More Torsion in the Homology of the Matching Complex

A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$ of size two. Using computers, we analyze the integral homology of the matching complex $M_n$, which is the simplicial complex of matchings on the set $\{1, >..., n\}$. The main result is the detection of elements of order $p$ in the homology for $p \in \{5,7,11,13\}$. Specifically, we show that there are elements of order 5 in the homology of $M_n$ for $n \ge 18$ and for $n \in {14,16}$. The only previously known value was $n = 14$, and in this particular case we have a new computer-free proof. Moreover, we show that there are elements of order 7 in the homology of $M_n$ for all odd $n$ between 23 and 41 and for $n=30$. In addition, there are elements of order 11 in the homology of $M_{47}$ and elements of order 13 in the homology of $M_{62}$. Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of $H_d(M_n;Z)$ for $13 \le n \le 16$; a complete description of the homology already exists for $n \le 12$. To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of $M_n$ obtained by letting certain groups act on the chain complex.Comment: 35 pages, 10 figure

Exact Sequences for the Homology of the Matching Complex

Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex $M_n$, which is the simplicial complex of matchings in the complete graph $K_n$. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of $M_n$. First, we demonstrate that there is nonvanishing 3-torsion in $H_d(M_n;Z)$ whenever \nu_n \le d \le (n-6}/2, where $\nu_n= \lceil (n-4)/3 \rceil$. By results due to Bouc and to Shareshian and Wachs, $H_{\nu_n}(M_n;Z)$ is a nontrivial elementary 3-group for almost all $n$ and the bottom nonvanishing homology group of $M_n$ for all $n \neq 2$. Second, we prove that $H_d(M_n;Z)$ is a nontrivial 3-group whenever $\nu_n \le d \le (2n-9)/5$. Third, for each $k \ge 0$, we show that there is a polynomial $f_k(r)$ of degree 3k such that the dimension of $H_{k-1+r}(M_{2k+1+3r};Z_3)$, viewed as a vector space over $Z_3$, is at most $f_k(r)$ for all $r \ge k+2$.Comment: 31 page

El poder de los gobernadores en las constituciones provinciales

Los gobernadores argentinos son actores poderosos que influyen en la política nacional. Sin embargo, poco se sabe acerca del grado de poder con el que cuentan. Esta investigación propone una forma de medir el poder de los mandatarios provinciales a partir de los recursos que las constituciones provinciales les confieren: el Índice de Poder Gubernatorial A partir de los resultados, se reconocieron tres grupos de provincias: i) aquellas cuyas reglas formales promueven la concentración del poder en el gobernador; ii) las que distribuyen el poder entre las distintas instituciones provinciales; y iii) aquellas que se encuentran a mitad de camino entre los dos primeros grupos. El Índice de Poder Gubernatorial permite conocer cuáles son los instrumentos que tienen los titulares del ejecutivo provincial para gobernar, posibilita su comparación entre las distintas jurisdicciones y constituye un aporte para futuras investigaciones que pretendan medir el poder de los gobernadores en base a otro tipo de recursos, tales como los económicos o partidarios, o bien tengan como objetivo realizar inferencias causales

Simulating the market coefficient of relative risk aversion

Abstract: In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized. The coefficient of relative risk aversion (CRRA) that is commensurate with a 100% investment in the risky asset is simulated. The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return. Both the high extremes and the low extremes are considered. With these figures, the upper bound of the market CRRA is 3.021 and the lower bound is 0.466. Log utility, which corresponds to a CRRA of 1, is not excluded

Five-Torsion in the Homology of the Matching Complex on 14 Vertices

J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex $M_{14}$ on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case $n=14$ is exceptional; for all other $n$, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of $M_n$ when $n \ge 13$ and $n \neq 14$.Comment: 11 page

Medidas para la proteccion de los créditos de los terceros frente a las sociedades anónimas en crisis

Fil: Karaguezian, Maida Giselle. Universidad de San Andrés. Departamento de Derecho; Argentina

808-3 Reentrant Wavefronts During Wiggers’ Stage II Ventricular Fibrillation in Dogs

The mechanisms of ventricular fibrillation (VF) are unknown. Reentrant wavefronts have been shown to underlie the onset (Wiggers’ stage I) of electrically induced VF in intact canine ventricles. These reentrant wavefronts, however, have a limited lifespan (1–2s) while VF persists. Using computerized mapping techniques, we studied the mechanism by which VF is maintained beyond the initial few seconds (Wiggers’ stage II), both in normal and subendocardium-ablated canine ventricles. Eleven open-chest dogs were studied. In 6 of the dogs, the RV subendocardium was ablated with lugol's solution. A plaque electrode array with 317–509 bipolar recording electrodes was sutured on the RV epicardium. VF was induced by a strong premature stimulus (S2). Starting 2.5 s after the onset of VF, 2–5 s of data were analyzed. The activation patterns were visualized via dynamic display. Conventional isochronal maps were also constructed. Of the 15 runs of VF in dogs with intact ventricles, 3 episodes of reentrant wavefronts were detected. The mean lifespan was 4.5±2.1 rotations. The mean cycle length was 102.5±5.5msec. The incidence of reentry was 0.018±0.048 rotations/sec-cm2. Of the 18 runs of VF in dogs with ablated ventricles, 8 episodes of reentry were detected. The mean lifespan was 3.6±1.1 rotations (p=0.39 compared with intact ventricles). The mean cycle length was 107.2±9.6msec (p=0.16). The incidence of reentry was 0.075±0.097 rotations/sec-cm2 (p=0.048). In both groups of dogs, dynamic displays of the activation patterns demonstrate that the reentrant wavefronts spiral rather than follow a simple circular pathway.Conclusions(a) reentrant wavefronts are consistently present during Wiggers’ stage II VF, (b) ablation of the subendocardium and Purkinje fibers results in an increased incidence of reentrant wavefronts on the epicardium, and (c) the reentrant wavefronts are compatible with spiral waves of excitation