Generators for Cubic Surfaces with two Skew Lines over Finite Fields

Let S be a smooth cubic surface defined over a field K. As observed by Segre and Manin, there is a secant and tangent process on S that generates new K-rational points from old. It is natural to ask for the size of a minimal generating set for S(K). In a recent paper, for fields K with at least 13 elements, Siksek showed that if S contains a skew pair of K-lines then S(K) can be generated from one point. In this paper we prove the corresponding version of this result for fields K having at least 4 elements, and slightly milder results for #K=2 or 3.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1012.1838 by other author

A model for the emergence of cooperation, interdependence and structure in evolving networks

Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of cooperative molecular species arises and evolves to become more complex and structured. The network is modeled by a directed weighted graph whose positive and negative links represent `catalytic' and `inhibitory' interactions among the molecular species, and which evolves as the least populated species (typically those that go extinct) are replaced by new ones. A small autocatalytic set (ACS), appearing by chance, provides the seed for the spontaneous growth of connectivity and cooperation in the graph. A highly structured chemical organization arises inevitably as the ACS enlarges and percolates through the network in a short, analytically determined time scale. This self-organization does not require the presence of self-replicating species. The network also exhibits catastrophes over long time scales triggered by the chance elimination of `keystone' species, followed by recoveries.Comment: 8 pages, 4 figure

Monte-Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions

The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte-Carlo simulations for the unpolarized and single-polarized Drell-Yan $\bar{p} p^{(\uparrow)} \to \mu^+ \mu^- X$ at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the HESR ring at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.Comment: Deeply revised text with improved discussion of kinematics and results; added one table; 12 figures. Accepted for publication in Phys. Rev.

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi-Pasta-Ulam (FPU) paradox. We study $q$-breathers in one- two- and three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices -- theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of $q$-breathers is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter $q$-breathers delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into strong mode-mode interaction regime. In particular this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of $q$-breathers supplements these findings. For three-dimensional lattices, we find $q$-breather vortices, which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.Comment: 19 pages, 9 figure

Pfaffian representations of cubic surfaces

Let K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x_0,x_1,x_2,x_3] and a zero A of F in P^3_K and ensures a linear pfaffian representation of V(F) with entries in K[x_0,x_1,x_2,x_3], under mild assumptions on F and A. We use this result to give an explicit construction of (and to prove the existence of) a linear pfaffian representation of V(F), with entries in K'[x_0,x_1,x_2,x_3], being K' an algebraic extension of K of degree at most six. An explicit example of such a construction is given.Comment: 17 pages. Expanded with some remarks. Published with minor corrections in Geom. Dedicat

On Binary Matroid Minors and Applications to Data Storage over Small Fields

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of $\mathbb{F}_{2}$-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.Comment: 14 pages, 2 figure

Free-energy transition in a gas of non-interacting nonlinear wave-particles

We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.Comment: 4 pages, 3 figure

Infecção congênita pelo citomegalovírus: ocorrência em duas populações de nível sócio-econômico diferentes em São Paulo, Brasil

In São Paulo, Brazil, between November 1980 and July 1982, 1614 newborns of middle socioeconomic background and 1156 newborns of low socioeconomic background were examined for the occurrence of congenital cytomegalovirus (CMV) infection by isolation of virus from urine samples or detection of specific anti-CMV IgM in umbilical cord serum tested by immunofluorescence. In the low socioeconomic population prevalence of CMV complement-fixing antibodies in mothers was 84.4%(151/179) and the incidence of congenital infection assessed by virus isolation 0.98% (5/508), as compared with 0.46% (3/648) in the group of newborns tested by detection of specific anti-CMV IgM in umbilical cord-serum. In middle socioeconomic level population prevalence of CMV complement-fixing antibodies in mothers was 66.5% (284/427) and the incidence of CMV congenital infection was 0.39% (2/518) in the group of newborns screened by virus isolation and 0.18% (2/1096) in the group tested by detection of specific anti-CMV IgM. In the present study none of the 12 congenitally infected newborns presented clinical apparent disease at birth.Entre novembro de 1980 e julho de 1982, 1614 recém-nascidos (RNs) de nivel sócio-econômico médio e 1156 RNs de baixo nível sócioeconômico foram examinados para verificar a ocorrência de infecção congênita pelo citomegalovírus (CMV), através de isolamento do vírus em amostras de urina ou detecção de anticorpos IgM específicos em amostras de sangue de cordão umbilical. Na população de baixo nível sócio econômico a prevalência de anticorpos fixadores do complemento (Ac Fc) anti-CMV nas mães foi de 84,4% (151/179) e a incidência de infecção congênita determinada por isolamento do vírus foi de 0,90% (5/508). No grupo de RNs em que o diagnóstico baseou-se apenas na detecção de Ac IgM CMV-específicos no sangue de cordão a incidência de infecção congênita foi de apenas 0,46% (3/648). Na população de nivel sócio-econômico médio a prevalência de Ac Fc anti-CMV nas mães foi de 66,5% (284/427) e a incidência de infecção congênita foi de 0,39% (2/518) no grupo de RNs testados por isolamento de vírus na urina e 0,18% (2/1090) no grupo testado por detecção de Ac IgM específicos. No presente estudo nenhum dos 12 RNs infectados congenitamente apresentou sinais ou sintomas de doença ao nascimento

Variety of idempotents in nonassociative algebras

In this paper, we study the variety of all nonassociative (NA) algebras from the idempotent point of view. We are interested, in particular, in the spectral properties of idempotents when algebra is generic, i.e. idempotents are in general position. Our main result states that in this case, there exist at least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a generic NA algebra of dimension $n$. We also discuss the exceptionality of the eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in many classical examples of NA algebras and characterize its extremal properties in metrised algebras.Comment: 27 pages, 1 figure, submitte