum. The proposed probabilistic model was examined with two recorded heartbeat interval data sets. Preliminary results show that our model is beneficial to characterize the inherent nonlinearity of the heartbeat dynamics. PMID:19163282

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

    PubMed

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

    2012-06-01

    Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It is currently of particular concern as a possible mechanism for the spread of modified crop genes to wild populations. The hazard rate is the probability per time unit that such an escape takes place, given that it has not happened before. It is a quantitative measure of introgression risk that takes the stochastic elements inherent in introgression processes into account. We present a methodology to calculate the hazard rate for situations with time-varying gene flow from a crop to a large recipient wild population. As an illustration, several types of time-inhomogeneity are examined, including deterministic periodicity as well as random variation. Furthermore, we examine the effects of an extended fitness bottleneck of hybrids and backcrosses in combination with time-varying gene flow. It is found that bottlenecks decrease the hazard rate, but also slow down and delay its changes in reaction to changes in gene flow. Furthermore, we find that random variation in gene flow generates a lower hazard rate than analogous deterministic variation. We discuss the implications of our findings for crop management and introgression risk assessment. PMID:22178309

  17. Form, Function, and Information Processing in Stochastic Regulatory Networks

    NASA Astrophysics Data System (ADS)

    Wiggins, Chris

    2009-03-01

    The ability of a biological network to transduce signals, e.g., from chemical information about the abundance of small molecules into regulatory information about the rate of mRNA expression, is thwarted by numerous sources of noise. A great amount has been learned and conjectured in the last decade about the extent to which the form of a network --- specified by the connectivity and sign of regulation --- constrains or guides the networks function --- the particular noisy input-output relation(s) the network is capable of executing. In parallel, a great amount of research has sought to elucidate the role of inescapable or 'intrinsic' noise arising from the finite copy number of the participating molecules, which sets physical limits on information processing in small cells. I'll discuss how information theory may help illuminate these topics by providing a framework for quantifying function which does not rely on specifying the particular task to be performed a priori, as well as by providing a measure for the extent to which form follows function. En route I hope to show how stochastic chemical kinetics, modeled by the (linear) master equation describing the probability of copy counts for all reactants, benefits from the same spectral approaches fundamental to solving the (linear) diffusion equation.

  18. 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.

  19. 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.

  20. Probability-dependent H ∞ filtering for nonlinear stochastic systems with missing measurements and randomly occurring communication delays

    NASA Astrophysics Data System (ADS)

    Che, Yan; Shu, Huisheng; Yang, Hua; Ding, Derui

    2013-07-01

    In this article, the H ∞ filtering problem is investigated for a class of nonlinear stochastic systems with incomplete measurements. The considered incomplete measurements include both the missing measurements and the randomly occurring communication delays. By using a set of Kronecker delta functions, a unified measurement model is employed to describe the phenomena of random communication delays and missing measurements. The purpose of the problem addressed is to design an H ∞ filter such that, for all nonlinearities, incomplete measurements and external disturbances, the filtering error dynamics is exponentially mean-square stable and the H ∞-norm requirement is satisfied. A sufficient condition for the existence of the desired filter is established in terms of certain linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed filter scheme.

  1. Second order parametric processes in nonlinear silica microspheres.

    PubMed

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

    2008-04-25

    We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-Q nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally generate quantum entangled photon pairs. Practical issues regarding implementation of the nonlinear microsphere are also discussed. PMID:18518201

  2. Parametric Estimation of Stationary Stochastic Processes Under Indirect Observability

    NASA Astrophysics Data System (ADS)

    Azencott, R.; Beri, A.; Timofeyev, I.

    2011-07-01

    For many natural turbulent dynamic systems, observed high dimensional dynamic data can be approximated at slow time scales by a process X t driven by a systems of stochastic differential equations (SDEs). When one tries to estimate the parameters of this unobservable SDEs systems, there is a clear mismatch between the available data and the SDEs dynamics to be parametrized. Here, we formalize this Indirect Observability framework as follows. We consider an unobservable centered stationary Gaussian process X t with covariance function K( u, θ)= E[ X t X t+ u ], parametrized by an unknown vector θ which lies in a compact subset Θ of ℝ p . We assume that the only observable data are generated by centered stationary processes Yt^{\\varepsilon }, indexed by a scale separation parameter ɛ>0. These approximating processes have arbitrary probability distributions, exponentially decaying covariances, and are assumed to converge to X t in L 4 as ɛ→0. We show how to construct estimators of the underlying parameter vector θ which depend only on the observable data Yt^{\\varepsilon }, and converge to the true parameter values as ɛ→0. We study adaptive subsampling schemes involving [ N( ɛ)+ k( ɛ)]→∞ observations Vn = Y^{\\varepsilon }_{n Δ(\\varepsilon )} extracted from the approximating process Y^{\\varepsilon }t by subsampling at time intervals Δ( ɛ)→0. We focus on parameter estimators which are smooth functions of subsampled empirical covariance estimators hat{r}k(N,Δ) associated to non vanishing time lags k( ɛ)Δ( ɛ) tending to fixed positive limits as ɛ→0. We show that provided lim ɛ→0 N( ɛ)Δ( ɛ)=+∞, these subsampled approximate covariance estimators converge in L 2 to the true covariance function K( u, θ) of X t for all u, θ. Applying a generic version of the method of moments suitably boosted up by adequately adjusted multiple subsampling schemes, we show that this implies, in a very wide range of situations, the existence of

  3. A new class of non-linear stochastic population models with mass conservation.

    PubMed

    Kooijman, S A L M; Grasman, J; Kooi, B W

    2007-12-01

    We study the effects of random feeding, growing and dying in a closed nutrient-limited producer/consumer system, in which nutrient is fully conserved, not only in the mean, but, most importantly, also across random events. More specifically, we relate these random effects to the closest deterministic models, and evaluate the importance of the various times scales that are involved. These stochastic models differ from deterministic ones not only in stochasticity, but they also have more details that involve shorter times scales. We tried to separate the effects of more detail from that of stochasticity. The producers have (nutrient) reserve and (body) structure, and so a variable chemical composition. The consumers have only structure, so a constant chemical composition. The conversion efficiency from producer to consumer, therefore, varies. The consumers use reserve and structure of the producers as complementary compounds, following the rules of Dynamic Energy Budget theory. Consumers die at constant specific rate and decompose instantaneously. Stochasticity is incorporated in the behaviour of the consumers, where the switches to handling and searching, as well as dying are Poissonian point events. We show that the stochastic model has one parameter more than the deterministic formulation without time scale separation for conversions between searching and handling consumers, which itself has one parameter more than the deterministic formulation with time scale separation for these conversions. These extra parameters are the contributions of a single individual producer and consumer to their densities, and the ratio of the two, respectively. The tendency to oscillate increases with the number of parameters. The focus bifurcation point has more relevance for the asymptotic behaviour of the stochastic model than the Hopf bifurcation point, since a randomly perturbed damped oscillation exhibits a behaviour similar to that of the stochastic limit cycle particularly

  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 Mechanochemistry for Processive Motor Proteins: Kinesin Crouches before Sprinting.

    NASA Astrophysics Data System (ADS)

    Kim, Young C.

    2005-03-01

    Experiments by Block and coworkers (2003) applied assisting, resisting, and sideways loads F=(Fx,Fy,Fz) to single-molecules of kinesin as they moved along a microtubule (MT) taking steps of size d˜8.2 nm. The velocity, Vx, and the randomness were observed as functions of F and [ATP]. To uncover substeps and intermediate motions from such data, we have extended a discrete-state stochastic model, previously applied to kinesin^ 1 and myosin V,^2 to allow for the vectorial loading of processive motors by invoking a three- dimensional ``energy landscape'' with a potential φ(F).^3 The size of the attached bead and the resulting angle of the motor's tether relative to the track play a crucial role. The analysis for kinesin then indicates that on binding ATP (and, possibly, catalysing hydrolysis, etc.) the motor `crouches,' i.e., the point of attachment of the tether moves downwards (toward the MT) by 0.5-0.8 nm but forwards by only 0.1-0.2 nm, before completing a rapid swing of close to 8 nm. Unlike the scalar, Fx-only, analysis,^1 this is consistent with the observations of Higuchi and coworkers. Furthermore, assisting (i.e., forward) loads are opposed since the `upwards' component, Fz, is enhanced by ˜2 pN which reduces the velocity.1. M. E. Fisher and A. B. Kolomeisky, PNAS USA 98, 7748 (2001).2. A. B. Kolomeisky and M. E. Fisher, Biophys. J. 84, 1642 (2003).3. M. E. Fisher and Y. C. Kim, Biophys. J. 86, 527a, 2738-Plat. (2004).

  6. 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.

  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. Learning Process of a Stochastic Feed-Forward Neural Network

    NASA Astrophysics Data System (ADS)

    Fujiki, Sumiyoshi; Fujiki, Nahomi

    1995-03-01

    A positive reinforcement type learning algorithm is formulated for a stochastic feed-forward neural network by minimizing a relative entropic measure, and a learning equation similar to that of the Boltzmann machine is obtained. The learning of the network actually shows a similar result to that of the Boltzmann machine in the classification problems of AND and XOR, by numerical experiments.

  9. Nonlinear filtering for robust signal processing

    SciTech Connect

    Palmieri, F.

    1987-01-01

    A generalized framework for the description and design of a large class of nonlinear filters is proposed. Such a family includes, among others, the newly defined Ll-estimators, that generalize the order statistic filters (L-filters) and the nonrecursive linear filters (FIR). Such estimators are particularly efficient in filtering signals that do not follow gaussian distributions. They can be designed to restore signals and images corrupted by noise of impulsive type. Such filters are very appealing since they are suitable for being made robust against perturbations on the assumed model, or insensitive to the presence of spurious outliers in the data. The linear part of the filter is used to characterize their essential spectral behavior. It can be constrained to a given shape to obtain nonlinear filters that combine given frequency characteristics and noise immunity. The generalized nonlinear filters can also be used adaptively with the coefficients computed dynamically via LMS or RLS algorithms.

  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. Advanced Computer Simulations Of Nanomaterials And Stochastic Biological Processes

    NASA Astrophysics Data System (ADS)

    Minakova, Maria S.

    This dissertation consists of several parts. The first two chapters are devoted to of study of dynamic processes in cellular organelles called filopodia. A stochastic kinetics approach is used to describe non-equilibrium evolution of the filopodial system from nano- to micro scales. Dynamic coupling between chemistry and mechanics is also taken into account in order to investigate the influence of focal adhesions on cell motility. The second chapter explores the possibilities and effects of motor enhanced delivery of actin monomers to the polymerizing tips of filopodia, and how the steady-state filopodial length can exceed the limit set by pure diffusion. Finally, we also challenge the currently existing view of active transport and propose a new theoretical model that accurately describes the motor dynamics and concentration profiles seen in experiments in a physically meaningful way. The third chapter is a result of collaboration between three laboratories, as a part of Energy Frontier Research Center at the University of North Carolina at Chapel Hill. The work presented here unified the fields of synthetic chemistry, photochemistry, and computational physical chemistry in order to investigate a novel bio-synthetic compound and its energy transfer capabilities. This particular peptide-based design has never been studied via Molecular Dynamics with high precision, and it is the first attempt known to us to simulate the whole chromophore-peptide complex in solution in order to gain detailed information about its structural and dynamic features. The fourth chapter deals with the non-equilibrium relaxation induced transport of water molecules in a microemulsion. This problem required a different set of methodologies and a more detailed, all-atomistic treatment of the system. We found interesting water clustering effects and elucidated the most probable mechanism of water transfer through oil under the condition of saturated Langmuir monolayers. Together these

  12. Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

    NASA Astrophysics Data System (ADS)

    Ata, Metin; Kitaura, Francisco-Shu; Müller, Volker

    2015-02-01

    We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi N-body simulation at redshift z = 0, inferring the underlying dark matter density field from subsamples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-σ) from the posterior distribution up to scales of about k ˜ 1 h Mpc-1 in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood including a scale-dependent non-linear deterministic bias can yield reconstructions with power spectra deviating more than 10 per cent at k = 0.2 h Mpc-1. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.

  13. The distribution of species range size: a stochastic process.

    PubMed Central

    Gaston, Kevin J; He, Fangliang

    2002-01-01

    The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date. PMID:12028767

  14. Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed.

    PubMed

    Menzel, Andreas M

    2015-11-01

    Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient. PMID:26651690

  15. 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.

  16. 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.

  17. 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).

  18. Comparative analysis of nonlinear optofluidic processes in microdroplets

    NASA Astrophysics Data System (ADS)

    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.

  19. 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

  20. 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.

  1. Stochastic modeling of aphid population growth with nonlinear, power-law dynamics.

    PubMed

    Matis, James H; Kiffe, Thomas R; Matis, Timothy I; Stevenson, Douglass E

    2007-08-01

    This paper develops a deterministic and a stochastic population size model based on power-law kinetics for the black-margined pecan aphid. The deterministic model in current use incorporates cumulative-size dependency, but its solution is symmetric. The analogous stochastic model incorporates the prolific reproductive capacity of the aphid. These models are generalized in this paper to include a delayed feedback mechanism for aphid death. Whereas the per capita aphid death rate in the current model is proportional to cumulative size, delayed feedback is implemented by assuming that the per capita rate is proportional to some power of cumulative size, leading to so-called power-law dynamics. The solution to the resulting differential equations model is a left-skewed abundance curve. Such skewness is characteristic of observed aphid data, and the generalized model fits data well. The assumed stochastic model is solved using Kolmogrov equations, and differential equations are given for low order cumulants. Moment closure approximations, which are simple to apply, are shown to give accurate predictions of the two endpoints of practical interest, namely (1) a point estimate of peak aphid count and (2) an interval estimate of final cumulative aphid count. The new models should be widely applicable to other aphid species, as they are based on three fundamental properties of aphid population biology. PMID:17306309

  2. 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.

  3. Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

    NASA Astrophysics Data System (ADS)

    Yu, Zhaoxu; Li, Shugang; Li, Fangfei

    2016-01-01

    The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.

  4. 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. PMID:25794398

  5. Categorical Analysis of Human T Cell Heterogeneity with One-Dimensional Soli-Expression by Nonlinear Stochastic Embedding

    PubMed Central

    Cheng, Yang; Wong, Michael T.; van der Maaten, Laurens

    2016-01-01

    Rapid progress in single-cell analysis methods allow for exploration of cellular diversity at unprecedented depth and throughput. Visualizing and understanding these large, high-dimensional datasets poses a major analytical challenge. Mass cytometry allows for simultaneous measurement of >40 different proteins, permitting in-depth analysis of multiple aspects of cellular diversity. In this article, we present one-dimensional soli-expression by nonlinear stochastic embedding (One-SENSE), a dimensionality reduction method based on the t-distributed stochastic neighbor embedding (t-SNE) algorithm, for categorical analysis of mass cytometry data. With One-SENSE, measured parameters are grouped into predefined categories, and cells are projected onto a space composed of one dimension for each category. In contrast with higher-dimensional t-SNE, each dimension (plot axis) in One-SENSE has biological meaning that can be easily annotated with binned heat plots. We applied One-SENSE to probe relationships between categories of human T cell phenotypes and observed previously unappreciated cellular populations within an orchestrated view of immune cell diversity. The presentation of high-dimensional cytometric data using One-SENSE showed a significant improvement in distinguished T cell diversity compared with the original t-SNE algorithm and could be useful for any high-dimensional dataset. PMID:26667171

  6. Categorical Analysis of Human T Cell Heterogeneity with One-Dimensional Soli-Expression by Nonlinear Stochastic Embedding.

    PubMed

    Cheng, Yang; Wong, Michael T; van der Maaten, Laurens; Newell, Evan W

    2016-01-15

    Rapid progress in single-cell analysis methods allow for exploration of cellular diversity at unprecedented depth and throughput. Visualizing and understanding these large, high-dimensional datasets poses a major analytical challenge. Mass cytometry allows for simultaneous measurement of >40 different proteins, permitting in-depth analysis of multiple aspects of cellular diversity. In this article, we present one-dimensional soli-expression by nonlinear stochastic embedding (One-SENSE), a dimensionality reduction method based on the t-distributed stochastic neighbor embedding (t-SNE) algorithm, for categorical analysis of mass cytometry data. With One-SENSE, measured parameters are grouped into predefined categories, and cells are projected onto a space composed of one dimension for each category. In contrast with higher-dimensional t-SNE, each dimension (plot axis) in One-SENSE has biological meaning that can be easily annotated with binned heat plots. We applied One-SENSE to probe relationships between categories of human T cell phenotypes and observed previously unappreciated cellular populations within an orchestrated view of immune cell diversity. The presentation of high-dimensional cytometric data using One-SENSE showed a significant improvement in distinguished T cell diversity compared with the original t-SNE algorithm and could be useful for any high-dimensional dataset. PMID:26667171

  7. 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.

  8. 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

  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. 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.

  12. Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

    PubMed

    Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

    2016-01-01

    Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169

  13. Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models

    PubMed Central

    Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

    2016-01-01

    Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169

  14. Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.

    2010-01-01

    Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

  15. Replication timing and its emergence from stochastic processes

    PubMed Central

    Bechhoefer, John; Rhind, Nicholas

    2012-01-01

    The temporal organization of DNA replication has puzzled cell biologists since before the mechanism of replication was understood. The realization that replication timing correlates with important features, such as transcription, chromatin structure and genome evolution, and is misregulated in cancer and aging has only deepened the fascination. Many ideas about replication timing have been proposed, but most have been short on mechanistic detail. However, recent work has begun to elucidate basic principles of replication timing. In particular, mathematical modeling of replication kinetics in several systems has shown that the reproducible replication timing patterns seen in population studies can be explained by stochastic origin firing at the single-cell level. This work suggests that replication timing need not be controlled by a hierarchical mechanism that imposes replication timing from a central regulator, but instead results from simple rules that affect individual origins. PMID:22520729

  16. Distinguishing between discreteness effects in stochastic reaction processes.

    PubMed

    Haruna, Taichi

    2015-05-01

    The effect of discreteness on stochastic dynamics of chemically reacting systems is studied analytically. We apply the scheme bridging the chemical master equation and the chemical Fokker-Planck equation by a parameter representing the degree of discreteness previously proposed by the author for two concrete systems. One is an autocatalytic reaction system, and the other is a branching-annihilation reaction system. It is revealed that the change in characteristic time scales when discreteness is decreased is yielded between the two systems for different reasons. In the former system, it originates from the boundaries where one of the chemical species is zero, whereas in the latter system, it is due to modification of the most probable extinction path caused by discreteness loss. PMID:26066219

  17. Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

    NASA Astrophysics Data System (ADS)

    de Souza, David R.; Tomé, Tânia

    2010-03-01

    We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S → I → R → S (SIRS). The open process S → I → R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations.

  18. 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.

  19. 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. PMID:26216975

  20. 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

  1. 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.

  2. Sensitivity of membranes to their environment. Role of stochastic processes.

    PubMed Central

    Offner, F F

    1984-01-01

    Ionic flow through biomembranes often exhibits a sensitivity to the environment, which is difficult to explain by classical theory, that usually assumes that the free energy available to change the membrane permeability results from the environmental change acting directly on the permeability control mechanism. This implies, for example, that a change delta V in the trans-membrane potential can produce a maximum free energy change, delta V X q, on a gate (control mechanism) carrying a charge q. The analysis presented here shows that when stochastic fluctuations are considered, under suitable conditions (gate cycle times rapid compared with the field relaxation time within a channel), the change in free energy is limited, not by the magnitude of the stimulus, but by the electrochemical potential difference across the membrane, which may be very much greater. Conformational channel gates probably relax more slowly than the field within the channel; this would preclude appreciable direct amplification of the stimulus. It is shown, however, that the effect of impermeable cations such as Ca++ is to restore the amplification of the stimulus through its interaction with the electric field. The analysis predicts that the effect of Ca++ should be primarily to affect the number of channels that are open, while only slightly affecting the conductivity of an open channel. PMID:6093903

  3. 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.

  4. Stochasticity and Determinism: How Density-Independent and Density-Dependent Processes Affect Population Variability

    PubMed Central

    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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. Punctuated Equilibrium Behavior and Zipf's Law in the Stochastic Branching Process Model of Phylogeny

    NASA Astrophysics Data System (ADS)

    Matsumoto, T.; Aizawa, Y.

    1999-11-01

    A stochastic branching process model of phylogeny with niche space and interactions among species is considered. For an intermediate interaction range, the time series of diversity has long periods of stasis divided by periods of rapid increase. The concept of monophyletic size is introduced, and it is shown that the size distribution obeys Zipf's law.

  10. 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

  11. 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

  12. 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.

  13. Error variance-constrained ℋ∞ filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

    NASA Astrophysics Data System (ADS)

    Ma, Lifeng; Bo, Yuming; Zhou, Yuchen; Guo, Zhi

    2012-12-01

    This article is concerned with the robust ℋ∞ filtering problem for a class of time-varying nonlinear stochastic systems with error variance constraint. The stochastic nonlinearities considered are quite general, which contain several well-studied stochastic nonlinear systems as special cases. The purpose of the filtering problem is to design a filter which is capable of achieving the pre-specified ℋ∞ performance and meanwhile guaranteeing a minimised upper-bounded on the filtering error variance. By means of the adjoint system method, a necessary and sufficient condition for satisfying the ℋ∞ constraint is first given, expressed as a forward Riccati-like difference equation. Then an upper-bound on the variance of filtering error system is given, guaranteeing the error variance is not more than a certain value at each sampling instant. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time, hence is suitable for online computation. A numerical example is presented finally to show the effectiveness and applicability of the proposed method.

  14. 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

  15. Non-Markov stochastic processes satisfying equations usually associated with a Markov process

    NASA Astrophysics Data System (ADS)

    McCauley, J. L.

    2012-04-01

    There are non-Markov Ito processes that satisfy the Fokker-Planck, backward time Kolmogorov, and Chapman-Kolmogorov equations. These processes are non-Markov in that they may remember an initial condition formed at the start of the ensemble. Some may even admit 1-point densities that satisfy a nonlinear 1-point diffusion equation. However, these processes are linear, the Fokker-Planck equation for the conditional density (the 2-point density) is linear. The memory may be in the drift coefficient (representing a flow), in the diffusion coefficient, or in both. We illustrate the phenomena via exactly solvable examples. In the last section we show how such memory may appear in cooperative phenomena.

  16. 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…

  17. Predictive Aspects of a Stochastic Model for Citation Processes.

    ERIC Educational Resources Information Center

    Glanzel, W.; Schubert, A.

    1995-01-01

    A statistical model for citation processes is presented as a particular version of a nonhomogenous birth process. The mean value function and special transition probabilities, which can readily be calculated on the basis of known and estimated parameters, give essential information on the change of citation impact in time. (10 references) (KRN)

  18. 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

  19. 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

  20. Nonlinearity in the dynamics of photoinduced nucleation process.

    PubMed

    Ishida, Kunio; Nasu, Keiichiro

    2008-03-21

    Coherent nonlinear dynamics of photoinduced cooperative phenomena at 0 K is studied by numerical calculations on a model of molecular crystals. We found that the photoinduced nucleation process is triggered only when a certain amount of excitation energy is supplied in a narrow part of the system; i.e., there exists the smallest size of the cluster of excited molecules which makes the nucleation possible. As a result, the portion of the cooperatively converted molecules is nonlinearly dependent on the photoexcitation strength, which has been observed in various materials. PMID:18517805

  1. 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.

  2. Mapping Rule-Based And Stochastic Constraints To Connection Architectures: Implication For Hierarchical Image Processing

    NASA Astrophysics Data System (ADS)

    Miller, Michael I.; Roysam, Badrinath; Smith, Kurt R.

    1988-10-01

    Essential to the solution of ill posed problems in vision and image processing is the need to use object constraints in the reconstruction. While Bayesian methods have shown the greatest promise, a fundamental difficulty has persisted in that many of the available constraints are in the form of deterministic rules rather than as probability distributions and are thus not readily incorporated as Bayesian priors. In this paper, we propose a general method for mapping a large class of rule-based constraints to their equivalent stochastic Gibbs' distribution representation. This mapping allows us to solve stochastic estimation problems over rule-generated constraint spaces within a Bayesian framework. As part of this approach we derive a method based on Langevin's stochastic differential equation and a regularization technique based on the classical autologistic transfer function that allows us to update every site simultaneously regardless of the neighbourhood structure. This allows us to implement a completely parallel method for generating the constraint sets corresponding to the regular grammar languages on massively parallel networks. We illustrate these ideas by formulating the image reconstruction problem based on a hierarchy of rule-based and stochastic constraints, and derive a fully parallelestimator structure. We also present results computed on the AMT DAP500 massively parallel digital computer, a mesh-connected 32x32 array of processing elements which are configured in a Single-Instruction, Multiple Data stream architecture.

  3. 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.

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

    PubMed

    Zausner, Tobi

    2007-01-01

    Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life. PMID:17173732

  5. 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.

  6. 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.

  7. 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. PMID:18233821

  8. 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.

  9. Stochastic Process Model of Physiological Regeneration, Fertility and Aging

    NASA Astrophysics Data System (ADS)

    Akushevich, Igor; Manton, Kenneth

    2003-03-01

    A state space model of human birth, death processes is presented based upon a generalization of the Fokker-Planck-Kolmogorov (F-P-K) diffusion equation. In the model it is assumed that males and females are linked through the birth process and that birth and fetal growth, itself possibly described by a F-P-K equation, generates new probability mass in the population state space. Specific case of radiation as a risk factor is considered and analyzed. Life time generator is constructed on the basis of the developed model and its results are compared with existent physiological longitudinal data.

  10. 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.

  11. 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. PMID:25059312

  12. 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}

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

    NASA Technical Reports Server (NTRS)

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

    1980-01-01

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

  14. 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.

  15. Fractional Klein-Gordon Equations and Related Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Garra, Roberto; Orsingher, Enzo; Polito, Federico

    2014-03-01

    This paper presents finite-velocity random motions driven by fractional Klein-Gordon equations of order α in (0,1] . A key tool in the analysis is played by the McBride's theory which converts fractional hyper-Bessel operators into Erdélyi-Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein-Gordon equation. The distribution of the fractional telegraph process for α = 1 coincides with that of the classical telegraph process and its driving equation converts into the homogeneous Klein-Gordon equation. Fractional planar random motions at finite velocity are also investigated, the corresponding distributions obtained as well as the explicit form of the governing equations. Fractionality is reflected into the underlying random motion because in each time interval a binomial number of deviations B(n,α ) (with uniformly-distributed orientation) are considered. The parameter n of B(n,α ) is itself a random variable with fractional Poisson distribution, so that fractionality acts as a subsampling of the changes of direction. Finally the behaviour of each coordinate of the planar motion is examined and the corresponding densities obtained. Extensions to N -dimensional fractional random flights are envisaged as well as the fractional counterpart of the Euler-Poisson-Darboux equation to which our theory applies.

  16. A non-linear model of economic production processes

    NASA Astrophysics Data System (ADS)

    Ponzi, A.; Yasutomi, A.; Kaneko, K.

    2003-06-01

    We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

  17. 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.

  18. 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

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

    PubMed

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

    2016-03-01

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

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

    NASA Astrophysics Data System (ADS)

    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.

  1. 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

  2. Reliability and maintenance in European nuclear power plants: A structural analysis of a controlled stochastic process

    SciTech Connect

    Sturm, R.

    1991-01-01

    Two aspects of performance are of main concern: plant availability and plant reliability (defined as the conditional probability of an unplanned shutdown). The goal of the research is a unified framework that combines behavioral models of optimizing agents with models of complex technical systems that take into account the dynamic and stochastic features of the system. In order to achieve this synthesis, two liens of work are necessary. One line requires a deeper understanding of complex production systems and the type of data they give rise to; the other line involves the specification and estimation of a rigorously specified behavioral model. Plant operations are modeled as a controlled stochastic process, and the sequence of up and downtime spells is analyzed during failure time and point process models. Similar to work on rational expectations and structural econometric models, the behavior model of how the plant process is controlled is formulated at the level of basic processes, i.e., the objective function of the plant manager, technical constraints, and stochastic disturbances.

  3. 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.

  4. An adaptive algorithm for simulation of stochastic reaction-diffusion processes

    SciTech Connect

    Ferm, Lars Hellander, Andreas Loetstedt, Per

    2010-01-20

    We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.

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

    NASA Technical Reports Server (NTRS)

    Rao, S. S.

    1984-01-01

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

  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. PMID:26496618

  7. The Castalia stochastic generator and its applications to multivariate disaggregation of hydro-meteorological processes

    NASA Astrophysics Data System (ADS)

    Venediki, Anna; Giannoulis, Savvas; Ioannou, Christos; Malatesta, Lamprini; Theodoropoulos, Georgios; Tsekouras, Georgios; Dialynas, Yiannis G.; Papalexiou, Simon Michael; Efstratiadis, Andreas; Koutsoyiannis, Demetris

    2013-04-01

    Castalia is a software system that performs multivariate stochastic simulation preserving essential marginal statistics, specifically mean value, standard deviation and skewness, as well as joint second order statistics, namely auto- and cross-correlation. Furthermore, Castalia reproduces long-term persistence. It follows a disaggregation approach, starting from the annual time scale and proceeding to finer scales such as monthly and daily. To assess the performance of the Castalia system we test it for several hydrometeorological processes such as rainfall, sunshine duration, temperature and wind speed. To this aim we retrieve time series of these processes from a large database of daily records and we estimate their statistical properties, including long-term persistence. We generate synthetic time series using the Castalia software and we examine its efficiency in reproducing the important statistical properties of the observed data. Acknowledgment: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA).

  8. 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.

  9. 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. PMID:25733885

  10. 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

  11. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

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

    PubMed

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

    2015-10-01

    The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈10(4)). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications. PMID:26565363

  14. 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.

  15. Synchronization of noisy systems by stochastic signals

    SciTech Connect

    Neiman, A.; Schimansky-Geier, L.; Moss, F.; Schimansky-Geier, L.; Shulgin, B.; Collins, J.J.

    1999-07-01

    We study, in terms of synchronization, the {ital nonlinear response} of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level{emdash}this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train. {copyright} {ital 1999} {ital The American Physical Society}

  16. 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

  17. Using Numerical Solutions in the Fourier Method for the Fokker-Planck-Kolmogorov Equation in the Analysis of First-Order Stochastic Nonlinear Systems for Nonlinear Detectors

    NASA Astrophysics Data System (ADS)

    Nevolin, V. I.

    2003-04-01

    We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker-Planck-Kolmogorov (FPK) equations in the form of series of functions over Hermite-Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.

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

    PubMed Central

    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 (r2<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 a

  19. 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.

  20. 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.

  1. 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. PMID:24755621

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

    SciTech Connect

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

    2007-09-01

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

  3. 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

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

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

    PubMed Central

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

    2014-01-01

    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. PMID:24880267

  10. 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.

  11. 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

  12. Nonlinear effects of consumer density on multiple ecosystem processes.

    PubMed

    Klemmer, Amanda J; Wissinger, Scott A; Greig, Hamish S; Ostrofsky, Milton L

    2012-07-01

    1. In the face of human-induced declines in the abundance of common species, ecologists have become interested in quantifying how changes in density affect rates of biophysical processes, hence ecosystem function. We manipulated the density of a dominant detritivore (the cased caddisfly, Limnephilus externus) in subalpine ponds to measure effects on the release of detritus-bound nutrients and energy. 2. Detritus decay rates (k, mass loss) increased threefold, and the loss of nitrogen (N) and phosphorus (P) from detrital substrates doubled across a range of historically observed caddisfly densities. Ammonium and total soluble phosphorus concentrations in the water column also increased with caddisfly density on some dates. Decay rates, nutrient release and the change in total detritivore biomass all exhibited threshold or declining responses at the highest densities. 3. We attributed these threshold responses in biophysical processes to intraspecific competition for limiting resources manifested at the population level, as density-dependent per-capita consumption, growth, development and case : body size in caddisflies was observed. Moreover, caddisflies increasingly grazed on algae at high densities, presumably in response to limiting detrital resources. 4. These results provide evidence that changes in population size of a common species will have nonlinear, threshold effects on the rates of biophysical processes at the ecosystem level. Given the ubiquity of negative density dependence in nature, nonlinear consumer density-ecosystem function relationships should be common across species and ecosystems. PMID:22339437

  13. Nonlinear processes reinforce extreme Indian Ocean Dipole events.

    PubMed

    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

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. Kernel-based regression of drift and diffusion coefficients of stochastic processes

    NASA Astrophysics Data System (ADS)

    Lamouroux, David; Lehnertz, Klaus

    2009-09-01

    To improve the estimation of drift and diffusion coefficients of stochastic processes in case of a limited amount of usable data due to e.g. non-stationarity of natural systems we suggest to use kernel-based instead of histogram-based regression. We propose a method for bandwidth selection and compare it to a widely used cross-validation method. Kernel-based regression reveals an enhanced ability to estimate drift and diffusion especially for a small amount of data. This allows one to improve resolvability of changes in complex dynamical systems as evidenced by an exemplary analysis of electroencephalographic data recorded from a human epileptic brain.

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

    NASA Astrophysics Data System (ADS)

    Romanowicz, Renata; Karamuz, Emilia; Kochanek, Krzysztof

    2014-05-01

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

  2. A simple nonlinear PD controller for integrating processes.

    PubMed

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

    2014-01-01

    Many industrial processes are found to be integrating in nature, for which widely used Ziegler-Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system. PMID:24094507

  3. 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

  4. 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.

  5. Nonlinear Signal Processing Using Fiber-Optics Neurograms

    NASA Astrophysics Data System (ADS)

    Szu, Harold

    1986-02-01

    A novel optical device for nonlinear signal processing is described based upon the following observations: (a) A phase space for signal processing is identified with a time-frequency joint representation (TFJR) that appears almost everywhere naturally, for example in bats, in music, etc. (b) A sudden slow down mechanism is responsible for the transition from a phase coherent-to-incoherent wavefront and provides us the sharpest tone transduction from a Bekesy traveling wave in a model of the inner ear. The cause of the slowdown is physically identified to be due to three forces. This has been used to derive a cubic deceleration polynomial responsible for a cusp bifurcation phenomenon which occur for every tone transducted along the nonuniform elastic membrane. The liquid-filled inner ear cochlea channel is divided by the membrane into an upper duct that has hair cells for the forward sound-generated flow and the lower duct for the backward balance-return flow.

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. Stochastic modeling of the rainfall-runoff process for nonpoint source pollutant load estimation

    SciTech Connect

    Dickey, R.O.

    1989-01-01

    A stochastic simulation methodology was developed for the rainfall runoff process to assist in the assessment of nonpoint source pollutant loads, particularly for ungaged watersheds where there is a scarcity or complete lack of historical data. The methodology was developed based on simulating individual rainfall-runoff events. A simulation model employed a rainfall simulator to stochastically generate rainfall event characteristics for input into basin hydrologic transformation functions which then predicted the corresponding runoff hydrograph characteristics. Also addressed was the impact of limited data availability on the ability to model the rainfall-runoff process. An evaluation was conducted of the degree to which committing valuable resources to expand the data base would provide measurable improvement in model results. Specifically, the probability of achieving certain levels of accuracy with the simulation model was statistically assessed as a function of the number of observed rainfall-runoff events used for model development. The probability of monitoring various numbers of rainfall-runoff events in specified time intervals was also established as an aid for planning field monitoring studies. The simulation methodology was applied to a study watershed in the Lake Ray Hubbard reservoir drainage basin near Dallas, Texas. Regional rainfall characteristics were established using historical hourly data from the Federal Aviation Administration rain gage at Love Field Airport in Dallas, Texas. Hourly rainfall data were resolved into individual rainfall events and probability density functions were identified for event volume, time between events, and event duration.

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

    PubMed Central

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

    2015-01-01

    ABSTRACT Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds (<10 mm s−1) and then plateaus for higher values. Typical latencies are >1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models. PMID:25792753

  12. Field experimental evidence that stochastic processes predominate in the initial assembly of bacterial communities.

    PubMed

    Hao, Yi-Qi; Zhao, Xin-Feng; Zhang, Da-Yong

    2016-06-01

    To assess the relative importance of environmental selection, dispersal and stochastic processes in structuring ecological communities, we conducted a bacterial community assembly experiment using microcosms filled with sterile liquid medium under field conditions in the Inner Mongolian grasslands. Multiple replicate microcosms containing different carbon substrates were placed at nine locations across three spatial scales (10, 300 and 10 000 m distance between locations) in such a way that the environment of microcosms varies independently of the geographical distance. The operational taxonomic units within the experimental communities were assessed via the terminal restriction fragment length polymorphism techniques on the 10th and 17th days after the onset of the experiment. We found no evidence of distance decay in community similarity, and communities within a given location were more similar to each other regardless of environment than communities at other locations within the same spatial scale. Variance partitioning indicated that location explained more compositional variation in microbial communities than environment, particularly on the 17th day, despite that environment and location in combination could only explain less than half of the total variation. These results suggest that bacterial dispersal is not limited by distance in this experiment, and community assembly in microcosms is not environmentally determined but governed by stochastic processes. PMID:25809418

  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. 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.

  15. 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.

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

    PubMed

    Giordano, Peter J

    2014-06-01

    An important objective of personality psychology is to provide compelling descriptions and explanations of intraindividual personality dynamics that capture the unique qualities of persons. Among contemporary Western personality theories, the Five-Factor Model enjoys prominence in describing individual differences in personality traits. It falls short, however, in its ability to work with intraindividual personality function. This article argues that classical Confucianism, originating 2500 years ago in mainland China, offers Western personality psychologists important theoretical resources for capturing the complex and dynamic processes inherent in human personality. The Confucian perspective emphasizes a behaviorally anchored, continuous, stochastic, process-oriented understanding of the self as relationally constructed and proposes an elegant description of the relational virtuosity of exemplary persons. The article concludes with five characteristics of a Confucian inspired model of personality and questions the viability of a universal theory of personality. PMID:24101234

  17. 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.

  18. 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.

  19. Multivariate moment closure techniques for stochastic kinetic models.

    PubMed

    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. PMID:26342359

  20. 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.

  1. 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.

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

    SciTech Connect

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

    2006-12-31

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

  3. Using stochastic population process models to predict the impact of climate change

    NASA Astrophysics Data System (ADS)

    van der Meer, Jaap; Beukema, J. J.; Dekker, Rob

    2013-09-01

    More than ten years ago a paper was published in which stochastic population process models were fitted to time series of two marine polychaete species in the western Wadden Sea, The Netherlands (Van der Meer et al., 2000). For the predator species, model fits pointed to a strong effect of average sea surface winter temperature on the population dynamics, and one-year ahead model forecasts correlated well with true observations (r = 0.90). During the last decade a pronounced warming of the area occurred. Average winter temperature increased with 0.9 °C. Here we show that despite the high goodness-of-fit whilst using the original dataset, predictive capability of the models for the recent warm period was poor.

  4. 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.

  5. 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.

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

    NASA Technical Reports Server (NTRS)

    Menga, G.

    1975-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Robinson, P. A.; Roy, N.

    2015-06-01

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

  8. Ionic and electronic processes in non-linear optical crystals

    NASA Astrophysics Data System (ADS)

    Ogorodnikov, Igor N.; Yakovlev, Victor Yu.

    2005-01-01

    The paper presents the results of a study of the formation and decay of lattice defects in nonlinear optical crystals of NH4H2PO4 (ADP), KH2PO4 (KDP), Li2B4O7 (LTB) and LiB3O5 (LBO) with a sublattice of mobile hydrogen (ADP, KDP) and lithium (LTB, LBO) cations. By means of the luminescent and absorption optical spectroscopy with (the) a nanosecond time resolution under excitation with an electron beam, it was revealed that the optical absorption of these crystals in the visible and UV spectral ranges is produced by optical hole-transitions from the local defect level to the valence band states. The valence band density of the states determines the optical absorption spectral profile, and the relaxation kinetics is rated by the interdefect radiationless tunnel recombination between the trapped hole center and the H0 and Li0 electron trapped centers. At 290 K, the H0 and Li0 centers are subject to thermally stimulated migration. All manifestations of a radiative recombination observed in these crystals are accounted for by the involvement of additional electronic and hole centers of a different nature in the recombination process.

  9. Nonlinear dynamics of global atmospheric and Earth system processes

    NASA Technical Reports Server (NTRS)

    Saltzman, Barry

    1993-01-01

    During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.

  10. 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.

  11. 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.

  12. 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

  13. 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

  14. 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.

  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. Renewal stochastic processes with correlated events: Phase transitions along time evolution

    NASA Astrophysics Data System (ADS)

    Velázquez, Jorge; Robledo, Alberto

    2011-03-01

    We consider renewal stochastic processes generated by nonindependent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting degrees of freedom. Based on this fact we look briefly into the less-known case of processes that display phase transitions along time. When the density distribution ψn(t) for the occurrence of the nth event at time t is considered to be a partition function, of a “microcanonical” type for n “degrees of freedom” at fixed “energy” t, one obtains a set of four partition functions of which that for the generating function variable z and Laplace transform variable ɛ, conjugate to n and t, respectively, plays a central role. These partition functions relate to each other in the customary way and in accordance to the precepts of large deviations theory, while the entropy, or Massieu potential, derived from ψn(t) satisfies an Euler relation. We illustrate this scheme first for an ordinary renewal process of events generated by a simple exponential waiting-time distribution ψ(t). Then we examine a process modeled after the so-called Hamiltonian mean-field model that is representative of agents that perform a repeated task with an associated outcome, such as an opinion poll. When a sequence of (many) events takes place in a sufficiently short time the process exhibits clustering of the outcome, but for larger times the process resembles that of independent events. The two regimes are separated by a sharp transition, technically of the second order. Finally we point out the existence of a similar scheme for random-walk processes.

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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. PMID:24696664

  4. Preliminary investigation of the frequency response and distortion properties of nonlinear image processing algorithms

    NASA Astrophysics Data System (ADS)

    Wells, Jered R.; Dobbins, James T.

    2013-03-01

    Assessment of the resolution properties of nonlinear imaging systems is a useful but challenging task. While the modulation transfer function (MTF) fully describes contrast resolution as a function of spatial frequency for linear systems, an equivalent metric does not exist for systems with significant nonlinearity. Therefore, this preliminary investigation attempts to classify and quantify the amount of scaling and distortion imposed on a given image signal as the result of a nonlinear process (nonlinear image processing algorithm). As a proof-of-concept, a median filter is assessed in terms of its principle frequency response (PFR) and distortion response (DR) functions. These metrics are derived in frequency space using a sinusoidal basis function, and it is shown that, for a narrow-band sinusoidal input signal, the scaling and distortion properties of the nonlinear filter are described exactly by PFR and DR, respectively. The use of matched sinusoidal basis and input functions accurately reveals the frequency response to long linear structures of different scale. However, when more complex (multi-band) input signals are considered, PFR and DR fail to adequately characterize the frequency response due to nonlinear interaction effects between different frequency components during processing. Overall, the results reveal the context-dependent nature of nonlinear image processing algorithm performance, and they emphasize the importance of the basis function choice in algorithm assessment. In the future, more complex forms of nonlinear systems analysis may be necessary to fully characterize the frequency response properties of nonlinear algorithms in a context-dependent manner.

  5. 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

  6. 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.

  7. 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. PMID:23869163

  8. Nonlinear optical signal processing on multiwavelength sensitive materials.

    PubMed

    Azimipour, Mehdi; Pashaie, Ramin

    2013-11-01

    Exploiting salient features in the photodynamics of specific types of light sensitive materials, a new approach is presented for realization of parallel nonlinear operations with optics. We briefly review the quantum structure and mathematical models offered for the photodynamics of two multiwavelength sensitive materials, doped crystals of lithium niobate and thick layers of bacteriorhodopsin. Next, a special mode of these dynamics in each material is investigated and a graphical design procedure is offered to produce highly nonlinear optical responses that can be dynamically reshaped via applying minimum changes in the optical setup. PMID:24177084

  9. 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

  10. 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.

  11. Investigations into the Instructional Process. IV. Teaching as a Stochastic Process.

    ERIC Educational Resources Information Center

    Komulainen, Erkki

    This study examines quantification of the instructional process through the use of Markov chaining, and by considering the transition probabilities within a framework provided by the taxonomy used, attempts to obtain information about behavior sequences common to all lessons. (Author/DLG)

  12. 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…

  13. Correlation analysis for long time series by robustly estimated autoregressive stochastic processes

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

    Modern sensors and satellite missions deliver huge data sets and long time series of observations. These data sets have to be handled with care because of changing correlations, conspicuous data and possible outliers. Tailored concepts for data selection and robust techniques to estimate the correlation characteristics allow for a better/optimal exploitation of the information of these measurements. In this presentation we give an overview of standard techniques for estimating correlations occurring in long time series in the time domain as well as in the frequency domain. We discuss the pros and cons especially with the focus on the intensified occurrence of conspicuous data and outliers. We present a concept to classify the measurements and isolate conspicuous data. We propose to describe the varying correlation behavior of the measurement series by an autoregressive stochastic process and give some hints how to construct adaptive filters to decorrelate the measurement series and to handle the huge covariance matrices. As study object we use time series from gravity gradient data collected during the GOCE low orbit operation campaign (LOOC). Due to the low orbit these data from 13-Jun-2014 to 21-Oct-2014 have more or less the same potential to recover the Earth gravity field with the same accuracy than all the data from the rest of the entire mission. Therefore these data are extraordinarily valuable but hard to handle, because of conspicuous data due to maneuvers during the orbit lowering phases, overall increase in drag, saturation of ion thrusters and other (currently) unexplained effects.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  15. Sensitive Analysis of Observation Model for Human Tracking Using a Stochastic Process

    NASA Astrophysics Data System (ADS)

    Nakanishi, W.; Fuse, T.

    2014-06-01

    This paper aims at obtaining basic knowledge about characteristics of observation models for human tracking method as a stochastic process. As human tracking in actual cases are complicated, we cannot always use the same observation models for every situation. Thus in most cases observation models are set empirically so far. In order to achieve an efficient choice of models and parameters, understanding some advantages and disadvantages of such models regarding to observation conditions is important. In this paper we conduct a sensitive analysis on some types of observation models. In particular, we obtain both colour and range information at a railway station. We prepare six predictive distributions as well as six models and parameters for both colour and range observation models. We calculate posterior distributions of each pattern, namely 36 patterns for both colour and range models. As a sensitive analysis we compare a value of a ground truth and an expected value of posteriors. We also compare variances of predictive and posterior distributions. Through this experimental results, we confirm our analysis method is efficient to obtain information about observation models. In fact, all models analysed are good in whole. One suggestive result is that colour models can deal with a predictive error in mean values, while range models in variances. Another is that under occlusions range models show a good performance.

  16. Baseflow recession and recharge as nonlinear storage processes

    NASA Astrophysics Data System (ADS)

    Wittenberg, Hartmut

    1999-04-01

    Discharge in many rivers is often fed by outflow from a shallow groundwater reservoir. It is becoming clear that the outflow from this aquifer is not linearly proportional to storage as is commonly assumed in many algorithms. Numerical analysis of flow recession curves from about 100 river gauging stations instead reveals a nonlinear relationship between baseflow, Q, and storage, S, for which the equation S=aQb was adopted. Values of the exponent b are found by calibration to be between 0 and 1 but with a high concentration around 0·5, which is in accordance with the findings of other studies and theoretical approaches yielding b=0·5 for unconfined aquifers and relating the coefficient a to catchment properties, primarily area and shape of basin, pore volume and transmissivity. This non-linear reservoir function is proposed as a more realistic alternative to the linear reservoir function.The relatively fast response of groundwater flow to rainfall is mainly a result of the increase of hydraulic head of the groundwater reservoir accelerating the exfiltration of old, pre-event water into the river bed. As fissure and pore volumes communicate hydraulically, it appears physically reasonable to model the system by one non-linear reservoir for catchments, or parts of them, instead of applying independent parallel linear reservoirs. The non-linear reservoir algorithms are supported by an analytical derivation. They are extended for the automatic separation of baseflow from a time-series of daily discharge in rivers and the computation of storage and effective recharge of groundwater in river basins by inverse nonlinear reservoir routing. The time-series obtained allow the identification and quantification of long-term changes to the water balance. Relationships between computed groundwater storage and observed groundwater level can also be established.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model

    NASA Astrophysics Data System (ADS)

    Ritto, T. G.; Soize, Christian; Sampaio, R.

    2010-04-01

    This work proposes a strategy for the robust optimization of the nonlinear dynamics of a drill-string, which is a structure that rotates and digs into the rock to search for oil. The nonparametric probabilistic approach is employed to model the uncertainties of the structure as well as the uncertainties of the bit-rock interaction model. This paper is particularly concerned with the robust optimization of the rate of penetration of the column, i.e., we aim to maximize the mathematical expectation of the mean rate of penetration, respecting the integrity of the system. The variables of the optimization problem are the rotational speed at the top and the initial reaction force at the bit; they are considered deterministic. The goal is to find the set of variables that maximizes the expected mean rate of penetration, respecting, vibration limits, stress limit and fatigue limit of the dynamical system.

  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. 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

  4. Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions

    NASA Astrophysics Data System (ADS)

    Fujihara, Akihiro; Ohtsuki, Toshiya; Yamamoto, Hiroshi

    2004-09-01

    We consider stochastic processes where randomly chosen particles with positive quantities x,y(>0) interact and exchange the quantities asymmetrically by the rule x'=c{(1-a)x+by} , y'=d{ax+(1-b)y} (x⩾y) , where (0⩽)a,b(⩽1) and c,d(>0) are interaction parameters. Noninteger power-law tails in the probability distribution function of scaled quantities are analyzed in a similar way as in inelastic Maxwell models. A transcendental equation to determine the growth rate γ of the processes and the exponent s of the tails is derived formally from moment equations in Fourier space. In the case c=d or a+b=1(a≠0,1) , the first-order moment equation admits a closed form solution and γ and s are calculated analytically from the transcendental equation. It becomes evident that at c=d , exchange rate b of small quantities is irrelevant to power-law tails. In the case c≠d and a+b≠1 , a closed form solution of the first-order moment equation cannot be obtained because of asymmetry of interactions. However, the moment equation for a singular term formally forms a closed solution and possibility for the presence of power-law tails is shown. Continuity of the exponent s with respect to parameters a,b,c,d is discussed. Then numerical simulations are carried out and campared with the theory. Good agreement is achieved for both γ and s .

  5. 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.

  6. 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

  7. Singular and nonlinear processes in applied mathematics. Final technical report

    SciTech Connect

    Tabor, M.

    1998-08-05

    A wide range of research topics were supported under this grant. These included: (1) complex space time singularities in nonlinear differential equations; (2) singularities in magneto-hydrodynamics; (3) the dynamics of knots and curves; and (4) the structure and dynamics of foams and grain boundaries. A brief summary of results achieved in each of these four areas is given below along with the associated publications acknowledging DOE support.

  8. 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. PMID:26357217

  9. 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.

  10. 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

  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. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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

  18. 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

  19. 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.

  20. 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

  1. 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

  2. Stochastic Nonlinear Evolutional Model of the Large-Scaled Neuronal Population and Dynamic Neural Coding Subject to Stimulation

    SciTech Connect

    Wang Rubin; Yu Wei

    2005-08-25

    In this paper, we investigate how the population of neuronal oscillators deals with information and the dynamic evolution of neural coding when the external stimulation acts on it. Numerically computing method is used to describe the evolution process of neural coding in three-dimensioned space. The numerical result proves that only the suitable stimulation can change the coupling structure and plasticity of neurons.

  3. 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.

  4. Multichannel active control of nonlinear noise processes using diagonal structure bilinear FXLMS algorithm

    NASA Astrophysics Data System (ADS)

    Chen, Dong; Yuan, Ding; Li, Tan; Sidan, Du

    2015-12-01

    A novel nonlinear adaptive algorithm named as diagonal structure bilinear filtered-x least mean square (DBFXLMS) for multichannel nonlinear active noise control is proposed in this paper. The performances of the proposed algorithm are shown below and the computational complexity is compared with the second-order Volterra filtered-x LMS (VFXLMS) algorithm and the filtered-s least mean square (FSLMS) algorithm, in terms of normalized mean square error (NMSE), for multichannel active control of nonlinear noise processes. Both the simulations and the computational complexity analyses demonstrate that the proposed method has an improvement as compared to the proposed algorithms.

  5. A Low Processing Cost Adaptive Algorithm Identifying Nonlinear Unknown System with Piecewise Linear Curve

    NASA Astrophysics Data System (ADS)

    Fujii, Kensaku; Aoki, Ryo; Muneyasu, Mitsuji

    This paper proposes an adaptive algorithm for identifying unknown systems containing nonlinear amplitude characteristics. Usually, the nonlinearity is so small as to be negligible. However, in low cost systems, such as acoustic echo canceller using a small loudspeaker, the nonlinearity deteriorates the performance of the identification. Several methods preventing the deterioration, polynomial or Volterra series approximations, have been hence proposed and studied. However, the conventional methods require high processing cost. In this paper, we propose a method approximating the nonlinear characteristics with a piecewise linear curve and show using computer simulations that the performance can be extremely improved. The proposed method can also reduce the processing cost to only about twice that of the linear adaptive filter system.

  6. Nonlinear k⊥-factorization: a New Paradigm for Hard Processes in a Nuclear Medium

    NASA Astrophysics Data System (ADS)

    Nikolaev, N. N.; Schäfer, W.; Zakharov, B. G.; Zoller, V. R.

    2006-04-01

    We review the origin, and salient features, of the breaking of the conventional linear k⊥-factorization for hard processes in a nuclear environment. A realization of the nonlinear k ⊥-factorization which emerges instead is shown to depend on color properties of the underlying pQCD subprocesses. We discuss the emerging universality classes and extend nonlinear k ⊥-factorization to AGK unitarity rules for the excitation of the target nucleus.

  7. Nonlinear joint transmit-receive processing for coordinated multi-cell systems: centralized and decentralized

    NASA Astrophysics Data System (ADS)

    Hu, Zhirui; Feng, Chunyan; Zhang, Tiankui; Niu, Qin; Chen, Yue

    2015-12-01

    This paper proposes a nonlinear joint transmit-receive (tx-rx) processing scheme for downlink-coordinated multi-cell systems with multi-stream multi-antenna users. The nonlinear joint tx-rx processing is formulated as an optimization problem to maximize the minimum signal-to-interference noise ratio (SINR) of streams to guarantee the fairness among streams of each user. Nonlinear Tomlinson-Harashima precoding (THP) is applied at transmitters, and linear receive processing is applied at receivers, to eliminate the inter-user interference and inter-stream interference. We consider multi-cell systems under two coordinated modes: centralized and decentralized, corresponding to systems with high- and low-capacity backhaul links, respectively. For the centralized coordinated mode, transmit and receive processing matrices are jointly determined by the central processing unit based on the global channel state information (CSI) shared by base stations (BSs). For the decentralized coordinated mode, transmit and receive processing matrices are computed independently based on the local CSI at each BS. In correspondence, we propose both a centralized and a decentralized algorithm to solve the optimization problem under the two modes, respectively. Feasibility and computational complexity of the proposed algorithms are also analyzed. Simulation results prove that the proposed nonlinear joint tx-rx processing scheme can achieve user fairness by equalizing the bit error rate (BER) among streams of each user and the proposed scheme outperforms the existing linear joint tx-rx processing. Moreover, consistent with previous research results, performance of the proposed centralized nonlinear joint tx-rx processing scheme is proved to be better than that of the decentralized nonlinear joint tx-rx processing.

  8. Bayesian hierarchical models for multivariate nonlinear spatio-temporal dynamical processes in the atmosphere and ocean

    NASA Astrophysics Data System (ADS)

    Leeds, W. B.; Wikle, C. K.

    2012-12-01

    Spatio-temporal statistical models, and in particular Bayesian hierarchical models (BHMs), have become increasingly popular as means of representing natural processes such as climate and weather that evolve over space and time. Hierarchical models make it possible to specify separate, conditional probability distributions that account for uncertainty in the observations, the underlying process, and parameters in situations when specifying these sources of uncertainty in a joint probability distribution may be difficult. As a result, BHMs are a natural setting for climatologists, meteorologists, and other environmental scientists to incorporate scientific information (e.g., PDEs, IDEs, etc.) a priori into a rigorous statistical framework that accounts for error in measurements, uncertainty in the understanding of the true underlying process, and uncertainty in the parameters that describe the process. While much work has been done in the development of statistical models for linear dynamic spatio-temporal processes, statistical modeling for nonlinear (and particularly, multivariate nonlinear) spatio-temporal dynamical processes is still a relatively open area of inquiry. As a result, general statistical models for environmental scientists to model complicated nonlinear processes is limited. We address this limitation in the methodology by introducing a multivariate "general quadratic nonlinear" framework for modeling multivariate, nonlinear spatio-temporal random processes inside of a BHM in a way that is especially applicable for problems in the ocean and atmospheric sciences. We show that in addition to the fact that this model addresses the previously mentioned sources of uncertainty for a wide spectrum of multivariate, nonlinear spatio-temporal processes, it is also a natural framework for data assimilation, allowing for the fusing of observations with computer models, computer model emulators, computer model output, or "mechanistically motivated" statistical

  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. 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.

  11. 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.

  12. Nonlinear dynamics of global atmospheric and Earth-system processes

    NASA Technical Reports Server (NTRS)

    Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel

    1990-01-01

    Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

  13. 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.

  14. 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

  15. Process fault detection and nonlinear time series analysis for anomaly detection in safeguards

    SciTech Connect

    Burr, T.L.; Mullen, M.F.; Wangen, L.E.

    1994-02-01

    In this paper we discuss two advanced techniques, process fault detection and nonlinear time series analysis, and apply them to the analysis of vector-valued and single-valued time-series data. We investigate model-based process fault detection methods for analyzing simulated, multivariate, time-series data from a three-tank system. The model-predictions are compared with simulated measurements of the same variables to form residual vectors that are tested for the presence of faults (possible diversions in safeguards terminology). We evaluate two methods, testing all individual residuals with a univariate z-score and testing all variables simultaneously with the Mahalanobis distance, for their ability to detect loss of material from two different leak scenarios from the three-tank system: a leak without and with replacement of the lost volume. Nonlinear time-series analysis tools were compared with the linear methods popularized by Box and Jenkins. We compare prediction results using three nonlinear and two linear modeling methods on each of six simulated time series: two nonlinear and four linear. The nonlinear methods performed better at predicting the nonlinear time series and did as well as the linear methods at predicting the linear values.

  16. Nonlinear structural response using adaptive dynamic relaxation on a massively-parallel-processing system

    NASA Technical Reports Server (NTRS)

    Oakley, David R.; Knight, Norman F., Jr.

    1994-01-01

    A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.

  17. 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.

  18. 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.

  19. Derivation of stochastic differential equations for scrape-off layer plasma fluctuations from experimentally measured statistics

    SciTech Connect

    Mekkaoui, A.

    2013-01-15

    A stochastic differential equation for intermittent plasma density dynamics in magnetic fusion edge plasma is derived, which is consistent with the experimentally measured gamma distribution and the theoretically expected quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the nonlinear Langevin representation of the beta process, which leads to a root-square nonlinearity.

  20. A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes.

    PubMed

    Savran, Aydogan; Kahraman, Gokalp

    2014-03-01

    We develop a novel adaptive tuning method for classical proportional-integral-derivative (PID) controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in industry, to the control of nonlinear processes, we introduce a method which can readily be used by the industry. In this method, controller design does not require a first principal model of the process which is usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from the measured input-output data of the process. A soft limiter is used to impose industrial limits on the control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear process involving instabilities. Several tests showed the method's success in tracking, robustness to noise, and adaptation properties. We as well compared our system's performance to those of a plant with altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude, we present a novel adaptive control method that is built upon the well-known PID architecture that successfully controls highly nonlinear industrial processes, even under conditions such as strong parameter variations, noise, and instabilities. PMID:24140160

  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. Linear and nonlinear optical processing of polymer matrix nanocomposites

    NASA Astrophysics Data System (ADS)

    DeJournett, Travis J.; Han, Karen; Olasov, Lauren R.; Zeng, Fan W.; Lee, Brennan; Spicer, James B.

    2015-08-01

    This work focuses on the scalable synthesis and processing of nanostructures in polymer matrix nanocomposites (PMNCs) for applications that require photochemical functionality of these nanostructures. An in situ vapor deposition process using various metal and metal oxide precursors has been used to create a range of nanocomposites that display photochromic and photocatalytic behaviors. Under specific processing conditions, these composites consist of discrete nanoparticles distributed uniformly throughout the bulk of an optically transparent polymer matrix. Incorporating other chemical species as supplementary deposition agents in the synthesis process can modify these particles and produce complicated nanostructures with enhanced properties. In particular, work has been carried out to structure nanoparticles using laser irradiation. Starting with metallic or metal oxide nanoparticles in the polymer matrix, localized chemical vapor deposition in the near-particle environment has been carried out using laser irradiation to decompose chemical precursors leading to the formation of secondary structures surrounding the seed nanoparticles. Control of the spatial and temporal characteristics of the excitation source allows for synthesis of nanocomposites with a high degree of control over the location, composition and size of nanoparticles in the matrix and presents the opportunity to produce patterned materials with spatially varying properties.

  3. 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…

  4. 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

  5. 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.

  6. 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

  7. 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

  8. 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.

  9. 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

  10. 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.

  11. 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. PMID:25871061

  12. 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.

  13. 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…

  14. 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.

  15. The role of nonlinear processes in the formation of the radiospectrum of pulsars

    NASA Astrophysics Data System (ADS)

    Machabeli, G. Z.

    Radiation mechanisms in pulsars, which determine the observed spectra and polarization of the pulsar's radio emission, are analytically investigated with an emphasis on the nonlinear processes in the relativistic electron-positron plasma. The analysis centers on the generation and parameters of the transverse linearly polarized t-waves. An accurate agreement is noted between the analytical results and observational data.

  16. Experimental dynamic modelling of peripheral milling with process damping, structural and cutting force nonlinearities

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

    In this paper, an extended dynamic model of peripheral milling process including process damping, structural and cutting force nonlinearities is presented. Cutting forces are described through a third-order polynomial function of chip thickness while a cubic nonlinear function is considered for the structural stiffness. Under stable and regenerative chatter conditions and using Fourier series components, closed form expressions for the nonlinear cutting forces are derived. Parameters of the proposed model are identified through a set of experiments. For this purpose, modal experiments and measurement of cutting forces (at various feed rates) are performed to determine the modal parameters and the coefficients of nonlinear cutting force model. In addition, coefficients of the structural stiffness and process damping are identified through the analysis of experimental and simulated stability lobes diagrams. Simulated stability lobes diagram is constructed based on two approaches: a trial and error (TE) based algorithm and semi-discretization method (SDM). The presented experimental method for model identification can be implemented on any industrial milling process.

  17. Connecting Massive Galaxies to Dark Matter Halos in BOSS. I: Is Galaxy Color a Stochastic Process in High Mass Halos?

    NASA Astrophysics Data System (ADS)

    Saito, Shun; Leauthaud, Alexie; Hearin, Andrew P.; Bundy, Kevin; Zentner, Andrew R.; Behroozi, Peter S.; Reid, Beth A.; Sinha, Manodeep; Coupon, Jean; Tinker, Jeremy L.; White, Martin; Schneider, Donald P.

    2016-05-01

    We use subhalo abundance matching (SHAM) to model the stellar mass function (SMF) and clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) "CMASS" sample at z ˜ 0.5. We introduce a novel method which accounts for the stellar mass incompleteness of CMASS as a function of redshift, and produce CMASS mock catalogs which include selection effects, reproduce the overall SMF, the projected two-point correlation function wp, the CMASS dn/dz, and are made publicly available. We study the effects of assembly bias above collapse mass in the context of "age matching" and show that these effects are markedly different compared to the ones explored by Hearin et al. (2013) at lower stellar masses. We construct two models, one in which galaxy color is stochastic ("AbM" model) as well as a model which contains assembly bias effects ("AgM" model). By confronting the redshift dependent clustering of CMASS with the predictions from our model, we argue that that galaxy colors are not a stochastic process in high-mass halos. Our results suggest that the colors of galaxies in high-mass halos are determined by other halo properties besides halo peak velocity and that assembly bias effects play an important role in determining the clustering properties of this sample.

  18. 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

  19. 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.

  20. 2-D nonlinear IIR-filters for image processing - An exploratory analysis

    NASA Technical Reports Server (NTRS)

    Bauer, P. H.; Sartori, M.

    1991-01-01

    A new nonlinear IIR filter structure is introduced and its deterministic properties are analyzed. It is shown to be better suited for image processing applications than its linear shift-invariant counterpart. The new structure is obtained from causality inversion of a 2D quarterplane causal linear filter with respect to the two directions of propagation. It is demonstrated, that by using this design, a nonlinear 2D lowpass filter can be constructed, which is capable of effectively suppressing Gaussian or impulse noise without destroying important image information.

  1. Sensitivity Analysis and Stochastic Simulations of Non-equilibrium Plasma Flow

    SciTech Connect

    Lin, Guang; Karniadakis, George E.

    2009-11-05

    We study parametric uncertainties involved in plasma flows and apply stochastic sensitivity analysis to rank the importance of all inputs to guide large-scale stochastic simulations. Specifically, we employ different gradient-based sensitivity methods, namely Morris, multi-element probabilistic collocation method (ME-PCM) on sparse grids, Quasi-Monte Carlo, and Monte Carlo methods. These approaches go beyond the standard ``One-At-a-Time" sensitivity analysis and provide a measure of the nonlinear interaction effects for the uncertain inputs. The objective is to perform systematic stochastic simulations of plasma flows treating only as {\\em stochastic processes} the inputs with the highest sensitivity index, hence reducing substantially the computational cost. Two plasma flow examples are presented to demonstrate the capability and efficiency of the stochastic sensitivity analysis. The first one is a two-fluid model in a shock tube while the second one is a one-fluid/two-temperature model in flow past a cylinder.

  2. Efficient and coherent frequency conversions and nonlinear interference in optical parametric and atomic Raman processes

    NASA Astrophysics Data System (ADS)

    Ding, Yu

    By implementing a parametric down-conversion process with a strong signal field injection, we demonstrate that frequency down-conversion from pump photons to idler photons can be a coherent process. Contrary to a common misconception, we show that the process can be free of quantum noise. With an interference experiment, we demonstrate that coherence is preserved in the conversion process. This technique could lead to a high-fidelity quantum state transfer from a high-frequency photon to a low-frequency photon and connect a missing link in quantum networks. Coherent and efficient nonlinear interaction and frequency conversion are of great interest in many areas of quantum optics. Traditionally, the low efficiency of Raman scattering is improved by a high-finesse optical resonator or stimulated Raman conversion. It was recently found that the atomic spin wave initially built through electromagnetically induced transparency or a weak Raman process can actively enhance the Raman frequency conversion. An experimental demonstration of an efficient Raman conversion scheme with coherent feedback of both pump and Stokes fields is presented. The temporal profile of the generated Raman pulse shows that the coherence time of the atomic spin wave is ˜1.8 ms. A laser-like power threshold is observed and its low threshold is attributed to the long coherence time of the atomic spin wave. The mechanism of the conversion enhancement process is discussed and the conversion efficiency of a single pass of the beams is compared with that of double passes. Finally, a beat signal is observed between the two Stokes fields and its Fourier transform shows that the frequency difference is caused by the AC Stark effect. Precision phase measurement is traditionally restricted by the standard quantum limit. However, this limit is not as fundamental as the Heisenberg limit and can be circumvented by use of nonclassical quantum states and structure modification of the interferometers. Several

  3. S-cone contributions to linear and non-linear motion processing.

    PubMed

    Michna, Magda L; Yoshizawa, Tatsuya; Mullen, Kathy T

    2007-04-01

    We investigated the characteristics of mechanisms mediating motion discrimination of S-cone isolating stimuli and found a double dissociation between the effects of luminance noise, which masks linear but not non-linear motion, and chromatic noise, which masks non-linear but not linear motion. We conclude that S-cones contribute to motion via two different pathways: a non-linear motion mechanism via a chromatic pathway and a linear motion mechanism via a luminance pathway. Additionally, motion discrimination and detection thresholds for drifting, S-cone isolating Gabors are unaffected by luminance noise, indicating that grating motion is mediated via chromatic mechanisms and based on higher-order motion processing. PMID:17343890

  4. Nonlinear optical signal processing in high figure of merit CMOS compatible platforms

    NASA Astrophysics Data System (ADS)

    Moss, D. J.; Morandotti, R.

    2015-05-01

    Photonic integrated circuits that exploit nonlinear optics in order to generate and process signals all-optically have achieved performance far superior to that possible electronically - particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics for some time, its high two-photon absorption at telecommunications wavelengths poses a fundamental limitation. We review the recent achievements based in new CMOS-compatible platforms that are better suited than SOI for nonlinear optics, focusing on amorphous silicon and Hydex glass. We highlight their potential as well as the challenges to achieving practical solutions for many key applications. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement.

  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. 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.

  8. Confidence estimation as a stochastic process in a neurodynamical system of decision making.

    PubMed

    Wei, Ziqiang; Wang, Xiao-Jing

    2015-07-01

    Evaluation of confidence about one's knowledge is key to the brain's ability to monitor cognition. To investigate the neural mechanism of confidence assessment, we examined a biologically realistic spiking network model and found that it reproduced salient behavioral observations and single-neuron activity data from a monkey experiment designed to study confidence about a decision under uncertainty. Interestingly, the model predicts that changes of mind can occur in a mnemonic delay when confidence is low; the probability of changes of mind increases (decreases) with task difficulty in correct (error) trials. Furthermore, a so-called "hard-easy effect" observed in humans naturally emerges, i.e., behavior shows underconfidence (underestimation of correct rate) for easy or moderately difficult tasks and overconfidence (overestimation of correct rate) for very difficult tasks. Importantly, in the model, confidence is computed using a simple neural signal in individual trials, without explicit representation of probability functions. Therefore, even a concept of metacognition can be explained by sampling a stochastic neural activity pattern. PMID:25948870

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    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.

  10. Nonequilibrium entropic temperature and its lower bound for quantum stochastic processes

    NASA Astrophysics Data System (ADS)

    Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra

    2014-03-01

    In this paper, we have studied the Shannon "entropic" nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the c-number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.

  11. Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

    PubMed Central

    Guan, Yongtao; Li, Yehua; Sinha, Rajita

    2011-01-01

    In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material. PMID:21984854

  12. 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.

  13. 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.

  14. An approximate internal model-based neural control for unknown nonlinear discrete processes.

    PubMed

    Li, Han-Xiong; Deng, Hua

    2006-05-01

    An approximate internal model-based neural control (AIMNC) strategy is proposed for unknown nonaffine nonlinear discrete processes under disturbed environment. The proposed control strategy has some clear advantages in respect to existing neural internal model control methods. It can be used for open-loop unstable nonlinear processes or a class of systems with unstable zero dynamics. Based on a novel input-output approximation, the proposed neural control law can be derived directly and implemented straightforward for an unknown process. Only one neural network needs to be trained and control algorithm can be directly obtained from model identification without further training. The stability and robustness of a closed-loop system can be derived analytically. Extensive simulations demonstrate the superior performance of the proposed AIMNC strategy. PMID:16722170

  15. Cascading processes in the nonlinear diffraction of light by standing acoustic waves

    NASA Astrophysics Data System (ADS)

    Dadoenkova, Yu. S.; Dadoenkova, N. N.; Bentivegna, F. F. L.; Lyubchanskii, I. L.; Lee, Y. P.

    2016-01-01

    The contribution of two types of cascading process to the nonlinear optical diffraction of electromagnetic waves from a standing acoustic wave in a GaAs crystal is theoretically studied. The first type of cascading process results from second-harmonic generation followed by linear acousto-optical diffraction, while the second type involves linear acousto-optical diffraction from the standing acoustic wave and subsequent sum-frequency generation. In contrast to the third, direct, nonlinear acousto-optical diffraction process we previously investigated, the photoelastic interaction between electromagnetic and acoustic waves is here linear. We establish the rules governing the cascading processes and show that in most cases the output signal simultaneously results from two or even three of the possible nonlinear diffraction mechanisms. However, we demonstrate that a careful choice of the incidence angles of the incoming electromagnetic waves, of the polarization combinations of the incoming and diffracted waves, and of the type of acoustic wave (longitudinal or transverse) makes it always possible to distinguish between the direct and either of the two cascading processes.

  16. 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

  17. Design and implementation of non-linear image processing functions for CMOS image sensor

    NASA Astrophysics Data System (ADS)

    Musa, Purnawarman; Sudiro, Sunny A.; Wibowo, Eri P.; Harmanto, Suryadi; Paindavoine, Michel

    2012-11-01

    Today, solid state image sensors are used in many applications like in mobile phones, video surveillance systems, embedded medical imaging and industrial vision systems. These image sensors require the integration in the focal plane (or near the focal plane) of complex image processing algorithms. Such devices must meet the constraints related to the quality of acquired images, speed and performance of embedded processing, as well as low power consumption. To achieve these objectives, low-level analog processing allows extracting the useful information in the scene directly. For example, edge detection step followed by a local maxima extraction will facilitate the high-level processing like objects pattern recognition in a visual scene. Our goal was to design an intelligent image sensor prototype achieving high-speed image acquisition and non-linear image processing (like local minima and maxima calculations). For this purpose, we present in this article the design and test of a 64×64 pixels image sensor built in a standard CMOS Technology 0.35 μm including non-linear image processing. The architecture of our sensor, named nLiRIC (non-Linear Rapid Image Capture), is based on the implementation of an analog Minima/Maxima Unit. This MMU calculates the minimum and maximum values (non-linear functions), in real time, in a 2×2 pixels neighbourhood. Each MMU needs 52 transistors and the pitch of one pixel is 40×40 mu m. The total area of the 64×64 pixels is 12.5mm2. Our tests have shown the validity of the main functions of our new image sensor like fast image acquisition (10K frames per second), minima/maxima calculations in less then one ms.

  18. 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.

  19. Linear and non-linear studies of Alfven waves in space. Stationary and dynamic processes in magnetospheric plasmas

    NASA Technical Reports Server (NTRS)

    Bhattacharjee, A.; Hasegawa, A.

    1990-01-01

    The Final Technical Report on linear and non-linear studies of Alfven waves in space is presented. Areas of research included relaxation of magnetotail plasmas with field-aligned currents; the equilibrium dayside magnetosphere; macroscale particle simulation of kinetic Alfven wave physics; ballooning stability of plasmas with sheared equilibrium flows; theory of the drift-mirror instability; collisionless tearing instability in magnetotail plasmas; and nonadiabatic behavior of the magnetic moment of a charged particle in a dipole magnetic field and the development of stochastic webs.

  20. Information geometric nonlinear filtering

    NASA Astrophysics Data System (ADS)

    Newton, Nigel J.

    2015-06-01

    This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.