A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.

Memory and burstiness in dynamic networks

A discrete-time random process is described, which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time t is given by a fixed probability x, is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding t. For small values of x the interevent time distribution follows a power law with exponent −2−x. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of x for each node depends on the fitness distribution, \rho(x), from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data, such as online social communications and fMRI scans.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

RUMOR PROCESSES ON N

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand-based on the distribution of the random variables-whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

QoS Evaluation of BandwidthSchedulers in IPTV Networks OfferedSRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB).IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth datatransmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] First, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one incontinuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be include CAC, traffic policing used for traffic control.QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator andanalytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.

QoS evaluation of Bandwidth Schedulers in IPTV Networks Offered SRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB). IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth data transmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] first, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one in continuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be including CAC, traffic policing used for traffic control. QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator and analytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.

On a uniform turnpike of the third kind in the Robinson-Solow-Srinivasan model

On using McKenzie’s taxonomy of optimal accumulation in the longrun, we report a “uniform turnpike” theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of strictly concave felicity functions, or alternatively, on the value of a “marginal rate of transformation”, ξσ, from one period to the next not being unity. Our results, despite their specificity, contribute to the methodology of intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.

Phase transition of demand explained by the heterogeneity of consumers' intrinsic preferences

In 1991 Gary S. Becker presented A Note on Restaurant Pricing and Other Examples of Social In uences on Price explaining why many successful restaurants, plays, sporting events, and other activities do not raise their prices even with persistent excess demand. The main reason for this is due to the discontinuity of stable demands, which is explained in Becker's (1991) analysis. In the present paper we construct a discrete time stochastic model of socially interacting consumers deciding for one of two establishments. With this model we show that the discontinuity of stable demands, proposed by Gary S. Becker, depends crucially on an additional factor: the dispersion of the consumers' intrinsic preferences for the establishments.

Estimação do desconto de reequilíbrio ótimo em concessões rodoviárias através da metodologia das opções reais

Este trabalho propõe um novo modelo para avaliação, em tempo discreto, do desconto de reequilíbrio em contratos de concessão rodoviária, a partir de conceitos da Teoria Clássica de Finanças e da Teoria de Opções Reais. O modelo desenvolvido permitiu incorporar flexibilidades decorrentes de incertezas nas situações reais, como decisões gerenciais, vieses de comportamento e componentes políticos, comumente presentes em contratos de concessões rodoviária. Os resultados obtidos, utilizando-se como estudo de caso a BR-262, sinalizaram que há espaço para uma melhor intervenção regulatória com relação ao mecanismo do desconto de reequilíbrio, no sentido de prover melhores incentivos aos concessionários.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

As condições de ambiente térmico e aéreo, no interior de instalações para animais, alteram-se durante o dia, devido à influência do ambiente externo. Para que análises estatísticas e geoestatísticas sejam representativas, uma grande quantidade de pontos distribuídos espacialmente na área da instalação deve ser monitorada. Este trabalho propõe que a variação no tempo das variáveis ambientais de interesse para a produção animal, monitoradas no interior de instalações para animais, pode ser modelada com precisão a partir de registros discretos no tempo. O objetivo deste trabalho foi desenvolver um método numérico para corrigir as variações temporais dessas variáveis ambientais, transformando os dados para que tais observações independam do tempo gasto durante a aferição. O método proposto aproximou os valores registrados com retardos de tempo aos esperados no exato momento de interesse, caso os dados fossem medidos simultaneamente neste momento em todos os pontos distribuídos espacialmente. O modelo de correção numérica para variáveis ambientais foi validado para o parâmetro ambiental temperatura do ar, sendo que os valores corrigidos pelo método não diferiram pelo teste Tukey, a 5% de probabilidade dos valores reais registrados por meio de dataloggers.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Relaxed conditions for stability of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature. Numerical results exemplify this fact. These results are also used for fuzzy regulators and observers designs. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by linear matrix inequalities, that can be solved efficiently using convex programming techniques. The specification of the decay rate, constrains on control input and output are also discussed.

Frequency synthesizer using a hybrid analog/digital loop filter: A low complexity approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Adaptive filter feature identification for structural health monitoring in an aeronautical panel

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)