Tuning clustering in random networks with arbitrary degree distributions

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

Conserved chromosomal clustering of genes governed by chromatin regulators in Drosophila

Background: The trithorax group (trxG) and Polycomb group (PcG) proteins are responsible for the maintenance of stable transcriptional patterns of many developmental regulators. They bind to specific regions of DNA and direct the post-translational modifications of histones, playing a role in the dynamics of chromatin structure.Results: We have performed genome-wide expression studies of trx and ash2 mutants in Drosophila melanogaster. Using computational analysis of our microarray data, we have identified 25 clusters of genes potentially regulated by TRX. Most of these clusters consist of genes that encode structural proteins involved in cuticle formation. This organization appears to be a distinctive feature of the regulatory networks of TRX and other chromatin regulators, since we have observed the same arrangement in clusters after experiments performed with ASH2, as well as in experiments performed by others with NURF, dMyc, and ASH1. We have also found many of these clusters to be significantly conserved in D. simulans, D. yakuba, D. pseudoobscura and partially in Anopheles gambiae.Conclusion: The analysis of genes governed by chromatin regulators has led to the identification of clusters of functionally related genes conserved in other insect species, suggesting this chromosomal organization is biologically important. Moreover, our results indicate that TRX and other chromatin regulators may act globally on chromatin domains that contain transcriptionally co-regulated genes.

Subclass problem-dependent design for error-correcting output codes

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

Pionic branches in neutron matter and the problem of pion condensation

The pion spectrum for charged and neutral pions is investigated in pure neutron matter, by letting the pions interact with a neutron Fermi sea in a self-consistent scheme that renormalizes simultaneously the mesons, considered the source of the interaction, and the nucleons. The possibility of obtaining different kinds of pion condensates is investigated with the result that they cannot be reached even for values of the spin-spin correlation parameter, g', far below the range commonly accepted.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Infinitely many periodic orbits for the rhomboidal five-body problem

We prove the existence of infinitely many symmetric periodic orbits for a regularized rhomboidal five-body problem with four small masses placed at the vertices of a rhombus centered in the fifth mass. The main tool for proving the existence of such periodic orbits is the analytic continuation method of Poincaré together with the symmetries of the problem. © 2006 American Institute of Physics.

El proyecto ‘Ecosportech’ como ejemplo de universidad emprendedora. Una experiencia a base del ‘Problem Based Learning’

El objetivo de este artículo es presentar el proyecto EcoSPORTech, cuya finalidad es la creación de una empresa social con jóvenes para la realización de actividades deportivas/ocio en el medio natural, integrando las nuevas tecnologías. Este proyecto supone una colaboración interdisciplinaria dentro de la Universidad de Vic, entre las facultades de Empresa y Comunicación (FEC), la de Ciencias de la Salud y el Bienestar (FCSB) y la de Educación (FE) e integra un equipo de profesionales procedentes de los ámbitos de la empresa, el marketing, el periodismo, el deporte y la terapia ocupacional. Estos profesores formarán al grupo de jóvenes con los que se creará la empresa y dirigirán la misma. Esta empresa (cooperativa) se integra en el vivero de empresas sociales que se está creando en la Universidad de Vic.

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.

On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.

Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.

Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.