Data Independence in the Multi-dimensional Numbered Information Spaces

The concept of data independence designates the techniques that allow data to be changed without affecting the applications that process it. The different structures of the information bases require corresponded tools for supporting data independence. A kind of information bases (the Multi-dimensional Numbered Information Spaces) are pointed in the paper. The data independence in such information bases is discussed

The information paradox and the locality bound

Hawking's argument for information loss in black hole evaporation rests on the assumption of independent Hilbert spaces for the interior and exterior of a black hole. We argue that such independence cannot be established without incorporating strong gravitational effects that undermine locality and invalidate the use of quantum field theory in a semiclassical background geometry. These considerations should also play a role in a deeper understanding of horizon complementarity.Comment: 21 pages, harvmac; v2-3. minor corrections, references adde

Kernel methods for measuring independence

We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlation-based dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis

Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities

We prove existence and purification results for equilibria in which players choose extreme points of their feasible actions in a class of strategic environments exhibiting a product structure. We assume finite-dimensional action sets and allow for infinite-dimensional externalities. Applied to large games, we obtain existence of Nash equilibrium in pure strategies while allowing a continuum of groups and general dependence of payoffs on average actions across groups, without resorting to saturated measure spaces. Applied to games of incomplete information, we obtain a new purification result for Bayes-Nash equilibria that permits substantial correlation across types, without assuming conditional independence given the realization of a finite environmental state. We highlight our results in examples of industrial organization, auctions, and voting.

Modified linear dependence and the capacity of a cyclic graph

AbstractIn 1956 Shannon raised a problem in information theory, which amounts to this geometric question: How many n-dimensional cubes of width 2 can be packed in the n-dimensional torus described by the nth power of the cyclic group Cm? The present paper examines this question in the special circumstance that the set of centers of the cubes form a subgroup—that is, a lattice packing. In this case, the machinery of vector spaces is available when m is a prime. This approach introduces a modified definition of linear independence, obtains some known results with its aid, and suggests a promising direction for future computation and theory. The paper concludes by showing that, in return, combinatorial information can yield results about finite vector spaces