Curvature representation of the gonihedric action

We analyse the curvature representation of the gonihedric action $A(M)$ for the cases when the dependence on the dihedral angle is arbitrary.Comment: 10 pages, LaTeX, 3 embedded figures with psfig, submitted to Phys.Lett.

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figure

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

Redirecting research efforts on the diversification-performance linkage: The search for synergy

We review the literature on the diversification-performance (D-P) relationship to a) propose that the time is ripe for a renewed attack on understanding the relationship between diversification and firm performance, and b) outline a new approach to attacking the question. Our paper makes four main contributions. First, through a review of the literature we establish the inherent complexities in the D-P relationship and the methodological challenges confronted by the literature in reaching its current conclusion of a non-linear relationship between diversification and performance. Second, we argue that to better guide managers the literature needs to develop along a complementary path – whereas past research has often focused on answering the big question of does diversification affect firm performance, this second path would focus more on identifying the precise micro-mechanisms through which diversification adds or subtracts value. Third, we outline a new approach to the investigation of this topic, based on (a) identifying the precise underlying mechanisms through which diversification affects performance; (b) identifying performance outcomes that are “proximate” to the mechanism that the researcher is studying, and (c) identifying an appropriate research design that can enable a causal claim. Finally, we outline a set of directions for future research

The Beta-Wishart Ensemble

We introduce a “Broken-Arrow” matrix model for the β-Wishart ensemble, which improves on the traditional bidiagonal model by generalizing to non-identity covariance parameters. We prove that its joint eigenvalue density involves the correct hypergeometric function of two matrix arguments, and a continuous parameter β> 0. If we choose β = 1, 2, 4, we recover the classical Wishart ensembles of general covariance over the reals, complexes, and quaternions. The derivation of the joint density requires an interesting new identity about Jack polynomials in n variables. Jack polynomials are often defined as the eigenfunctions of the Laplace-Beltrami Operator. We prove that Jack polynomials are in addition eigenfunctions of an integral operator defined as an average over a β-dependent measure on the sphere. When combined with an identity due to Stanley, 32 we derive a new definition of Jack polynomials. An efficient numerical algorithm is also presented for simulations. The algorithm makes use of secular equation software for broken arrow matrices currently unavailable in the popular technical computing languages. The simulations are matched against the cdf’s for the extreme eigenvalues. The techniques here suggest that arrow and broken arrow matrices can play an important role in theoretical and computational random matrix theory including the study of corners processes