Qubit-Qutrit Separability-Probability Ratios

Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the (separable and nonseparable) N x N density matrices, based on the Bures (minimal monotone) metric -- and also their analogous formulas (quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same seven billion well-distributed (``low-discrepancy'') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-six (rank-five) density matrices. The (rank-six) separability probabilities obtained based on the 35-dimensional volumes appear to be -- independently of the metric (each of the seven inducing Haar measure) employed -- twice as large as those (rank-five ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last paragraph presenting qubit-qutrit probability ratios disaggregated by the two distinct forms of partial transpositio

Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors

The Horodecki family employed the Jaynes maximum-entropy principle, fitting the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We further extend the Horodecki one-parameter model in both these manners, obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for which we find a highly interesting/intricate continuum (-\infty < \alpha < \infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the golden ratio is featured. Our model can be contrasted with the three-parameter (b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a q(Tsallis)-parameter rather than $\alpha$, and has simply q-invariant HS separability probabilities of 1/2. Our results emerge in a study initially focused on embedding certain information metrics over the two-level quantum systems into a q-framework. We find evidence that Srednicki's recently-stated biasedness criterion for noninformative priors yields rankings of priors fully consistent with an information-theoretic test of Clarke, previously applied to quantum systems by Slater.Comment: 26 pages, 12 figure

Prevalencia de bullying en escolares de la ciudad de Corrientes

El término bullying refiere al comportamiento agresivo entre pares, repetido en el tiempo, que se ejerce en forma intimidatoria al más débil con la intención premeditada de causar daño. El objetivo del presente estudio consistió en estimar el conocimiento y la prevalencia acerca del bullying en alumnos de 12 a 20 años en dos escuelas de la ciudad de Corrientes con la finalidad de identificar posibles causas, contexto, frecuencia y continuidad con que se presentan, determinando a su vez, la actitud personal y escolar frente a estas situaciones.  La recolección de datos se realizó a partir de una encuesta cuyo instrumento fue un formulario estructurado. Se trata de un estudio observacional, descriptivo y de corte transversal.  Se analizaron 338 encuestas en las que se tomó en cuenta la relación femenino/masculino: 1,34; y la media de edad: 16 años. El 95% refirió conocer sobre el bullying; sin embargo, el 35% presentó alguna situación de maltrato por las siguientes causas: molestia 32%, bromas 28%, ser diferente 24%, provocación 7% y otras causas 9%. En su mayoría, el 70 % de estas situaciones ocurrieron en el mismo salón. El 54% expresó que las intimidaciones ocurrieron pocas veces, y el 36% restante presentaba una continuidad de varias semanas. Frente a estos escenarios de maltrato, el 48% respondió que nadie actuaba, el 25% que el profesor intervenía, el 24% otros compañeros, y el 3% otras personas. Con respecto a la actitud personal, el 45% cortaba la situación personalmente, el 38% avisó a terceros, mientras que el 17% no realizó nada por miedo. Las consecuencias del maltrato entre pares afecta a todos los agentes implicados, e indirectamente, al resto de la comunidad que debe convivir con los efectos derivados del mismo.

Differential information in large games with strategic complementarities

We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required

A conjecture of Biggs concerning the resistance of a distance-regular graph

Biggs conjectured that the resistance between any two points on a distance-regular graph of valency greater than 2 is bounded by twice the resistance between adjacent points. We prove this conjecture, give the sharp constant for the inequality, and display the graphs for which the conjecture most nearly fails. Some necessary background material is included, as well as some consequences.X111sciescopu

Analysis of a Universal Class of Hash Functions

In this paper we use linear algebraic methods to analyze the performance of several classes of hash functions, including the class H2 presented by Carter and Wegman. Suppose H is a suitable class, the hash functions in H map A to B, S is any subset of A whose size is equal to that of B, and x is any element of A. We show that the probability of choosing a function from H which maps x to the same value as more than t other elements of S is no greater than min (1/t2, 11/t4). Consider a database storage and retrieval system implemented using hashing and a linked list collision resolution strategy. A corollary of the main result is that the probability that the system would perform more than t times more slowly than expected is no greater than min(1/t2,11/t4). The “performance” being considered can be either the number of memory references required to process any individual request or the number required to process an arbitrary sequence of requests. Notice that these results do not assume that the requests to the database are random or uniformly distributed. Instead, the averaging is done over the possible choices of the actual hash function from H. Since the system designer can be sure that this choice is made randomly, the probabilities given hold for any input. It is also shown that the bound on poor performance when balanced trees are used in place of linked lists is approximately min (1/(4t), 11/(16t)). The formulas are generalized to any size S

There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k(2)/k and large diameter

In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k(2)/k <= C. This extends a conjecture of Bannai and Ito. (C) 2013 Elsevier Inc. All rights reserved.X1121sciescopu