Acoustic oscillations and viscosity

Using a simple thermo-hydrodynamic model that respects relativistic causality, we revisit the analysis of qualitative features of acoustic oscillations in the photon-baryon fluid. The growing photon mean free path introduces transient effects that can be modelled by the causal generalization of relativistic Navier-Stokes-Fourier theory. Causal thermodynamics provides a more satisfactory hydrodynamic approximation to kinetic theory than the quasi-stationary (and non-causal) approximations arising from standard thermodynamics or from expanding the photon distribution to first order in the Thomson scattering time. The causal approach introduces small corrections to the dispersion relation obtained in quasi-stationary treatments. A dissipative contribution to the speed of sound slightly increases the frequency of the oscillations. The diffusion damping scale is slightly increased by the causal corrections. Thus quasi-stationary approximations tend to over-estimate the spacing and under-estimate the damping of acoustic peaks. In our simple model, the fractional corrections at decoupling are $\gtrsim 10^{-3}$.Comment: Improved version with new quantitative estimates and some corrections. We show how quasi-stationary approximations based on expanding the photon distribution to first order in the Thomson time tend to under-estimate the frequency and damping of acoustic oscillation

Sub-ideal causal smoothing filters for real sequences

The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal smoothing filters with transfer functions vanishing at a point of the unit circle and such that they transfer processes into predictable ones. In this sense, the suggested filters are near-ideal; a faster gain decay would lead to the loss of causality. Applications to predicting algorithms are discussed and illustrated by experiments with forecasting of autoregressions with the coefficients that are deemed to be untraceable

Analytic Approach to Perturbative QCD

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.

Sub-Optimality of a Dyadic Adaptive Control Architecture

The dyadic adaptive control architecture evolved as a solution to the problem of designing control laws for nonlinear systems with unmatched nonlinearities, disturbances and uncertainties. A salient feature of this framework is its ability to work with infinite as well as finite dimensional systems, and with a wide range of control and adaptive laws. In this paper, we consider the case where a control law based on the linear quadratic regulator theory is employed for designing the control law. We benchmark the closed-loop system against standard linear quadratic control laws as well as those based on the state-dependent Riccati equation. We pose the problem of designing a part of the control law as a Nehari problem. We obtain analytical expressions for the bounds on the sub-optimality of the control law

A step toward reusable model fragments.

In this paper we describe a system to elaborate models which are suitable for model based reasoning. A set of model fragments selected from a library will be put together to build a model candidate. The system relies on the bond graph notation, which allows a uniform approach for the different physical domains and offers a compositional view of the system. Modeling requires the exploration of a search space of potential model candidates. These models are checked to be consistent with a set of behavior constraints and modeling hypotheses provided by the user

Derivative-free online learning of inverse dynamics models

This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the literature typically exploit joint velocities and accelerations, which need to be approximated resorting to numerical differentiation schemes, in this paper a new `derivative-free' framework is proposed that does not require this preprocessing step. An extensive experimental study with real data from the right arm of the iCub robot is presented, comparing different model classes and estimation procedures, showing that the proposed `derivative-free' methods outperform existing methodologies.Comment: 14 pages, 11 figure

Near-ideal causal smoothing filters for the real sequences

The paper considers causal smoothing of the real sequences, i.e., discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal ideal smoothing filters with transfer functions vanishing at a point of the unit circle and such that they transfer processes into predictable ones. In this sense, the suggested filters are near-ideal; a faster gain decay would lead to the loss of causality. Applications to predicting algorithms are discussed and illustrated by experiments with forecasting of autoregressions with the coefficients that are deemed to be untraceable

Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields

We present \emph{telescoping} recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (a hypersurface in $\R^d$, $d \ge 1$) and telescope inwards. For example, for images, the telescoping representation reduce recursions from $d = 2$ to $d = 1$, i.e., to recursions on a single dimension. Under appropriate conditions, the recursions for the random field are linear stochastic differential/difference equations driven by white noise, for which we derive recursive estimation algorithms, that extend standard algorithms, like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal Markov random fields.Comment: To appear in the Transactions on Information Theor