I will sketch a proof that the short distance behavior of the even scaling functions for the Ising model that arise by taking the scaling limit of the Ising correlation functions from below the critical temperature is given by the Luther–Peschel formula [6] (see below). The fact that the Luther–Peschel formula is consistent with conformal field theory insights into the correlations for the larg...

In this paper we develop the concept of a polygon-ooset distance function and show how to compute the respective nearest-and furthest-site Voronoi diagrams of point sites in the plane. We provide optimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for computing compact representations of both diagrams.

In lecture-based distance learning system, various activities must be supported in addition to transmission of lecture contents. However, many conventional systems only support video image of the lecture. VIEW Classroom is a distance learning system supports various activities related with a lecture. For example, lecture record and self-study support function, online quiz function and discussio...

We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used "key function plus series adjustment" (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow...

We present a novel approach to the characterization of complex sensory neurons. One of the main goals of characterizing sensory neurons is to characterize dimensions in stimulus space to which the neurons are highly sensitive (causing large gradients in the neural responses) or alternatively dimensions in stimulus space to which the neuronal response are invariant (defining iso-response manifol...

Distance functions between points in a domain are sometimes used to automatically plan a gradient-descent path towards a given target point in the domain, avoiding obstacles that may be present. A key requirement from such distance functions is the absence of spurious local minima, which may foil such an approach, and this has led to the common use of harmonic potential functions. Based on the ...

A good distance function is an essential tool in applications which involve querying large databases, such as image retrieval and bioinformatics. We describe a non-parametric algorithm for distance function learning which is based on the boosting of low grade weak learners in a product space. The algorithm learns a function defined over pairs of points, using supervision in the form of equivale...

The NGPCA method, a combination of the robust neural gas vector quantization method and a fast neural principal component analyzer, has proved to be a valuable tool for the generalized learning of high–dimensional data. At its core, the method uses a competitive ranking to adapt its units. The competition is guided by a specialized distance function — known as the normalized Mahalanobis distanc...

MOTIVATION The development of epitope-based vaccines crucially relies on the ability to classify Human Leukocyte Antigen (HLA) molecules into sets that have similar peptide binding specificities, termed supertypes. In their seminal work, Sette and Sidney defined nine HLA class I supertypes and claimed that these provide an almost perfect coverage of the entire repertoire of HLA class I molecule...

We propose a new method for the reconstruction of the signed distance function in the context of level set methods. The new method is a modification of the algorithm which makes use of the PDE equation for the distance function introduced by M. Sussman, P. Smereka, and S. Osher (1994, J. Comput. Phys. 119, 146). It is based mainly on the use of a truly upwind discretization near the interface. ...