Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

Определение оптимальных параметров источника рентгеновского излучения на базе малогабаритного ускорителя электронов

Проведено моделирование спектров рентгеновского излучения, генерируемого электронами с энергией 4…10 МэВ в мишенях из различных материалов и разной толщины. Определены оптимальные параметры мишени-конвертора для использования ее в медицинских источниках монохроматического рентгеновского излучения на базе малогабаритных электронных ускорителей. Проведены оценки интенсивности излучения и сравнение источников на базе разных ускорителей

Increasing compliance with wearing a medical device in children with autism

Health professionals often recommend the use of medical devices to assess the health, monitor the well-being, or improve the quality of life of their patients. Children with autism may present challenges in these situations as their sensory peculiarities may increase refusals to wear such devices. To address this issue, we systematically replicated prior research by examining the effects of differential reinforcement of other behavior (DRO) to increase compliance with wearing a heart rate monitor in 2 children with autism. The intervention increased compliance to 100% for both participants when an edible reinforcer was delivered every 90 s. The results indicate that DRO does not require the implementation of extinction to increase compliance with wearing a medical device. More research is needed to examine whether the reinforcement schedule can be further thinned

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

Structure of a 30S pre-initiation complex stalled by GE81112 reveals structural parallels in bacterial and eukaryotic protein synthesis initiation pathways

In bacteria, the start site and the reading frame of the messenger RNA are selected by the small ribosomal subunit (30S) when the start codon, typically an AUG, is decoded in the P-site by the initiator tRNA in a process guided and controlled by three initiation factors. This process can be efficiently inhibited by GE81112, a natural tetrapeptide antibiotic that is highly specific toward bacteria. Here GE81112 was used to stabilize the 30S pre-initiation complex and obtain its structure by cryo-electron microscopy. The results obtained reveal the occurrence of changes in both the ribosome conformation and initiator tRNA position that may play a critical role in controlling translational fidelity. Furthermore, the structure highlights similarities with the early steps of initiation in eukaryotes suggesting that shared structural features guide initiation in all kingdoms of life

An Algebraic Approach to Mso-Definability on Countable Linear Orderings

We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three logical applications. First, we establish the first known collapse result for the quantifier alternation of MSO logic over countable linear orderings. Second, we solve an open problem posed by Gurevich and Rabinovich, concerning the MSO-definability of sets of rational numbers using the reals in the background. Third, we establish the MSO-definability of the set of yields induced by an MSO-definable set of trees, confirming a conjecture posed by Bruyère, Carton, and Sénizergues

Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model

Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 µg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures

Gas Accretion and Galactic Chemical Evolution: Theory and Observations

This chapter reviews how galactic inflows influence galaxy metallicity. The goal is to discuss predictions from theoretical models, but particular emphasis is placed on the insights that result from using models to interpret observations. Even as the classical G-dwarf problem endures in the latest round of observational confirmation, a rich and tantalizing new phenomenology of relationships between $M_*$, $Z$, SFR, and gas fraction is emerging both in observations and in theoretical models. A consensus interpretation is emerging in which star-forming galaxies do most of their growing in a quiescent way that balances gas inflows and gas processing, and metal dilution with enrichment. Models that explicitly invoke this idea via equilibrium conditions can be used to infer inflow rates from observations, while models that do not assume equilibrium growth tend to recover it self-consistently. Mergers are an overall subdominant mechanism for delivering fresh gas to galaxies, but they trigger radial flows of previously-accreted gas that flatten radial gas-phase metallicity gradients and temporarily suppress central metallicities. Radial gradients are generically expected to be steep at early times and then flattened by mergers and enriched inflows of recycled gas at late times. However, further theoretical work is required in order to understand how to interpret observations. Likewise, more observational work is needed in order to understand how metallicity gradients evolve to high redshifts.Comment: Invited review to appear in Gas Accretion onto Galaxies, Astrophysics and Space Science Library, eds. A. J. Fox & R. Dav\'e, to be published by Springer. 29 pages, 2 figure

Estudio de necesidades de residencialización de la margen izquierda de la ría del Nervión

El presente estudio está contenido en una comunicación presentada en las I Jornadas de Gerontología Psicosocial del País Vasco, celebradas en Bergara, los días 23 y 24 de Junio de 1995.En él se pretende localizar las necesidades de residencialización de la Margen Izquierda de la Ría del Nervión. Las conclusiones son expuestas por colectivos atendidos: tercera edad, minusválidos físicos, enfermos convalecientes, infancia, juventud y sin techo