Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

On global linearization of planar involutions

Let phi: a"e(2) -> a"e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = {Eigenvalues of D phi(p) | p a a"e(2)}. We prove that if Spc(phi) aS, a"e or Spc(phi) a (c) [1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a"e(2) -> a"e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a"e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled.

TRANSITIVITY AND ROTATION SETS WITH NONEMPTY INTERIOR FOR HOMEOMORPHISMS OF THE 2-TORUS

We show that if f is a homeomorphism of the 2-torus isotopic to the identity and its lift (f) over tilde is transitive, or even if it is transitive outside the lift of the elliptic islands, then (0,0) is in the interior of the rotation set of (f) over tilde. This proves a particular case of Boyland's conjecture.

Leishmania amazonensis Arginase Compartmentalization in the Glycosome Is Important for Parasite Infectivity

In Leishmania, de novo polyamine synthesis is initiated by the cleavage of L-arginine to urea and L-ornithine by the action of arginase (ARG, E.C. 3.5.3.1). Previous studies in L. major and L. mexicana showed that ARG is essential for in vitro growth in the absence of polyamines and needed for full infectivity in animal infections. The ARG protein is normally found within the parasite glycosome, and here we examined whether this localization is required for survival and infectivity. First, the localization of L. amazonensis ARG in the glycosome was confirmed in both the promastigote and amastigote stages. As in other species, arg(-) L. amazonensis required putrescine for growth and presented an attenuated infectivity. Restoration of a wild type ARG to the arg(-) mutant restored ARG expression, growth and infectivity. In contrast, restoration of a cytosol-targeted ARG lacking the glycosomal SKL targeting sequence (arg Delta SKL) restored growth but failed to restore infectivity. Further study showed that the ARG Delta SKL protein was found in the cytosol as expected, but at very low levels. Our results indicate that the proper compartmentalization of L. amazonensis arginase in the glycosome is important for enzyme activity and optimal infectivity. Our conjecture is that parasite arginase participates in a complex equilibrium that defines the fate of L-arginine and that its proper subcellular location may be essential for this physiological orchestration.

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

MODULARITY, NOISE, AND NATURAL SELECTION

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates. In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results.

Effective number of accessed nodes in complex networks

The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.

Helical buckling of Skyrme-Faddeev solitons

Solitons in the Skyrme-Faddeev model on R-2 x S-1 are shown to undergo buckling transitions as the circumference of the S-1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.

Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012

The Tripartite Ramsey Number for Trees

We prove that for all epsilon>0 there are alpha>0 and n(0)is an element of N such that for all n >= n(0) the following holds. For any two-coloring of the edges of Kn, n, n one color contains copies of all trees T of order t <=(3 - epsilon)n/2 and with maximum degree Delta(T)<= n(alpha). This confirms a conjecture of Schelp. (c) 2011 Wiley Periodicals, Inc. J Graph Theory 69: 264300, 2012

O Recuo Brutalista

Em conformidade com a dúvida de seu título, o difundido livro The New Brutalism: Ethic or Aesthetic? de Reyner Banham não é possível explicar o Brutalismo como manifestação artística coesa, dotada de consistência e reprodutibilidade formal. A citação de arquitetos famosos, porém divergentes, parece associar e comparar obras ásperas com a pretensão de reerguer uma arquitetura moderna considerada ascética, monótona e insuficiente e gera um teoricismo da aparência crua e do moralismo dos objetos. Discurso que oculta, ou desvia a atenção do retorno artístico à sublimidade e construção artesanal. O Brutalismo é aceito como evolução natural dos estágios modernos anteriores e sanciona artefatos toscos, pesados e inacabados como se fossem filiados ao processo moderno desinfestado. Esconde contradições e disfarça seu rompimento com o moderno para prolongar a expressão Movimento moderno. Mas o objeto claro, econômico e preciso é repudiado pelo consumidor e, por ser pouco representativo, o artista faz sua maquiagem com episódios contrastantes e monumentais na informalidade das cidades espontâneas. No entanto, parece possível suspender a noção positiva e corretiva do Brutalismo para entendê-lo como um recuo artístico vulgarizador que despreza aperfeiçoamento e afronta a atitude moderna com banalização conceptiva, exagero, figuralidade, musculação estrutural, grandeza tectônica, rudimento e rudeza. Assim, moralismo, retorno rústico e originalidade desqualificam a expressão International Style entendida como a culminação da arquitetura moderna do pós-guerra, ao depreciá-la como decadente, como produto imobiliário, comercial e corporativo a serviço do capital. Essa interpretação desvela uma crítica anti-industrial, portanto antimodernista e diversa da pós-modernidade, porém contestadora e realista para fornecer imagens à cultura e aos insensíveis à estrutura da forma moderna. Diverso da pós-modernidade pela dependência ao moderno e ausência de apelo popular. Tornada insignificante a configuração oportuna do artefato, o arquiteto tenta reter sua notabilidade artística, ou o prestígio que parece enfraquecer na aparência símile da especificação de catálogo, no rigor modular. Indispõe-se e repudia componentes, Standards e acabamentos impessoais da indústria da construção para insistir em autoria e inspiração, mas repete cacoetes estilísticos de época e o inexplicável uso intensivo de concreto bruto e aparente para sentir-se engajado e atualizado. Porém, é necessário distinguir obras de aparência severa concebidas pela atitude moderna mais autêntica das de concreto aparente em tipos ou configurações aberrantes. Para avançar na discussão do Brutalismo propõe-se entender este fenômeno com a substituição do juízo estético moderno de sentido visual postulado por Immanuel Kant (1724-1804) por um sentimento estético fácil e relacionado com a sensação da empatia, com a Einfühlung de Robert Vischer (1847-1933). Na época da cultura de massas, admite-se o rebaixamento das exigências no artefato e a adaptação brutalista com a transfiguração dos processos de arquitetura moderna. Assim, a forma é substituída pela figura ou pelo resumo material; a estrutura formal subjacente pelo ritmo e exposição da estrutura física; o reconhecimento visual pelo entusiasmo psicológico ou pelo impulso dionisíaco; a concepção substituída pelo partido, ou, ainda, pelo conceito; a sistematização e a ordem pela moldagem e a organização; a abstração e síntese pela originalidade e essencialidade, o sentido construtivo pela honestidade material; a identidade das partes pela fundição ou pela unicidade objetal e a residência pela cabana primitiva.

Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.