The role of predator overlap in the robustness and extinction of a four species predator-prey network

Predators and preys often form species networks with asymmetric patterns of interaction. We study the dynamics of a four species network consisting of two weakly connected predator-prey pairs. We focus our analysis on the effects of the cross interaction between the predator of the first pair and the prey of the second pair. This is an example where the predator overlap, which is the proportion of predators that a given prey shares with other preys, is not uniform across the network due to asymmetries in patterns of interaction. We explore the behavior of the system under different interaction strengths and study the dynamics of survival and extinction. In particular, we consider situations in which the four species have initial populations lower than their long-term equilibrium, simulating catastrophic situations in which their abundances are reduced due to human action or environmental change. We show that, under these reduced initial conditions, and depending on the strength of the cross interaction, the populations tend to oscillate before re-equilibrating, disturbing the community equilibrium and sometimes reaching values that are only a small fraction of the equilibrium population, potentially leading to their extinction. We predict that, contrary to one`s intuition, the most likely scenario is the extinction of the less predated preys. (C) 2010 Elsevier B.V. All rights reserved.

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.

A QCD sum rule calculation for the Y(4140) narrow structure

We use the QCD sum rules to evaluate the mass of a possible scalar mesonic state that couples to a molecular D(s)*(D) over bar (s)* current. We find a mass m(Ds)*(Ds)* = (4.14 +/- 0.09) GeV, which is in an excellent agreement with the recently observed Y(4140) charmonium state. We consider the contributions of condensates up to dimension-eight, we work at leading order in alpha(s) and we keep terms which are linear in the strange quark mass m(s). We also consider a molecular D*(D) over bar* current and we obtain m m(D)*(D)* = (4.13 +/- 0.10), around 200 MeV above the mass of the Y(3930) charmonium state. We conclude that it is possible to describe the Y(4140) structure as a D(s)*(D) over bar (s)* molecular state or even as a mixture of D(s)*(D) over bar (s)* and D*(D) over bar* molecular states. (C) 2009 Elsevier B.V. All rights reserved.

QCD sum rule calculation for the charmonium-like structures in the J/psi phi and J/psi omega invariant mass spectra

Using the QCD sum rules we test if the charmonium-like structure Y(4274), observed in the J/psi phi invariant mass spectrum, can be described with a D(s)(D) over bar (s0)(2317)+ h.c. molecular current with J(PC) = 0(-+). We consider the contributions of condensates up to dimension ten and we work at leading order in alpha(s). We keep terms which are linear in the strange quark mass m(s). The mass obtained for such state is mD(s)D(s0) = (4.78 +/- 0.54) GeV. We also consider a molecular 0(-+) D (D) over bar (0)(2400)+ h.c. current and we obtain m(DD0) = (4.55 +/- 0.49) GeV. Our study shows that the newly observed Y(4274) in the J/psi phi invariant mass spectrum can be, considering the uncertainties, described using a molecular charmonium current. (C) 2011 Elsevier B.V. All rights reserved.

The degree of polydispersity in micellar dispersions: A sum rule approach

Statistical properties of a two-dimensional ideal dispersion of polydisperse micelles are derived by analyzing the convergence properties of a sum rule set by mass conservation. Internal micellar degrees of freedom are accounted for by a microscopic model describing small displacements of the constituting amphiphiles with respect to their equilibrium positions. The transfer matrix (TM) method is employed to compute internal micelle partition function. We show that the conditions under which the sum rule is saturated by the largest eigenvalue of the TM determine the value of amphiphile concentration above which the dispersion becomes highly polydisperse and micelle sizes approach a Schultz distribution. (C) 2011 Elsevier B.V. All rights reserved.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Triply periodic minimal surfaces which converge to the Hoffman-Wohlgemuth example

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk`s second surface and Hoffman-Wohlgemuth`s example as limit-members.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.