Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters I. Algorithm

The simultaneous state and parameter estimation problem for a linear discrete-time system with unknown noise statistics is treated as a large-scale optimization problem. The a posterioriprobability density function is maximized directly with respect to the states and parameters subject to the constraint of the system dynamics. The resulting optimization problem is too large for any of the standard non-linear programming techniques and hence an hierarchical optimization approach is proposed. It turns out that the states can be computed at the first levelfor given noise and system parameters. These, in turn, are to be modified at the second level.The states are to be computed from a large system of linear equations and two solution methods are considered for solving these equations, limiting the horizon to a suitable length. The resulting algorithm is a filter-smoother, suitable for off-line as well as on-line state estimation for given noise and system parameters. The second level problem is split up into two, one for modifying the noise statistics and the other for modifying the system parameters. An adaptive relaxation technique is proposed for modifying the noise statistics and a modified Gauss-Newton technique is used to adjust the system parameters.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters II. Numerical performance

A very general and numerically quite robust algorithm has been proposed by Sastry and Gauvrit (1980) for system identification. The present paper takes it up and examines its performance on a real test example. The example considered is the lateral dynamics of an aircraft. This is used as a vehicle for demonstrating the performance of various aspects of the algorithm in several possible modes.

Worst inputs and a bound on the highest peak statistics of a class of non-linear systems

A method is developed by which the input leading to the highest possible response in an interval of time can be determined for a class of non-linear systems. The input, if deterministic, is constrained to have a known finite energy (or norm) in the interval under consideration. In the case of random inputs, the energy is constrained to have a known probability distribution function. The approach has applications when a system has to be put to maximum advantage by getting the largest possible output or when a system has to be designed to the highest maximum response with only the input energy or the energy distribution known. The method is also useful in arriving at a bound on the highest peak distribution of the response, when the excitation is a known random process.As an illustration the Duffing oscillator has been analysed and some numerical results have also been presented.

The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles-active matter-with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

The recently evaluated two-pion contribution to the muon g - 2 and the phase of the pion electromagnetic form factor in the elastic region, known from pi pi scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t = 0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations, and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, < r(pi)(2)> = (0.435 +/- 0.005) fm(2) and F(-1.6 GeV2) = 0.243(-0.014)(+0.022), we obtain the allowed ranges 3.75 GeV-4 less than or similar to c less than or similar to 3.98 GeV-4 and 9.91 GeV-6 less than or similar to d less than or similar to 10.46 GeV-6 for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Subspace-based DOA estimation using Fractional Lower Order statistics

Direction Of Arrival (DOA) estimation, using a sensor array, in the presence of non-Gaussian noise using Fractional Lower-Order Moments (FLOM)matrices is studied. In this paper, a new FLOM based technique using the Fractional Lower Order Infinity Norm based Covariance (FLIC) Matrix is proposed. The bounded property and the low-rank subspace structure of the FLIC matrix is derived. Performance of FLIC based DOA estimation using MUSIC, ESPRIT, is shown to be better than other FLOM based methods.

Kannada WordNet - a lexical database

This paper presents the preliminary analysis of Kannada WordNet and the set of relevant computational tools. Although the design has been inspired by the famous English WordNet, and to certain extent, by the Hindi WordNet, the unique features of Kannada WordNet are graded antonyms and meronymy relationships, nominal as well as verbal compoundings, complex verb constructions and efficient underlying database design (designed to handle storage and display of Kannada unicode characters). Kannada WordNet would not only add to the sparse collection of machine-readable Kannada dictionaries, but also will give new insights into the Kannada vocabulary. It provides sufficient interface for applications involved in Kannada machine translation, spell checker and semantic analyser.

Elliptical tracers in two-dimensional, homogeneous, isotropic fluid turbulence: The statistics of alignment, rotation, and nematic order

We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous, and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For intermediate-scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate increases as the aspect ratio increases.

Flame surface statistics of constant-pressure turbulent expanding premixed flames

In this paper we investigate the local flame surface statistics of constant-pressure turbulent expanding flames. First the statistics of local length ratio is experimentally determined from high-speed planar Mie scattering images of spherically expanding flames, with the length ratio on the measurement plane, at predefined equiangular sectors, defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we then convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at the corresponding area-ratio pdfs. It is found that both the length ratio and area ratio pdfs are near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. (C) 2014 AIP Publishing LLC.

Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence

We present a detailed direct numerical simulation of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We examine the dependence of the statistical properties of such turbulence on dissipation and friction coefficients. We extend earlier work significantly by calculating fluid and magnetic spectra, probability distribution functions (PDFs) of the velocity, magnetic, vorticity, current, stream-function, and magnetic-vector-potential fields, and their increments. We quantify the deviations of these PDFs from Gaussian ones by computing their flatnesses and hyperflatnesses. We also present PDFs of the Okubo-Weiss parameter, which distinguishes between vortical and extensional flow regions, and its magnetic analog. We show that the hyperflatnesses of PDFs of the increments of the stream function and the magnetic vector potential exhibit significant scale dependence and we examine the implication of this for the multiscaling of structure functions. We compare our results with those of earlier studies.

Probing a spin-glass state in SrRuO3 thin films through higher-order statistics of resistance fluctuations

The complex perovskite oxide SrRuO3 shows intriguing transport properties at low temperatures due to the interplay of spin, charge, and orbital degrees of freedom. One of the open questions in this system is regarding the origin and nature of the low-temperature glassy state. In this paper we report on measurements of higher-order statistics of resistance fluctuations performed in epitaxial thin films of SrRuO3 to probe this issue. We observe large low-frequency non-Gaussian resistance fluctuations over a certain temperature range. Our observations are compatible with that of a spin-glass system with properties described by hierarchical dynamics rather than with that of a simple ferromagnet with a large coercivity.

Electron transfer statistics and thermal fluctuations in molecular junctions

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects. (C) 2015 AIP Publishing LLC.

Anomalous lifetime statistics of ligand-receptor binding in a tethered polymer system

In this paper, motivated by observations of non-exponential decay times in the stochastic binding and release of ligand-receptor systems, exemplified by the work of Rogers et al on optically trapped DNA-coated colloids (Rogers et al 2013 Soft Matter 9 6412), we explore the general problem of polymer-mediated surface adhesion using a simplified model of the phenomenon in which a single polymer molecule, fixed at one end, binds through a ligand at its opposite end to a flat surface a fixed distance L away and uniformly covered with receptor sites. Working within the Wilemski-Fixman approximation to diffusion-controlled reactions, we show that for a flexible Gaussian chain, the predicted distribution of times f(t) for which the ligand and receptor are bound is given, for times much shorter than the longest relaxation time of the polymer, by a power law of the form t(-1/4). We also show when the effects of chain stiffness are incorporated into this model (approximately), the structure of f(t) is altered to t(-1/2). These results broadly mirror the experimental trends in the work cited above.