Real Bruhat cells give an important and well studied stratification of such spaces as GL n+1 , Flag n+1 = SL n+1 /B, SO n+1 and Spin n+1 . We study the intersections of a top dimensional cell with another cell (for another basis). Such an intersection is naturally identified with a subset of the lower nilpotent group Lo 1 n+1 . We are particularly interested in the homotopy type of such intersections. In this paper we define a stratification of such intersections. As a consequence, we obtain a finite CW complex which is homotopically equivalent to the intersection.We compute the homotopy type for several examples. It turns out that for n ≤ 4 all connected components of such subsets of Lo 1 n+1 are contractible: we prove this by explicitly constructing the corresponding CW complexes. Conversely, for n ≥ 5 and the top permutation, there is always a connected component with even Euler characteristic, and therefore not contractible. This follows from formulas for the number of cells per dimension of the corresponding CW complex. For instance, for the top permutation S 6 , there exists a connected component with Euler characteristic equal to 2. We also give an example of a permutation in S 6 for which there exists a connected component which is homotopically equivalent to the circle S 1 .

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The aim of this study was to compare the tactical knowledge of young football players in different playing positions during a three-a-side small-sided game (SSG). Observational data was collected from 71 players (M = 12.16; SD = 1.55 years): 11 goalkeepers, 22 defenders, 15 midfielders, and 23 forwards. In total, 4 min of three-a-side SSGs (GR + 3 vs. 3 + GR) were recorded to assess tactical performance using a digital camera (GoPro Hero 6® version 02.01). The SSGs were performed on a field with a constant area (36 × 27 m). Video analyses were performed using LongoMatch® version 1.5.9 to record football performance; we then assessed tactical performance by using the Football Tactical Assessment System (Fut-Sat). This instrument evaluates the average of well-defined action indexes for each game in decision making principle and motor skills, specifically: (i) Decision Making Index (DMI); (ii) Motor Effectiveness Index (MEI); (iii) Effectiveness Index (I). The indexes were calculated by the ratio between the correct actions and the total. The Kruskal–Wallis test was used to evaluate differences between playing positions. The results showed that tactical performance by principles seems to be significantly different according to playing position. Differences were found between defenders and forwards (H = −11.92; p = 0.03) and defenders and midfielders (H = −16.13; p = 0.01) in contention principle. In conclusion, tactical knowledge of training based on the principles of the game can help coaches and players better understand and predict each player’s actions during the game.

RESUMOA radiação ionizante quando interage com a matéria remove um elétron de seu orbital, formando íons ou partículas ionizadas. Quando um indivíduo é exposto a radiações ionizantes, existe a possibilidade de se produzir danos para o organismo, danos reversíveis ou não, dependendo basicamente do tempo de exposição, do nível de dano e da dose absorvida. Esse trabalho teve como objetivo caracterizar a produção científica sobre danos genéticos causados por radiações ionizantes, desde o ano de 1970 até o ano de 2014 a fim de verificar as tendências e perspectivas do desenvolvimento científico por meio da análise cienciométrica. Para isso foi realizado um levantamento bibliográfico no sítio Scopus®, utilizando as palavraschaves "ionizing radiation" and mutation and effects and human. Foram realizadas diferentes dados os artigos: tipo de publicação, número de artigos/ano, periódicos que mais publicaram e patologias abordados nos estudos. Constatou-se um aumento no número de publicações relacionadas aos danos no DNA e radiação ionizante no decorrer dos anos. A maior parte dos trabalhos foi desenvolvida por autores de origem dos Estados Unidos da América (42%). A maioria dos artigos relacionou seus achados ao desenvolvimento do câncer (41%). O estudo mostra que há interesse em relação ao estudo de danos no DNA causados por radiação ionizante, uma vez que estes danos podem ser responsáveis por inúmeros efeitos biológicos desfavoráveis à saúde humana. PALAVRAS-CHAVE:Cienciometria; Danos ao DNA; Mutação. EFFECT OF EXPOSURE TO IONIZING RADIATION ON DNA:A SCIENTIFIC ASSESSMENT ABSTRACT Ionizing radiation, when interacting with matter, removes an electron from its orbital and generates ions or ionized particles. When an individual is exposed to ionizing radiation, reversible or irreversible harms to the body may arise, depending basically

Locally convex (or nondegenerate) curves in the sphere S n (or the projective space) have been studied for several reasons, including the study of linear ordinary differential equations of order n + 1. Taking Frenet frames allows us to obtain corresponding curves Γ in the group Spin n+1 ; recall that Π : Spin n+1 → Flag n+1 is the universal cover of the space of flags. Let L n (z 0 ; z 1 ) be the space of such curves Γ with prescribed endpoints Γ(0) = z 0 , Γ(1) = z 1 . The aim of this paper is to determine the homotopy type of the spaces L 3 (z 0 ; z 1 ) for all z 0 , z 1 ∈ Spin 4 . Recall that Spin 4 = S 3 × S 3 ⊂ H × H, where H is the ring of quaternions.This paper relies heavily on previous publications by the authors. The earliest such paper solves the corresponding problem for n = 2 (i.e., for curves in S 2 ). Another previous result (with B. Shapiro) reduces the problem to z 0 = 1 and z 1 ∈ Quat 4 where Quat 4 ⊂ Spin 4 is a finite group of order 16 with center Z(Quat 4 ) = {(±1, ±1)}. A more recent paper shows that for z 1 ∈ Quat 4 Z(Quat 4 ) we have a homotopy equivalence L 3 (1; z 1 ) ≈ Ω Spin 4 . In this paper we compute the homotopy type of L 3 (1; z 1 ) for z 1 ∈ Z(Quat 4 ): it is equivalent to the infinite wedge of Ω Spin 4 with an infinite countable family of spheres (as for the case n = 2).The structure of the proof is roughly the same as for the case n = 2 but some of the steps are much harder. In both cases we construct explicit subsets Y ⊂ L n (z 0 ; z 1 ) for which the inclusion Y ⊂ Ω Spin n+1 (z 0 ; z 1 ) is a homotopy equivalence. For n = 3, this is done by considering the itineraries of such curves. The itinerary of a curve in L n (1; z 1 ) is a finite word in the alphabet S n+1 {e} of nontrivial permutations.