Prediction-Based Control for Linear Systems with Input- and State- Delay - Robustness to Delay Mismatch

International audienceThis paper addresses the design of a robust prediction-based controller for linear systems with both input and state delays. We extend the usual prediction-based scheme to state delay and prove its robustness to sufficiently small delay mismatches. Our approach is grounded on the linking of two recently proposed infinite-dimensional techniques: a Complete-Type Lyapunov functional, which enables state delay systems stability analysis, and tools from the field of Partial Differential Equations, reformulating the delays as transport equations and introducing a tailored backstepping transformation. We illustrate the merits of the proposed technique with simulations on a process dryer system

Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.Comment: 46 pages (draft version); extended version of the paper with same title, submitted to IEEE Transactions on Communication

A shallow water model conserving energy and potential enstrophy in the presence of boundaries

We extend a previously developed method for constructing shallow water models that conserve energy and potential enstrophy to the case of flow bounded by rigid walls. This allows the method to be applied to ocean models. Our procedure splits the dynamics into a set of prognostic equations for variables (vorticity, divergence, and depth) chosen for their relation to the Casimir invariants of mass, circulation and potential enstrophy, and a set of diagnostic equations for variables that are the functional derivatives of the Hamiltonian with respect to the chosen prognostic variables. The form of the energy determines the form of the diagnostic equations. Our emphasis on conservation laws produces a novel form of the boundary conditions, but numerical test cases demonstrate the accuracy of our model and its extreme robustness, even in the case of vanishing viscosity

Evolution favors protein mutational robustness in sufficiently large populations

BACKGROUND: An important question is whether evolution favors properties such as mutational robustness or evolvability that do not directly benefit any individual, but can influence the course of future evolution. Functionally similar proteins can differ substantially in their robustness to mutations and capacity to evolve new functions, but it has remained unclear whether any of these differences might be due to evolutionary selection for these properties. RESULTS: Here we use laboratory experiments to demonstrate that evolution favors protein mutational robustness if the evolving population is sufficiently large. We neutrally evolve cytochrome P450 proteins under identical selection pressures and mutation rates in populations of different sizes, and show that proteins from the larger and thus more polymorphic population tend towards higher mutational robustness. Proteins from the larger population also evolve greater stability, a biophysical property that is known to enhance both mutational robustness and evolvability. The excess mutational robustness and stability is well described by existing mathematical theories, and can be quantitatively related to the way that the proteins occupy their neutral network. CONCLUSIONS: Our work is the first experimental demonstration of the general tendency of evolution to favor mutational robustness and protein stability in highly polymorphic populations. We suggest that this phenomenon may contribute to the mutational robustness and evolvability of viruses and bacteria that exist in large populations

Robustness of the nonlinear filter: the correlated case

We consider the question of robustness of the optimal nonlinear filter when the signal process X and the observation noise are possibly correlated. The signal X and observations Y are given by a SDE where the coefficients can depend on the entire past. Using results on pathwise solutions of stochastic differential equations we express X as a functional of two independent Brownian motions under the reference probability measure P0. This allows us to write the filter p as a ratio of two expectations. This is the main step in proving robustness. In this framework we show that when (Xn,Yn) converge to (X,Y) in law, then the corresponding filters also converge in law. Moreover, when the signal and observation processes converge in probability, so do the filters. We also prove that the paths of the filter are continuous in this framework

Robustness and Conditional Independence Ideals

We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to describe the system's behaviour after knockouts. Robustness imposes structural constraints on these potentials. Robustness of probability distributions is defined via conditional independence statements. These statements can be studied algebraically. The corresponding conditional independence ideals are related to binary edge ideals. The set of robust probability distributions lies on an algebraic variety. We compute a Gr\"obner basis of this ideal and study the irreducible decomposition of the variety. These algebraic results allow to parametrize the set of all robust probability distributions.Comment: 16 page

dftatom: A robust and general Schr\"odinger and Dirac solver for atomic structure calculations

A robust and general solver for the radial Schr\"odinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of $10^{-8}$ Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number $Z$ = 1--92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, \ttt{dftatom}, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.Comment: Submitted to Computer Physics Communication on August 27, 2012, revised February 1, 201