The galaxy of Coxeter groups

In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest.Comment: 30 pages, 6 figures. v2: Incorporated referee's suggestions; Corrected a mistake in the proof of Theorem 4.25 (formerly 4.24), improved other proofs and text; Final version, to appear in the Journal of Algebr

Finiteness properties of split extensions of linear groups

Santos Rego Y. Finiteness properties of split extensions of linear groups. Bielefeld: Universität Bielefeld; 2019.We investigate presentation problems for certain split extensions of discrete matrix groups. In the soluble front, we classify finitely presented Abels groups over arbitrary commutative rings R in terms of their ranks and the Borel subgroup of SL(2,R). In the classical set-up we prove that, under mild conditions, a parabolic subgroup of a classical group is relatively finitely presented with respect to its extended Levi factor. This yields, in particular, a partial classification of finitely presented S-arithmetic parabolic groups. Furthermore, we consider higher dimensional finiteness properties and establish an upper bound on the finiteness length of groups that admit certain representations with soluble image

Twisted conjugacy in soluble arithmetic groups

We investigate the ongoing problem of classifying which S-arithmetic groups have the so-called property $R_\infty$. While non-amenable S-arithmetic groups tend to have $R_\infty$, the soluble case seems more delicate. Here we address Borel subgroups in type A and show how the problem reduces to determining whether a metabelian subgroup of $\mathrm{GL}_2$ has $R_\infty$. For higher solubility class we show how automorphisms of the base ring give $R_\infty$. Our results yield many families of soluble S-arithmetic groups with $R_\infty$ but we also exhibit metabelian families not manifesting it. We formulate a conjecture concerning $R_\infty$ for the groups in question, addressing their geometric properties and algebraic structure.Comment: 47 page

Thompson-like groups, Reidemeister numbers, and fixed points

We investigate fixed-point properties of automorphisms of groups similar to R. Thompson's group $F$. Revisiting work of Gon\c{c}alves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property $R_\infty$. Using the BNS $\Sigma$-invariant and drawing from works of Gon\c{c}alves-Sankaran-Strebel and Zaremsky, we show that our tool applies to many $F$-like groups, including Stein's $F_{2,3}$, Cleary's $F_\tau$, the Lodha-Moore groups, and the braided version of $F$.Comment: v3: 25 pages, 4 figures; Incorporated referees' suggestions, corrected Proposition 2.7, included new remarks. Final version, to appear in Geometriae Dedicat

DIAGNOSIS FOR BIOCLIMATIC MESOREGION METROPOLITAN AREA OF CURITIBA

O objetivo deste trabalho é analisar dados climatológicos da mesorregião Metropolitana de Curitiba do Estado do Paraná com intuito de relaciona-los com as exigências bioclimáticas para a produção de aves, para verificar a viabilidade da criação, como também, servir de orientação a avicultores e futuros criadores na implantação de sistemas de controle ambiental utilizando a metodologia proposta por ABREU e ABREU (2001). A análise foi realizada com os dados climáticos fornecidos pelo Instituto Agronômico do Paraná (IAPAR) normais climatológicas das seguintes microrregiões: Antonina, Cerro Azul, Guaraqueçaba, Lapa, Morretes e Pinhais; os valores da Temperatura Média do Ar Compensada e Umidade Relativa foram utilizados para comparar com as condições de conforto térmico para aves, em função da idade das mesmas. As comparações realizadas em cada microrregião mostraram a necessidade de corrigir o microclima dos galpões para alcançar condições ideais para produção de aves. As microrregiões de Antonina, Lapa e Pinhais não apresentam condições ideais para desenvolvimento da atividade durante todas as fases de vida, portanto, para tal exige investimentos em controle ambiental, ou seja o aquecimento contínuo do galpão de criação; As microrregiões de Cerro Azul e Guaraqueçaba exigem sistemas de controle ambiental, aquecimento e principalmente resfriamento na última semana de vida.The objective of this work is to analyze climatology data of the Metropolitan meso-region of Curitiba, Paraná State with objective of relate them with the demands bioclimáticas for the production of poultry, to verify the viability of the creation, as well as, to serve of orientation to poultry keepers and future poultry keepers in the implantation of systems of environmental control. The analysis was accomplished with the climatic data supplied by climatology normal IAPAR of the following micro-region: Antonina, Cerro Azul, Guaraqueçaba, Lapa, Morretes and Pinhais; the values of the Medium Temperature of the Compensated Air and Relative Humidity, they were used to compare with the conditions of thermal comfort for poultry, in function of the age of the same ones ABREU e ABREU (2001). The comparisons accomplished in each micro-region showed the need to correct the climate of the sheed to reach ideal conditions for production of poultry. The micro-region of Antonina, Lapa and Pinhais not present ideal conditions for development of the activity during whole you make them of life, therefore, for such it demands investments in environmental control, that is to say continuous heating of the creation sheed; The micro-regions of Cerro Azul and Guaraqueçaba demand systems of environmental control, heating and mainly cooling in the last week of life

Global, regional, and national under-5 mortality, adult mortality, age-specific mortality, and life expectancy, 1970–2016: a systematic analysis for the Global Burden of Disease Study 2016

BACKGROUND: Detailed assessments of mortality patterns, particularly age-specific mortality, represent a crucial input that enables health systems to target interventions to specific populations. Understanding how all-cause mortality has changed with respect to development status can identify exemplars for best practice. To accomplish this, the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) estimated age-specific and sex-specific all-cause mortality between 1970 and 2016 for 195 countries and territories and at the subnational level for the five countries with a population greater than 200 million in 2016. METHODS: We have evaluated how well civil registration systems captured deaths using a set of demographic methods called death distribution methods for adults and from consideration of survey and census data for children younger than 5 years. We generated an overall assessment of completeness of registration of deaths by dividing registered deaths in each location-year by our estimate of all-age deaths generated from our overall estimation process. For 163 locations, including subnational units in countries with a population greater than 200 million with complete vital registration (VR) systems, our estimates were largely driven by the observed data, with corrections for small fluctuations in numbers and estimation for recent years where there were lags in data reporting (lags were variable by location, generally between 1 year and 6 years). For other locations, we took advantage of different data sources available to measure under-5 mortality rates (U5MR) using complete birth histories, summary birth histories, and incomplete VR with adjustments; we measured adult mortality rate (the probability of death in individuals aged 15-60 years) using adjusted incomplete VR, sibling histories, and household death recall. We used the U5MR and adult mortality rate, together with crude death rate due to HIV in the GBD model life table system, to estimate age-specific and sex-specific death rates for each location-year. Using various international databases, we identified fatal discontinuities, which we defined as increases in the death rate of more than one death per million, resulting from conflict and terrorism, natural disasters, major transport or technological accidents, and a subset of epidemic infectious diseases; these were added to estimates in the relevant years. In 47 countries with an identified peak adult prevalence for HIV/AIDS of more than 0·5% and where VR systems were less than 65% complete, we informed our estimates of age-sex-specific mortality using the Estimation and Projection Package (EPP)-Spectrum model fitted to national HIV/AIDS prevalence surveys and antenatal clinic serosurveillance systems. We estimated stillbirths, early neonatal, late neonatal, and childhood mortality using both survey and VR data in spatiotemporal Gaussian process regression models. We estimated abridged life tables for all location-years using age-specific death rates. We grouped locations into development quintiles based on the Socio-demographic Index (SDI) and analysed mortality trends by quintile. Using spline regression, we estimated the expected mortality rate for each age-sex group as a function of SDI. We identified countries with higher life expectancy than expected by comparing observed life expectancy to anticipated life expectancy on the basis of development status alone. FINDINGS: Completeness in the registration of deaths increased from 28% in 1970 to a peak of 45% in 2013; completeness was lower after 2013 because of lags in reporting. Total deaths in children younger than 5 years decreased from 1970 to 2016, and slower decreases occurred at ages 5-24 years. By contrast, numbers of adult deaths increased in each 5-year age bracket above the age of 25 years. The distribution of annualised rates of change in age-specific mortality rate differed over the period 2000 to 2016 compared with earlier decades: increasing annualised rates of change were less frequent, although rising annualised rates of change still occurred in some locations, particularly for adolescent and younger adult age groups. Rates of stillbirths and under-5 mortality both decreased globally from 1970. Evidence for global convergence of death rates was mixed; although the absolute difference between age-standardised death rates narrowed between countries at the lowest and highest levels of SDI, the ratio of these death rates-a measure of relative inequality-increased slightly. There was a strong shift between 1970 and 2016 toward higher life expectancy, most noticeably at higher levels of SDI. Among countries with populations greater than 1 million in 2016, life expectancy at birth was highest for women in Japan, at 86·9 years (95% UI 86·7-87·2), and for men in Singapore, at 81·3 years (78·8-83·7) in 2016. Male life expectancy was generally lower than female life expectancy between 1970 and 2016, an

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

Formalization in PVS of Balancing Properties Necessary for Proving Security of the Dolev-Yao Cascade Protocol Model

In this work, we present an algebraic approach for modeling the two-party cascade protocol of Dolev-Yao and for fully formalizing its security in the specification language of the Prototype Verification System PVS. Although cascade protocols could be argued to be a very limited model, it should be stressed here that they are the basis of more sophisticated protocols of great applicability, such as those which allow treatment of multiparty, tuples, nonces, name-stamps, signatures, etc. In the current algebraic approach, steps of the protocol are modeled in a monoid freely generated by the cryptographic operators. Words in this monoid are specified as finite sequences and the whole protocol as a finite sequence of protocol steps, that are functions from pairs of users to sequences of cryptographic operators. In a previous work, assuming that for balanced protocols admissible words produced by a potential intruder should be balanced, a formalization of the characterization of security of this kind of protocols was given in PVS. In this work, the previously assumed property is also formalized, obtaining in this way a complete formalization which mathematically guarantees the security of these protocols. Despite such property being relatively easy to specify, obtaining a complete formalization requires a great amount of effort, because several algebraic properties, that are related to the preservation of the balancing property of the admissible language of the intruder, should be formalized in the granularity of the underlying data structure (of finite sequences used in the specification). Among these properties, the most complex are related to the notion of linkage property, which allows for a systematic analysis of words of the admissible language of a potential saboteur, showing how he/she is unable to isolate private keys of other users under the assumption of balanced protocols. The difficulties that arose in conducting this formalization are also presented in this work

Diagnóstico bioclimático para mesorregião metropolitana de curitiba PR

O objetivo deste trabalho é analisar dados climatológicos da mesorregião Metropolitana de Curitiba do Estado do Paraná com intuito de relaciona-los com as exigências bioclimáticas para a produção de aves, para verificar a viabilidade da criação, como também, servir de orientação a avicultores e futuros criadores na implantação de sistemas de controle ambiental utilizando a metodologia proposta por ABREU e ABREU (2001). A análise foi realizada com os dados climáticos fornecidos pelo Instituto Agronômico do Paraná (IAPAR) normais climatológicas das seguintes microrregiões: Antonina, Cerro Azul, Guaraqueçaba, Lapa, Morretes e Pinhais; os valores da Temperatura Média do Ar Compensada e Umidade Relativa foram utilizados para comparar com as condições de conforto térmico para aves, em função da idade das mesmas. As comparações realizadas em cada microrregião mostraram a necessidade de corrigir o microclima dos galpões para alcançar condições ideais para produção de aves. As microrregiões de Antonina, Lapa e Pinhais não apresentam condições ideais para desenvolvimento da atividade durante todas as fases de vida, portanto, para tal exige investimentos em controle ambiental, ou seja o aquecimento contínuo do galpão de criação; As microrregiões de Cerro Azul e Guaraqueçaba exigem sistemas de controle ambiental, aquecimento e principalmente resfriamento na última semana de vida