Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

Association between antiarrhythmic, electrophysiological and antioxidative effects of melatonin in ischemia/reperfusion

Melatonin is assumed to confer cardioprotective action via antioxidative properties. We evaluated the association between ventricular tachycardia and/or ventricular fibrillation (VT/VF) incidence, oxidative stress, and myocardial electrophysiological parameters in experimental ischemia/reperfusion under melatonin treatment. Melatonin was given to 28 rats (10 mg/kg/day, orally, for 7 days) and 13 animals received placebo. In the anesthetized animals, coronary occlusion was induced for 5 min followed by reperfusion with recording of unipolar electrograms from ventricular epicardium with a 64-lead array. Effects of melatonin on transmembrane potentials were studied in ventricular preparations of 7 rats in normal and ?ischemic? conditions. Melatonin treatment was associated with lower VT/VF incidence at reperfusion, shorter baseline activation times (ATs), and activation-repolarization intervals and more complete recovery of repolarization times (RTs) at reperfusion (less baseline-reperfusion difference, ΔRT) (p < 0.05). Superoxide dismutase (SOD) activity was higher in the treated animals and associated with ΔRT (p = 0.001), whereas VT/VF incidence was associated with baseline ATs (p = 0.020). In vitro, melatonin led to a more complete restoration of action potential durations and resting membrane potentials at reoxygenation (p < 0.05). Thus, the antioxidative properties of melatonin were associated with its influence on repolarization duration, whereas the melatonin-related antiarrhythmic effect was associated with its oxidative stress-independent action on ventricular activation.Fil: Sedova, Ksenia A.. Czech Technical University In Prague; República ChecaFil: Bernikova, Olesya G.. Ural Branch of Russian Academy of Sciences; RusiaFil: Cuprova, Julia I.. Czech Technical University In Prague; República ChecaFil: Ivanova, Alexandra D.. Lomonosov Moscow State University; RusiaFil: Kutaeva, Galina A.. Pitirim Sorokin Syktyvkar State University; RusiaFil: Pliss, Michael G.. Almazov National Medical Research Centre; RusiaFil: Lopatina, Ekaterina V.. University of Saint Petersburg; RusiaFil: Vaykshnorayte, Marina A.. Ural Branch Of Russian Academy Of Sciences; RusiaFil: Diez, Emiliano Raúl. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Medicina y Biología Experimental de Cuyo; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Medicas. Instituto de Fisiologia; ArgentinaFil: Azarov, Jan E.. Ural Branch of Russian Academy of Sciences; Rusia. Pitirim Sorokin Syktyvkar State University; Rusi

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

Uniparental Genetic Heritage of Belarusians: Encounter of Rare Middle Eastern Matrilineages with a Central European Mitochondrial DNA Pool

Ethnic Belarusians make up more than 80% of the nine and half million people inhabiting the Republic of Belarus. Belarusians together with Ukrainians and Russians represent the East Slavic linguistic group, largest both in numbers and territory, inhabiting East Europe alongside Baltic-, Finno-Permic- and Turkic-speaking people. Till date, only a limited number of low resolution genetic studies have been performed on this population. Therefore, with the phylogeographic analysis of 565 Y-chromosomes and 267 mitochondrial DNAs from six well covered geographic sub-regions of Belarus we strove to complement the existing genetic profile of eastern Europeans. Our results reveal that around 80% of the paternal Belarusian gene pool is composed of R1a, I2a and N1c Y-chromosome haplogroups – a profile which is very similar to the two other eastern European populations – Ukrainians and Russians. The maternal Belarusian gene pool encompasses a full range of West Eurasian haplogroups and agrees well with the genetic structure of central-east European populations. Our data attest that latitudinal gradients characterize the variation of the uniparentally transmitted gene pools of modern Belarusians. In particular, the Y-chromosome reflects movements of people in central-east Europe, starting probably as early as the beginning of the Holocene. Furthermore, the matrilineal legacy of Belarusians retains two rare mitochondrial DNA haplogroups, N1a3 and N3, whose phylogeographies were explored in detail after de novo sequencing of 20 and 13 complete mitogenomes, respectively, from all over Eurasia. Our phylogeographic analyses reveal that two mitochondrial DNA lineages, N3 and N1a3, both of Middle Eastern origin, might mark distinct events of matrilineal gene flow to Europe: during the mid-Holocene period and around the Pleistocene-Holocene transition, respectively

Aggregation methods in dynamical systems and applications in population and community dynamics

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations

Structure of Metaphase Chromosomes: A Role for Effects of Macromolecular Crowding

In metaphase chromosomes, chromatin is compacted to a concentration of several hundred mg/ml by mechanisms which remain elusive. Effects mediated by the ionic environment are considered most frequently because mono- and di-valent cations cause polynucleosome chains to form compact ∼30-nm diameter fibres in vitro, but this conformation is not detected in chromosomes in situ. A further unconsidered factor is predicted to influence the compaction of chromosomes, namely the forces which arise from crowding by macromolecules in the surrounding cytoplasm whose measured concentration is 100–200 mg/ml. To mimic these conditions, chromosomes were released from mitotic CHO cells in solutions containing an inert volume-occupying macromolecule (8 kDa polyethylene glycol, 10.5 kDa dextran, or 70 kDa Ficoll) in 100 µM K-Hepes buffer, with contaminating cations at only low micromolar concentrations. Optical and electron microscopy showed that these chromosomes conserved their characteristic structure and compaction, and their volume varied inversely with the concentration of a crowding macromolecule. They showed a canonical nucleosomal structure and contained the characteristic proteins topoisomerase IIα and the condensin subunit SMC2. These observations, together with evidence that the cytoplasm is crowded in vivo, suggest that macromolecular crowding effects should be considered a significant and perhaps major factor in compacting chromosomes. This model may explain why ∼30-nm fibres characteristic of cation-mediated compaction are not seen in chromosomes in situ. Considering that crowding by cytoplasmic macromolecules maintains the compaction of bacterial chromosomes and has been proposed to form the liquid crystalline chromosomes of dinoflagellates, a crowded environment may be an essential characteristic of all genomes

Mitophagy plays a central role in mitochondrial ageing

The mechanisms underlying ageing have been discussed for decades, and advances in molecular and cell biology of the last three decades have accelerated research in this area. Over this period, it has become clear that mitochondrial function, which plays a major role in many cellular pathways from ATP production to nuclear gene expression and epigenetics alterations, declines with age. The emerging concepts suggest novel mechanisms, involving mtDNA quality, mitochondrial dynamics or mitochondrial quality control. In this review, we discuss the impact of mitochondria in the ageing process, the role of mitochondria in reactive oxygen species production, in nuclear gene expression, the accumulation of mtDNA damage and the importance of mitochondrial dynamics and recycling. Declining mitophagy (mitochondrial quality control) may be an important component of human ageing