The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

GNSS array: diseño de una antena con polarización circular

Aquest projecte es centra en el disseny d’una antena microstrip per a GNSS. Una antena per a GNSS ha de tenir adaptació de impedància d’entrada i polarització circular a dretes, com a principals especificacions, en el rang de 1.15-1.6 GHz. El tipus d’alimentació d’una antena microstrip amb el major ample de banda d’adaptació és l’alimentació mitjançant acoblament per apertura. Si a l’antena s’introdueixen dos apertures de forma ortogonal, alimentades amb un desfasament de 90º entre elles, s’aconsegueix polarització circular. L’opció de separar les apertures redueix la transferència de potència entre elles, i disminueix el guany de polarització creuada. La xarxa d’alimentació dissenyada és un divisor de Wilkinson amb una línia de λ/4 a la freqüència central, encara que el desfasament als extrems de la banda no sigui de 90º. Com a xarxa d’alimentació es va provar un hibrid de 90º, però l’elevat valor del paràmetre S21 de l’antena impossibilita l’adaptació a l’entrada del hibrid.

Genetic architecture of ambulatory blood pressure in the general population: insights from cardiovascular gene-centric array.

Genetic determinants of blood pressure are poorly defined. We undertook a large-scale, gene-centric analysis to identify loci and pathways associated with ambulatory systolic and diastolic blood pressure. We measured 24-hour ambulatory blood pressure in 2020 individuals from 520 white European nuclear families (the Genetic Regulation of Arterial Pressure of Humans in the Community Study) and genotyped their DNA using the Illumina HumanCVD BeadChip array, which contains ≈50 000 single nucleotide polymorphisms in >2000 cardiovascular candidate loci. We found a strong association between rs13306560 polymorphism in the promoter region of MTHFR and CLCN6 and mean 24-hour diastolic blood pressure; each minor allele copy of rs13306560 was associated with 2.6 mm Hg lower mean 24-hour diastolic blood pressure (P=1.2×10(-8)). rs13306560 was also associated with clinic diastolic blood pressure in a combined analysis of 8129 subjects from the Genetic Regulation of Arterial Pressure of Humans in the Community Study, the CoLaus Study, and the Silesian Cardiovascular Study (P=5.4×10(-6)). Additional analysis of associations between variants in gene ontology-defined pathways and mean 24-hour blood pressure in the Genetic Regulation of Arterial Pressure of Humans in the Community Study showed that cell survival control signaling cascades could play a role in blood pressure regulation. There was also a significant overrepresentation of rare variants (minor allele frequency: <0.05) among polymorphisms showing at least nominal association with mean 24-hour blood pressure indicating that a considerable proportion of its heritability may be explained by uncommon alleles. Through a large-scale gene-centric analysis of ambulatory blood pressure, we identified an association of a novel variant at the MTHFR/CLNC6 locus with diastolic blood pressure and provided new insights into the genetic architecture of blood pressure.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Inter-specific and developmental differences on the array of antennal chemoreceptors in four species of triatominae (Hemiptera: Reduviidae)

The aim of the work was to investigate the pattern of chemoreceptor sensilla in adults and fifth stage nymphs of Rhodnius prolixus, R. neglectus, Triatoma infestans and T. sordida in order to study differences and similarities between genera and species. Three types of sensilla were analyzed by light microscopy: thin-walled trichoidea, thick-walled trichoidea and basiconica. The number of sensilla of each three types were counted. The length of the antennal segments were also used as a variable for the analysis. The statistical analysis showed that the number of these antennal chemoreceptors had significant differences between species and between adults and nymphs of each species. Discriminant analysis separates incompletely the fifth stage nymphs of the four species and showed similarity between them. Discriminant analysis performed with 12 variables of the antennae, allowed a complete separation of the adults of the four species.