The unbounded dead-end depth propertie is not a group invariant

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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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Doenças intestinais em cidades brasileiras: associação com elementos climáticos

Enteric fevers and dysenteries showed, during the period 1940-44, a summer prevalence in brazilian cities of the temperate zone. The distribu¬tion of the diseases by four-months periods, selected in acordance with the highest of lowest values of rainfall, mean temperature and absolute humidity induced to suppose that, in those cities, and also in tropical ones, both enteric fevers and dysenteries were closely associated with such climatic factors: enteric fevers mainly with absolute humidity and temperature, and dysenteries with humidity and rainfall. Correlation coefficients, statistically significant, have been obtained comparing monthly waves of climatic factors and corresponding waves of prevalence of the diseases. For enteric fevers, clear associations have been disclosed: with temperature variations in all temperate cities (coefficients ranging from + 0.42 to + 0.75, higher with mean temperature in the previous month) and in two of the four tropical cities (from + 0.26 to ± 0.30); with absolute humidity variations in cities of the first group (from + 0.51 to 0.71) and in the tropical city of Rio ( + 0.26 ± 0.12 and + 0.28 ± 0.12); and also with rainfall variations but only in two temperate cities (from + 0.28 to + 0.64). For dysenteric diseases, in cities of temperate zone similar associations have been found with absolute humidity (values of r, ranging from + 0.32 to + 0.45), with temperature (from + 0.26 to + 0.44); and with rainfall only in Curitiba ( + 0.25 ± 0.12). Recife (tropical city) yielded two significant values : r = — 0.27 ± 0.12 (correlation with mean temperature in the same month) and r = + 0.40 ± 0.11 and -h 0.37 ± 0.11 (between monthly morbidity rates and rainfall, respectively in the same month and in the previous one). Deaths by diarrhea and enteritis, in the cities of the temperate zone, prevailed in spring-summer seasons, also in four-months periods of highest temperature and humidity, for those cities and for the tropical ones, with the exception of Belem in which percentages were identical to those of opposite periods. Still with the exception of Belem, in all cities studied positive correla¬tion coefficients, statistically significant, have been obtained with temperature variations (ranging from + 0.25 to + 0.65 in tropical cities, and from + 0.47 to + 0.76 in temperate zone) and with humidity variations (from + 0.34 to + 0.44 in the first group, and from + 0.43 and + 0.74 in the second) . With rainfall, only Rio (in the tropical region) showed a significant value for r ( + 0.26 ±0:12); similarly in S. Paulo and Curitiba, the values ranged from + 0.46 to + 0.56, while in Porto Alegre there were found — 0.26 ± 0.12 and — 0.32 ± 012, for rainfall variations in the same and previous months.

Temperatura, humidade e pluviosidade nas suas relações com doenças respiratórias, em cidades brasileiras

During the period 1940-44, deaths by respiratory diseases and particularly by influenza and pneumonias prevailed during the winter in brazilian cities of the temperate zone (S. Paulo, Curitiba, Porto Alegre) and, with the exception of Rio de Janeiro, in tropical ones (Belem, Recife, Salvador) particularly during the four-months period of highest absolute humidity. For the first group of cities, negative correlation coefficients, statistically significant, have been uniformly obtained comparing monthly death-rates both with temperature - in the same month and in the previous one (values of r ranging from - 0.36 to - 0.640 - and with similar humidity variations (values of r from - 0.33 to - 0.59); also with rainfall, but only in S. Paulo and Curitiba (values of r from - 0.33 to - 0.61). Such associations have been disclosed irregularly and less frequently for the group of tropical cities: statistically significant values of r, in the death-rates correlations with temperature and humidity variations, have been eventually either positive (Recife, Salvador) or negative (Belem, Rio). Whooping cough showed during the same period a winter incidence in Curitiba and Porto Alegre: the compulsory notification of the disease is not required in S. Paulo, a third one brazilian city of the temperate zone. In the brazilian tropical cities of Belem, Recife, Salvador and Rio, the whooping cough distribution by four-months periods - selected in accordance with the highest or lowest values of rainfall, mean temperature and absolute humidity - induced to suppose that the disease was associated more uniformly with a high rainfall than with a low temperature or a low absolute humidity. However, only a few correlation coefficients statistically significant have been found out: between monthly morbidity rates and mean humidity in the same month and in the previous one in recife (-0.43 and - 0.39), and in Porto Alegre (-0.35 and - 0.46); and between the same rates and temperature variations in this last city (-0.28 and - 0.43).

Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

The density of injective endomorphisms of a free group

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Organisational structure, communication and group ethics

This paper investigates experimentally how organisational decision processes affect the moral motivations of actors inside a firm that must forego profits to reduce harming a third party. In a "vertical" treatment, one insider unilaterally sets the harm-reduction strategy; the other can only accept or quit. In a "horizontal" treatment, the insiders decide by consensus. Our 2-by-2 design also controls for communication effects. In our data, communication makes vertical firms more ethical; voice appears to mitigate "responsibility-alleviation" in that subordinates with voice feel responsible for what their firms do. Vertical firms are then more ethical than the horizontal firms for which our bargaining data reveal a dynamic form of responsibility-alleviation and our chat data indicate a strong "insider-outsider" effect.

A Model of ethnic conflict

We present a model of conflict, in which discriminatory government policy or social intolerance is responsive to various forms of ethnic activism, including violence. It is this perceived responsiveness -captured by the probability that the government gives in and accepts a proponed change in ethnic policy- that induces individuals to mobilize in support for their cause. Yet, mobilization is costly and demonstrators have to be compensated accordingly. Individuals have to weigh their ethnic radicalism with their material well-being to determine the size of their money contribution to the cause. Our main results are: (i) a one-sided increase in radicalism or in population size increases conflict; (ii) a one-sided increase in income has ambiguous effects depending on the elasticity of contributions to income; (iii) an increase in within-group inequality increases conflict; and (iv) an increase in the correlation between ethnic radicalism and inequality also increases conflict.

Simulium argentiscutum sp. nov. (Diptera: simuliidae), a member of the S. amazonicum-group of species; description of adults, pupa and larva

The adult, pupal and larval morphology of S. argentiscutum sp. nov., a member of the S. amazonicum-group, is compared with S. amazonicum Goeldi and its distribution, biology and medical importance are discussed. S. argentiscutum is one the most important anthropophilic species in the S. amazonicum-group as it is responsible, together with S. amazonicum, for the transmission of Mansonella ozzardi in Brazil.

The microps group of Lutzomyia França with descriptions of two new species from South America (Diptera: Psychodidae: Phlebotominae)

Six species of phlebotomine sand flies in the genus Lutzomyia França from South America are included in the newly-created species group microps. References and illustrations of the species are given, including descriptions of two new forms - L. nematoducta n.sp., male and female from northern Brazil, and l. preclara n.sp. male from Colombia and Peru. The males in the species group microps are keyed.