Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

EFFECTIVE NETWORKS FOR REAL-TIME DISTRIBUTED PROCESSING

This paper applies the concepts and methods of complex networks to the development of models and simulations of master-slave distributed real-time systems by introducing an upper bound in the allowable delivery time of the packets with computation results. Two representative interconnection models are taken into account: Uniformly random and scale free (Barabasi-Albert), including the presence of background traffic of packets. The obtained results include the identification of the uniformly random interconnectivity scheme as being largely more efficient than the scale-free counterpart. Also, increased latency tolerance of the application provides no help under congestion.

An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Bounds for the probability distribution function of the linear ACD process

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

From commitment to non-commitment: allowing type dynamic in Laffont and Tirole's regulation model

This paper investigates the introduction of type dynamic in the La ont and Tirole's regulation model. The regulator and the rm are engaged in a two period relationship governed by short-term contracts, where, the regulator observes cost but cannot distinguish how much of the cost is due to e ort on cost reduction or e ciency of rm's technology, named type. There is asymmetric information about the rm's type. Our model is developed in a framework in which the regulator learns with rm's choice in the rst period and uses that information to design the best second period incentive scheme. The regulator is aware of the possibility of changes in types and takes that into account. We show how type dynamic builds a bridge between com- mitment and non-commitment situations. In particular, the possibility of changing types mitigates the \ratchet e ect". We show that for small degree of type dynamic the equilibrium shows separation and the welfare achived is close to his upper bound (given by the commitment allocation).

General equilibrium model with restricted participation in financial markets

The paper analyses a general equilibrium model with financiaI markets in which households may face restrictions in trading financiaI assets such as borrowing constraints and collateral (restricted participation model). However, markets are not assumed to be incomplete. We consider a standard general equilibrium model with H > 1 households, 2 periods and S states of nature in the second period. We show that generically the set of equilibrium allocations ia indeterminate, provided the existence of at least one nominal asset and one household for who some restriction is binding. Suppose there are C > 1 commodities in each state of nature and assets pays in units of some commodity. In this case for each household with binding restrictions it is possible to reduce the set of feasible assets trading and obtain a new equilibrium that utility improve alI those households. There is however an upper bound on the number of households to be improved related to the number of states of nature and the number of commodities. In particular, if the number of households ia smaller than the number of states of nature it is possible to Pareto improve any equilibrium by reducing the feasible choice set for each household.

LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Photon mass and gravitational deflection

The deflection of a massive photon by an external gravitational field is energy-dependent. Interesting enough, any massive quantum particle, no matter what its spin is, undergoes dispersive deflection in external gravitational fields. Exploiting the dispersive deflection of the quantized massive electromagnetic radiation by the gravitational field of the Sun, we find an upper bound for the photon mass.

Search for the flavour-changing neutral current B-s(0)->mu+mu- in p(p)over-bar collisions at root s=1.96 TeV with the D0 dectector

We present the results of a search for the flavor-changing neutral current decay B-s(0)-->mu(+)mu(-) using a data set with integrated luminosity of 240 pb(-1) of p (p) over bar collisions at roots=1.96 TeV collected with the D0 detector in run II of the Fermilab Tevatron collider. We find the upper limit on the branching fraction to be B(B-s(0)-->mu(+)mu(-))less than or equal to5.0x10(-7) at the 95% C.L. assuming no contributions from the decay B-d(0)-->mu(+)mu(-) in the signal region. This limit is the most stringent upper bound on the branching fraction B-s(0)-->mu(+)mu(-) to date.

Search for the rare decay B-s(0)->phi mu(+)mu(-) with the D0 detector

We present a search for the flavor-changing neutral current decay B-s(0)->phi mu(+)mu(-) using about 0.45 fb(-1) of data collected in p (p) over bar collisions at root s=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. We find an upper limit on the branching ratio of this decay normalized to B-s(0)-> J/psi phi of B(B-s(0)->phi mu(+)mu(-))/B(B-s(0)-> J/psi phi)< 4.4x10(-3) at the 95% C.L. Using the central value of the world average branching fraction of B-s(0)-> J/psi phi, the limit corresponds to B(B-s(0)->phi mu(+)mu(-))< 4.1x10(-6) at the 95% C.L., the most stringent upper bound to date.

Search for single production of scalar leptoquarks in p(p)over-bar collisions decaying into muons and quarks with the D0 detector

lWe report on a search for second generation leptoquarks (LQ(2)) which decay into a muon plus quark in (p) over barp collisions at a center-of-mass energy of root s = 1.96 TeV in the DO detector using an integrated luminosity of about 300 pb(-1). No evidence for a leptoquark signal is observed and an upper bound on the product of the cross section for single leptoquark production times branching fraction into a quark and a muon was determined for second generation scalar leptoquaiks as a function of the leptoquark mass. This result has been combined with a previously published DO search for leptoquark pair production to obtain leptoquark mass limits as a function of the leptoquark-muon-quark coupling, lambda. Assuming lambda = 1, lower limits on the mass of a second generation scalar leptoquark coupling to a u quark and a muon are m(LQ2) > 274 GeV and m(LQ2) > 226 GeV for beta = 1 and beta = 1/2, respectively. (c) 2007 Elsevier B.V. All rights reserved.

DM particles: how warm they can be?

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)