On a zero speed sensitive cellular automaton

Using an unusual, yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at asymptotically null speed for almost all configurations. More specifically, we prove that Lyapunov Exponents measuring pointwise or average linear speeds of the faster perturbations are equal to zero. We show that this implies the nullity of the measurable entropy. The measure m we consider gives the m-expansiveness property to the automaton. It is constructed with respect to a factor dynamical system based on simple "counter dynamics". As a counterpart, we prove that in the case of positively expansive automata, the perturbations move at positive linear speed over all the configurations

Cellular automata and Lyapunov exponents

In this article we give a new definition of some analog of Lyapunov exponents for cellular automata . Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent

Space-time directional Lyapunov exponents for cellular automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved

The Polynomial Eigenvalue Problem is Well Conditioned for Random Inputs

We compute the exact expected value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian distribution, showing that in general this problem is quite well conditioned.The first author's work was partially supported by Agencia Nacional de Investigación e Innovación (ANII), Uruguay, and by CSIC group 618, Universidad de La República, Uruguay. The second author's work was partially supported by MTM2017-83816-P and MTM2017-90682-REDT from Spanish Ministry of Science MICINN and by 21.SI01.64658 from Universidad de Cantabria and Banco de Santander

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

The EcoThermo project: key and innovative aspects

In this paper we present the most innovative aspects of the EC-FP7 EcoThermo project. The main aim of the project consists on innovating the technique of heat cost allocation in buildings with a centralized heating system, overcoming the heat cost allocator drawbacks for reliability, measurement reproducibility and traceability and contexts of applications. Given the complexity of the project, we will focus on its main aspects, such as the use of a virtual sensor to estimate the radiators heating power, the design of electronic valves fitted out with an energy harvesting system and the original wireless communication protocol

Computing the broadband vibroacoustic response of arbitrarily thick layered panels by a wave finite element approach

A robust procedure for the prediction of the dynamic response of layered panels within a SEA wave-context approach is proposed hereby. The dispersion characteristics of two dimensional composite orthotropic structures are predicted using a Wave Finite Element method. By manipulating the mass and stiffness matrices of the modelled structural segment a polynomial eigenvalue problem is formed, the solutions of which correspond to the propagation constants of the waves travelling within the structure. The wavenumbers and group velocities for waves comprising out of plane structural displacements can then be calculated. Using the numerically extracted wave propagation data the most important SEA quantities of the structure, namely the modal density and the radiation efficiency of each wave type are calculated. The vibroacoustic response of the structure under a broadband diffused excitation is then computed within a SEA approach. The impact of the symmetric and the antisymmetric vibrational motion of the panel on its sound transmission loss is exhibited and the approach proves robust enough for thin as well as for thick layered structures

Computing the topology of a real algebraic plane curve whose defining equations are available only “by values”

This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only “by values”. This approach is based on the replacement of the usual algebraic manipulation of the polynomials (and their roots) appearing in the topology determination of the given curve with the computation of numerical matrices (and their eigenvalues). Such numerical matrices arise from a typical construction in Elimination Theory known as the Bézout matrix which in our case is specified by the values of the defining polynomial equations on several sample points