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In this paper, we consider estimation with lossy measurements. This problem can arise when measurements are communicated over wireless channels. We model the plant/measurement loss process as a Markovian jump linear system. While the time-varying Kalman estimator (TVKE) is known to be optimal, we introduce a simpler design, termed a jump linear estimator (JLE), to cope with losses. A JLE has predictor/corrector form, but at each time selects a corrector gain from a finite set of precalculated gains. The motivation for the JLE is twofold. The computational burden of the JLE is less than that of the TVKE and the estimation errors expected when using JLE provide an upper bound for those expected when using TVKE. We then introduce a special class of JLE, termed finite loss history estimators (FLHE), which uses a canonical gain selection logic. A notion of optimality for the FLHE is defined and an optimal synthesis method is given. The proposed design method is compared to TVKE in a simulation study. Index Terms--Linear estimation, Markov jump linear systems.

The bound of convergence rates for discrete-time Lurye (sometimes written Lur'e) systems has recently attracted much attention. The contributions of this technical note are twofold. Firstly, we show an example where the asymptotic convergence rate is slower than the linear case. This example can be seen as a counterexample of the Kalman conjecture extended to the analysis of convergence rates and motivates a rigorous analysis. Secondly, we develop a result to bound the convergence rate as a convex search over the suitable subclass of noncausal FIR Zames–Falb multipliers. The convex search is demonstrated with several numerical examples. [ABSTRACT FROM AUTHOR]

The selective infection of B cells producing neutralizing antibodies by the lymphocytic choriomeningitis virus (LCMV) causes their elimination by the virus-specific cytotoxic T cells in mice. Neutralizing antibodies are produced much earlier than protective antibodies in response to cytopathic viral infections. However, the opposite is true for infections like LCMV and hepatitis B due to the T cell-induced specific B cell elimination. This delay in the production of neutralizing antibodies may lead to persistent viral infections by non-cytopathic viruses.

The influence of CD8+ T cytolitic T cells and natural killer cells in perforin-deficient mice produced by homologous recombination, is mediated by perforin-stimulated pore formation. The mice exhibit fertility, viability and a regular amount of natural killer cells and CD8+ T cells. These cells are not capable of lysing virus-infected, natural killer target cells or allogenic fibroblasts within the body of an organism.

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix inequality (LMI) whose feasible points lead to convergence bounds of biased SGD. Based on this LMI condition, we develop a sequential minimization approach to analyze the intricate trade-offs that couple stepsize selection, convergence rate, optimization accuracy, and robustness to gradient inaccuracy. We also provide feasible points for this LMI and obtain theoretical formulas that quantify the convergence properties of biased SGD under various assumptions on the loss functions. [ABSTRACT FROM AUTHOR]