Abstract:
In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable. Variables that are represented by neighboring vertices may be arbitrarily dependent, but collections of variables that form an independent set in $G$ are $t$-wise independent.

Abstract:
We analyze a general framework for modeling agents whose utility is derived from both their actions and the perceptions of others about their type. We show that such perception games always have equilibria, and discuss two natural refinements. We demonstrate the applicability of our framework in a variety of contexts, with a particular emphasis on privacy-related issues.

Abstract:
Much of the literature on rational cryptography focuses on analyzing the strategic properties of cryptographic protocols. However, due to the presence of computationally-bounded players and the asymptotic nature of cryptographic security, a definition of sequential rationality for this setting has thus far eluded researchers. We propose a new framework for overcoming these obstacles, and provide the first definitions of computational solution concepts that guarantee sequential rationality. We argue that natural computational variants of subgame perfection are too strong for cryptographic protocols. As an alternative, we introduce a weakening called threat-free Nash equilibrium that is more permissive but still eliminates the undesirable ``empty threats'' of non-sequential solution concepts. To demonstrate the applicability of our framework, we revisit the problem of implementing a mediator for correlated equilibria (Dodis-Halevi-Rabin, Crypto'00), and propose a variant of their protocol that is sequentially rational for a non-trivial class of correlated equilibria. Our treatment provides a better understanding of the conditions under which mediators in a correlated equilibrium can be replaced by a stable protocol.

Abstract:
In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect, a bound that holds even when the players' inputs are only known to be pairwise independent. We also study the effect of a set of players, and show that there always exists a "small" set that, when eliminated, leaves every set with little effect. Finally, we ask whether there always exists a player with positive effect. We answer this question differently in various scenarios, depending on the properties of the function and the distribution of players' inputs. More specifically, we show that if the function is non-monotone or the distribution is only known to be pairwise independent, then it is possible that all players have 0 effect. If the distribution is pairwise independent with minimal support, on the other hand, then there must exist a player with "large" effect.

Abstract:
In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

Abstract:
In recent years, technological improvements have allowed for the creation of V.R. environments for different uses, especially in the training of pilots, astronauts, medical staff, soldiers, and athletes. In regards to physical activity, V.R. is currently being used in two main fields: Exergaming and Rehabilitation. The purpose of this article is to investigate the use of this technology as a means of demonstrating and learning motor abilities in many types of populations and situations. Three studies were done using V.R. In all three of them healthy participants were assigned to a control or test group. These studies were done using two main V.R. systems designed for motor learning: Timocco and IREX. Study 1 tested bi-lateral transfer in the upper limbs; Study 2 tested the differences in improvement using V.R. between internal and extrinsic focus of attention; Study 3 tested differences in different learning strategies in motor tasks—massed practice vs. distributed practice. Study 1 found significant differences between control and test groups; Study 2 did not find that external focus of attention was superior as expected but found a stronger correlation between tests at different days; Study 3 found no significant improvements (p > 0.05) for each group. In conclusion, V.R. can be an effective means of teaching and training basic motor skills, sometimes even superior to “real-life” because of the highly modifiable environment and difficulty in the comfort of one’s clinic or home.

Abstract:
Let f(z)= ￠ ‘k=0 ￠ akzk, a0 ￠ ‰ 0 be analytic in the unit disc. Any infinite complex vector =( 0, 1, 2, ￠ € |) such that | k|=1, k=0,1,2, ￠ € |, induces a function f (z)= ￠ ‘k=0 ￠ ak kzk which is still analytic in the unit disc.

Abstract:
En la Argentina la “sociología de cátedra” que inaugura el pensamiento de Ernesto Quesada, introdujo un desplazamiento en lo que eran los valores científicos positivistas de fines de siglo XIX contribuyendo, junto con otros intelectuales, para que en el posterior contexto ideológico de entreguerras la “ciencia social” local contara con la primacía de una cultura filosófica alemana, de la mano de sus introductores hispanos. Este trabajo propone analizar este desplazamiento científico unido a la nueva influencia intelectual espa ola, en una sociedad como la argentina que contaba con un secular resentimiento “hispanofóbico” durante gran parte del siglo XIX, para terminar produciéndose desde el cambio de siglo una inusitada revalorización positiva de lo espa ol en sus influencias culturales y sociales.

Abstract:
Let be a topological space. The semigroup of all the étale mappings of (the local homeomorphisms ) is denoted by . If , then the -right (left) composition operator on is defined by ？？, . When are the composition operators injective? The Problem originated in a new approach to study étale polynomial mappings and in particular the two-dimensional Jacobian conjecture. This approach constructs a fractal structure on the semigroup of the (normalized) Keller mappings and outlines a new method of a possible attack on this open problem (in preparation). The construction uses the left composition operator and the injectivity problem is essential. In this paper we will completely solve the injectivity problems of the two composition operators for (normalized) Keller mappings. We will also solve the much easier surjectivity problem of these composition operators. 1. Introduction Let be a topological space. A mapping is called a local homeomorphism of or an étale mapping of if for any point there exists a neighborhood of such that the restriction of to , denoted by , is an homeomorphism. The set of all the étale mappings of , denoted by , is a semigroup with a unit with the composition of mappings taken to be the binary operation. If , then the -right composition operator on is defined by The -left composition operator on is defined by We were interested in the injectivity of these two composition operators in two particular cases. The first is the case of entire functions that are étale (and normalized). The second case is that of the polynomial mappings with determinant of their Jacobian matrix equal (identically) to and whose -degrees equal their total degrees. For the first case we use the following. Definition 1. Consider the following Thus we use in this case the symbol instead of . Then we have the following. Proposition 2 (see [1]). Consider the following , is injective. Theorem 3 (see [1]). Let . Then is not injective if and only if This settled the first case. It should be noted (see [1]) that the proof for the left composition operator is much more involved than the proof for the right composition operator (which follows directly from the Picard little theorem). It is in fact the second case that initiated our interest in the injectivity of the composition operators. It results from a new approach to study étale polynomial mappings and in particular the two-dimensional Jacobian conjecture [2–4]. This approach constructs a fractal structure on the semigroup of the (normalized) Keller mappings and outlines a new method of a possible attack on this open