Decidability and Universality in Symbolic Dynamical Systems

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2: minor orthographic changes v3: section 5.2 (collatz functions) mathematically improved v4: orthographic corrections, one reference added v5:27 pages. Important modifications. The formalism is strengthened: temporal logic replaced by finite automata. New results. Submitte

Evaluando el poder efectivo de los Congresos

Dentro del contexto del interés actual por los regímenes presidenciales, un interés que por cierto es a menudo polémico, este volumen constituye un paso importante en el análisis de los diversos patrones de comportamiento de los sistemas políticos. El trabajo se enfoca en el rol y poder efectivo de los "Congresos" latinoamericanos, lo cual es especialmente bien recibido dado que tanto la naturaleza como el alcance del poder ejercido por las legislaturas continúan siendo escasamente conocidos, no sólo respecto de los sistemas presidenciales sino también de los sistemas parlamentarios

Party government: myth or reality?

"The question of the relationship between parties and the governments which they support has not so far been given the attention it deserves. This is surprising from both a normative and an empirical standpoint. The reasons why this question has not been studied so far have probably to do with the notion, held unconsciously but also strongly, that the problem is a simple one. As with all matters which are understudied, there is some tendency to simplify and in this case to believe that parliamentary government, in Western Europe at least, is party government. Yet, as one looks more closely at the problem, the simplicity of the answer begins to vanish. What we therefore need to do, first, is to examine what the expression ‘party government’ really means. This examination will begin to raise in our minds questions about the validity of the ‘idealised concept’ of party government. This will lead us to adopt a more sedate view of what party government consists of as well as to notice that there are substantial variations in the content of party government in different countries." [author's abstract

Sensitivity analysis of a branching process evolving on a network with application in epidemiology

We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more sensitive with respect to transmission rates within cities than travel rates between cities. More generally, we highlight the fact that branching processes offer a powerful stochastic modeling tool with analytical formulas for sensitivity which are easy to use in practice.Comment: 17 pages (30 with SI), Journal of Complex Networks, Feb 201

The Continuous Skolem-Pisot Problem: On the Complexity of Reachability for Linear Ordinary Differential Equations

We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent sequence. In particular, we show that the continuous version of the nonnegativity problem is NP-hard in general and we show that the presence of a zero is decidable for several subcases, including instances of depth two or less, although the decidability in general is left open. The problems may also be stated as reachability problems related to real zeros of exponential polynomials or solutions to initial value problems of linear differential equations, which are interesting problems in their own right.Comment: 14 pages, no figur

Fast unfolding of communities in large networks: 15 years later

The Louvain method was proposed 15 years ago as a heuristic method for the fast detection of communities in large networks. During this period, it has emerged as one of the most popular methods for community detection, the task of partitioning vertices of a network into dense groups, usually called communities or clusters. Here, after a short introduction to the method, we give an overview of the different generalizations and modifications that have been proposed in the literature, and also survey the quality functions, beyond modularity, for which it has been implemented

Governments and supporting parties : definitions and classifications

Digitised version produced by the EUI Library and made available online in 2020