On the critical group of matrices

Given a graph G with a distinguished vertex s, the critical group of (G,s) is the cokernel of their reduced Laplacian matrix L(G,s). In this article we generalize the concept of the critical group to the cokernel of any matrix with entries in a commutative ring with identity. In this article we find diagonal matrices that are equivalent to some matrices that generalize the reduced Laplacian matrix of the path, the cycle, and the complete graph over an arbitrary commutative ring with identity. We are mainly interested in those cases when the base ring is the ring of integers and some subrings of matrices. Using these equivalent diagonal matrices we calculate the critical group of the m-cones of the l-duplications of the path, the cycle, and the complete graph. Also, as byproduct, we calculate the critical group of another matrices, as the m-cones of the l-duplication of the bipartite complete graph with m vertices in each partition, the bipartite complete graph with 2m vertices minus a matching.Comment: 18 pages, 5 figure

On the critical ideals of graphs

We introduce some determinantal ideals of the generalized Laplacian matrix associated to a digraph G, that we call critical ideals of G. Critical ideals generalize the critical group and the characteristic polynomials of the adjacency and Laplacian matrices of a digraph. The main results of this article are the determination of some minimal generator sets and the reduced Grobner basis for the critical ideals of the complete graphs, the cycles and the paths. Also, we establish a bound between the number of trivial critical ideals and the stability and clique numbers of a graph.Comment: 23 pages. Some changes over the previous version. Accepted in Linear algebra and its Application

Optimización multiobjetivo de la operación en sistemas automatizados de distribución de energía eléctrica

El problema a tratar en este trabajo es la operación óptima de un sistema de distribución Automatizado con múltiples conexiones al sistema de transmisión. El tipo de sistema contemplado es una red de distribución de topología enmallada operada en forma radial, tal estudio se analiza para el perfil de carga en una hora dada y en condiciones normales de trabajo. Los objetivos a alcanzar en forma simultánea son: Minimizar las pérdidas de potencia y garantizar un perfil de tensión adecuado en los nodos del sistema. Para lograr tales objetivos es posible realizar control centralizado sobre los transformadores con control de derivaciones bajo carga en las subestaciones HV/MV, los reconectadotes en algunas ramas de la red y los bancos de capacitores shunt en las subestaciones HV/MV y en algunos nodos de la red, el estudio se realiza mediante un equivalente monofásico de red. Se tiene entonces un problema multiobjetivo de programación no lineal entera mixta (PNLEM) de optimización multiobjetivo con restricciones, en un espacio de búsqueda discreto. Solucionar este problema consiste en encontrar los puntos de operación, que satisfaciendo las necesidades de carga cumplan de forma simultánea los objetivos sin violar los límites de operación. En este trabajo se implementa el algoritmo evolutivo multiobjetivo de segunda generación NSGA II (Non dominated sorting genetic algorithm II), cuyo método de búsqueda se basa en el concepto de óptimo de pareto y que al incorporar el elitismo y una función explicita de apiñamiento encuentra soluciones de calidad

Armed Groups and Violence in Paraguay

Armed violence in Paraguay is not a recent phenomenon. During the second half of the XX Century, Paraguay saw the rise of a larger number of underground, revolutionary movements that sought the overthrow of the Alfredo Stroessner’s (1954-1989) government. From among those movements emerged the Partido Patria Libre (or, Free Fatherland, also known for its acronym PPL), made up of a two branches: one legal and the other one, operational. The latter was based on people’s power, as represented by “Ejército del Pueblo Paraguayo” (or, the Paraguayan People’s Army, with acronym EPP). After EPP broke with PPL in March 2008, this Marxist-oriented revolutionary project, which was apparently oriented to put an end to the social, political and economic inequalities in Paraguay, began to carry out markedly criminal activities, which included bank robberies, kidnappings, assassinations, terrorist attacks and armed confrontations. Its strategies and modus operandi utilized by the Armed Revolutionary Forces of Colombia (FARC). Paraguay features a farm sector in a state of crisis, in which cattle-ranchers, peasants and agro-exporting companies live in a constant strife. The Paraguayan Departments that are the most affected by this situation are Concepciόn, San Pedro, Canindeyú y Caazapá, which also suffer from a weak government presence. This deficiency has made these departments ripe for drug-trafficking activity by Brazilian groups such as Primer Comando Capital (i.e., First Capital command), also PCC and Comando Vermelho, (i.e., The Red Command). That is why many peasants, now recruited by EPP, have joined the drug-trafficking business and that, not only as marihuana growers but as “campanas” (i.e., early warning sentinels) for the organization. This helps shape their attitudes for their future involvement in all areas of drug-trafficking. Paraguayan society is the result of social inequity and inequality, such as those resulting from a lack of opportunity. Although Paraguay has successfully recovered from the last world economic crisis, economic growth, by itself, does not ensure an improvement in the quality of life. As long as such economic and social gaps persist and the government fails to enact the policies that would result in a more just society and toward EPP neutralization or containment, the latter is bound to grow stronger. In this context, the situation in Paraguay calls for more research into the EPP phenomenon. It would also seem necessary for Paraguay to promote an open national debate that includes all sectors of society in order to raise consciousness and to induce society to take actual steps to eliminate the EPP, as well as any other group that might arise in the immediate future. EPP has strong connections with the Frente Patriόtico Manuel Rodríguez in Chile and other armed groups and peasant movements in other countries of this region. Although most governments in the region are aware that the armed struggle is not a solution to current problems, it might be worth it to hold a regional debate about armed or insurgent groups in Latin American to seek common strategies and cooperation on dealing with them since the expansion of these armed groups is a problem for all

La empatía en estudiantes de psicología de dos universidades peruanas, 2017

El estudio de investigación “La empatía en estudiantes de psicología de dos universidades peruanas, 2017”, está centrada en conocer la predominancia de la dimensión en la empatía de los practicantes o internos de las escuelas de psicología de las universidades peruanas César Vallejo (UCV) y Sedes Sapientiae (UCSS) ubicadas en Lima Norte. Para ello hemos tomado como instrumento de evaluación el Test de Índice de Reactividad Interpersonal (IRI), que ha tenido que pasar por un análisis de confiabilidad a través de una prueba piloto que arrojó un resultado de 0,715 de buena confiabilidad. Utilizamos el muestreo aleatorio simple, para el caso de la UCV fueron 63 estudiantes y para la UCSS tomamos una muestra de 41 practicantes haciendo un total de 104 estudiantes. El presente estudio tiene un enfoque cuantitativo, de tipo sustantivo, de diseño no experimental, de corte transversal, de subtipo descriptivo, de carácter comparativo entre dos muestras que proceden de los estudiantes de psicología de los dos últimos semestres de las universidades UCV y UCSS. Se concluye que 46 estudiantes consideran un nivel moderado de empatía lo que equivale a un 73 %, mientras que en la universidad Sedes Sapientiae los estudiantes que se encuentran en el nivel moderado, corresponde a un 56 %. La dimensión que predomina es la Cognitiva en ambas universidades. En la dimensión cognitiva el indicador que predomina en la UCV es el malestar personal, mientras que en la UCSS el indicador predominante es la preocupación empática. Respecto a la dimensión afectiva, el indicador que predomina es la Toma de perspectiva en ambas universidades

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Biosignals events detection. A Morphological Signal independent Approach

This study presents a signal-independent algorithm, which detects significant events in a biosignal, withoutprevious knowledge or specific pre-processing steps. From a morphological analysis, the algorithm computesthe instants when the most significant standard deviation discontinuities occur. An iterative optimization stepis then applied. This assures that a minimal error is achieved when modeling the signal segments (betweenthe detected instants) with a polynomial regression. The detection scale can be modified by an optional inputscale factor. An objective algorithm performance evaluation procedure was designed, and applied on twotypes of synthetic signals, for which the events instants were previously known. An overall mean error of20.32 ( 16.01) samples between the detected and the real events show the high accuracy of the proposedalgorithm. The algorithm was also applied on accelerometry and electromyography raw signals collected indifferent experimental scenarios. The fact that this approach does not require any previous knowledge and thegood level of accuracy represents a relevant contribution in events detection and biosignal analysis