The Non-Archimedean Theory of Discrete Systems

In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair $a,b$ of finite words that have equal lengths, the system $\mathfrak A$, while evolution during (discrete) time, at a certain moment transforms $a$ into $b$. To every system $\mathfrak A$, we put into a correspondence a family $\mathcal F_{\mathfrak A}$ of continuous maps of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family $\mathcal F_{\mathfrak A}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyze behavior of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous maps of a (non-Archimedean) metric space $\mathbb Z_2$ of 2-adic integers.Comment: The extended version of the talk given at MACIS-201

Stress-Induced Premature Senescence Related to Oxidative Stress in the Developmental Programming of Nonalcoholic Fatty Liver Disease in a Rat Model of Intrauterine Growth Restriction.

Metabolic syndrome (MetS) refers to cardiometabolic risk factors, such as visceral obesity, dyslipidemia, hyperglycemia/insulin resistance, arterial hypertension and non-alcoholic fatty liver disease (NAFLD). Individuals born after intrauterine growth restriction (IUGR) are particularly at risk of developing metabolic/hepatic disorders later in life. Oxidative stress and cellular senescence have been associated with MetS and are observed in infants born following IUGR. However, whether these mechanisms could be particularly associated with the development of NAFLD in these individuals is still unknown. IUGR was induced in rats by a maternal low-protein diet during gestation versus. a control (CTRL) diet. In six-month-old offspring, we observed an increased visceral fat mass, glucose intolerance, and hepatic alterations (increased transaminase levels, triglyceride and neutral lipid deposit) in male rats with induced IUGR compared with the CTRL males; no differences were found in females. In IUGR male livers, we identified some markers of stress-induced premature senescence (SIPS) (lipofuscin deposit, increased protein expression of p21 <sup>WAF</sup> , p16 <sup>INK4a</sup> and Acp53, but decreased pRb/Rb ratio, foxo-1 and sirtuin-1 protein and mRNA expression) associated with oxidative stress (higher superoxide anion levels, DNA damages, decreased Cu/Zn SOD, increased catalase protein expression, increased nfe2 and decreased keap1 mRNA expression). Impaired lipogenesis pathways (decreased pAMPK/AMPK ratio, increased pAKT/AKT ratio, SREBP1 and PPARγ protein expression) were also observed in IUGR male livers. At birth, no differences were observed in liver histology, markers of SIPS and oxidative stress between CTRL and IUGR males. These data demonstrate that the livers of IUGR males at adulthood display SIPS and impaired liver structure and function related to oxidative stress and allow the identification of specific therapeutic strategies to limit or prevent adverse consequences of IUGR, particularly metabolic and hepatic disorders

Suites digitales et suites k-regulieres

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : TD 82022 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

FINITE AUTOMATA AND ZERO TEMPERATURE QUASICRYSTAL ISING CHAIN

Un automate fini est une machine qui engendre des suites déterministes (périodiques ou non périodiques). Nous étudions de telles suites et nous considérons des chaînes d'Ising dont la suite des coefficients de couplage est "quasicrystalline", c'est-à-dire engendrée par automate fini.A finite automaton is a machine which generates deterministic sequences (periodic or nonperiodic). We discuss such sequences and study Ising chains where the coupling coefficients form a "quasicrystalline" sequence (i.e. generated by automaton)

A final coalgebra for k-regular sequences

We study k-regular sequences from a coalgebraic perspective. Building on the observation that the set of streams over a semiring S can be turned into a final coalgebra, we obtain characterizations of k-regular sequences in terms of finite weighted automata, finite systems of behavioral differential equations, and recognizable power series. The latter characterization is obtained via an isomorphism of final coalgebras based on the k-adic numeration system