The high temperature series can be approximately summed so as to reproduce the Gaussian model. This correspondence provides a better understanding of why Gaussian behavior is applicable in high dimensions, and also prepares the way for the exact summation of the series in two dimensions in the next section. The high temperature series for the partition function of the Ising model on a d–dimensi...

This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1’s in the last W bits of a binary stream is considered. A lower bound of Ω( 1 +logW ) memory bits forW -additive approximations is derived. This is followed by an algorithm whose memory consumption is O( 1 + logW ) bits, indicating that th...

Directors noted that global fi nancial stability has endured a diffi cult period since the publication of the April 2007 Global Financial Stability Report (GFSR). Overall, fi nancial risks have risen and markets are continuing to experience bouts of turbulence. Directors agreed with staff that, while there has been some calming in certain respects, markets generally remain unsettled, and credit...

Analogous to Fourier frequency transforms of the integration and differentiation of a continuous-time function, Walsh sequency transforms of the summing and differencing of an arbitrary discrete-time function have been derived. These transforms can be represented numerically in the form of matrices of simple recursive structure. The matrices are not orthogonal, but they are the inverse of each ...

The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the embedding coordinates. A light-cone parameterization of such boundaries is also discussed. ⋆ email: [email protected] † email: [email protected] The i...

A basic sequence in a Banach space is called wide-(s) if it is bounded and dominates the summing basis. (Wide-(s) sequences were originally introduced by I. Singer, who termed them P ∗-sequences.) These sequences and their quantified versions, termed λ-wide-(s) sequences, are used to characterize various classes of operators between Banach spaces, such as the weakly compact, Tauberian, and supe...

Elliptic problems in a two-dimensional domain containing one or several small holes are studied asymptotically in the limit of small hole radius ". As a result of the perturbation , the asymptotic solution to this class of problems contains an innnite logarithmic expansion in powers of ?1= log ". A hybrid asymptotic-numerical technique is used to sum these innnite logarithmic expansions and to ...