Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Decision tree design and applications in speech processing

The design and operation of the minimum cost classifier, where the total cost is the sum of the measurement cost and the classification cost, is computationally complex. Noting the difficulties associated with this approach, decision tree design directly from a set of labelled samples is proposed in this paper. The feature space is first partitioned to transform the problem to one of discrete features. The resulting problem is solved by a dynamic programming algorithm over an explicitly ordered state space of all outcomes of all feature subsets. The solution procedure is very general and is applicable to any minimum cost pattern classification problem in which each feature has a finite number of outcomes. These techniques are applied to (i) voiced, unvoiced, and silence classification of speech, and (ii) spoken vowel recognition. The resulting decision trees are operationally very efficient and yield attractive classification accuracies.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

A Grassmann path from AdS(3) to flat space

We show that interpreting the inverse AdS(3) radius 1/l as a Grassmann variable results in a formal map from gravity in AdS(3) to gravity in flat space. The underlying reason for this is the fact that ISO(2, 1) is the Inonu-Wigner contraction of SO(2, 2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS(3) maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.

Models and algorithms for tracking of maneuvering objects using variable rate particle filters

Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter. © 2006 IEEE.

Kalman Filtering in R

Support in R for state space estimation via Kalman filtering was limited to one package, until fairly recently. In the last five years, the situation has changed with no less than four additional packages offering general implementations of the Kalman filter, including in some cases smoothing, simulation smoothing and other functionality. This paper reviews some of the offerings in R to help the prospective user to make an informed choice.

From organism to population: the role of life-history theory

The role of life-history theory in population and evolutionary analyses is outlined. In both cases general life histories can be analysed, but simpler life histories need fewer parameters for their description. The simplest case, of semelparous (breed-once-then-die) organisms, needs only three parameters: somatic growth rate, mortality rate and fecundity. This case is analysed in detail. If fecundity is fixed, population growth rate can be calculated direct from mortality rate and somatic growth rate, and isoclines on which population growth rate is constant can be drawn in a ”state space” with axes for mortality rate and somatic growth rate. In this space density-dependence is likely to result in a population trajectory from low density, when mortality rate is low and somatic growth rate is high and the population increases (positive population growth rate) to high density, after which the process reverses to return to low density. Possible effects of pollution on this system are discussed. The state-space approach allows direct population analysis of the twin effects of pollution and density on population growth rate. Evolutionary analysis uses related methods to identify likely evolutionary outcomes when an organism's genetic options are subject to trade-offs. The trade-off considered here is between somatic growth rate and mortality rate. Such a trade-off could arise because of an energy allocation trade-off if resources spent on personal defence (reducing mortality rate) are not available for somatic growth rate. The evolutionary implications of pollution acting on such a trade-off are outlined.

工业机器人的小脑模型控制

本文为动力学控制工业机器人提出了一种综合学习算法,这种学习算法可将以前所学的信息用于新的控制输入.这种控制方法不需要事先知道机器人动力学,它易于应用于特殊的控制问题或修改以适应实际系统中的变化,控制方法在时间上是有效的,且很适合于定点实现.学习控制算法的有效性通过4自由度的直接驱动机器人前两个关节在重复运动中的计算机仿真实验得到了验证.

Tracking Human Body Pose on a Learned Smooth Space

Particle filtering is a popular method used in systems for tracking human body pose in video. One key difficulty in using particle filtering is caused by the curse of dimensionality: generally a very large number of particles is required to adequately approximate the underlying pose distribution in a high-dimensional state space. Although the number of degrees of freedom in the human body is quite large, in reality, the subset of allowable configurations in state space is generally restricted by human biomechanics, and the trajectories in this allowable subspace tend to be smooth. Therefore, a framework is proposed to learn a low-dimensional representation of the high-dimensional human poses state space. This mapping can be learned using a Gaussian Process Latent Variable Model (GPLVM) framework. One important advantage of the GPLVM framework is that both the mapping to, and mapping from the embedded space are smooth; this facilitates sampling in the low-dimensional space, and samples generated in the low-dimensional embedded space are easily mapped back into the original highdimensional space. Moreover, human body poses that are similar in the original space tend to be mapped close to each other in the embedded space; this property can be exploited when sampling in the embedded space. The proposed framework is tested in tracking 2D human body pose using a Scaled Prismatic Model. Experiments on real life video sequences demonstrate the strength of the approach. In comparison with the Multiple Hypothesis Tracking and the standard Condensation algorithm, the proposed algorithm is able to maintain tracking reliably throughout the long test sequences. It also handles singularity and self occlusion robustly.

Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Communication system model for information rate evaluation of differential detection over time-varying channels

A communication system model for mutual information performance analysis of multiple-symbol differential M-phase shift keying over time-correlated, time-varying flat-fading communication channels is developed. This model is a finite-state Markov (FSM) equivalent channel representing the cascade of the differential encoder, FSM channel model and differential decoder. A state-space approach is used to model channel phase time correlations. The equivalent model falls in a class that facilitates the use of the forward backward algorithm, enabling the important information theoretic results to be evaluated. Using such a model, one is able to calculate mutual information for differential detection over time-varying fading channels with an essentially finite time set of correlations, including the Clarke fading channel. Using the equivalent channel, it is proved and corroborated by simulations that multiple-symbol differential detection preserves the channel information capacity when the observation interval approaches infinity.

Mutual information performance of differential MPSK detection over time-varying channels

This paper provides mutual information performance analysis of multiple-symbol differential WSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals

Modelação e previsão de vendas no setor do retalho de calçado

Dissertação apresentada ao Instituto Politécnico do Porto para obtenção do Grau de Mestre em Logística Orientada por: Professora Doutora Patrícia Alexandra Gregório Ramos

Latent Variable Models for Stochastic Discount Factors.

Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns, given a small number of state variables. In this paper, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is, a conditional independence between contemporaneous returns of a large number of assets, given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing.