Let hλ, eλ, and mλ denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition λ respectively. We give combinatorial interpretations for the coefficients that arise in expanding mλ in terms of homogeneous symmetric functions and the elementary symmetric functions. Such coefficients are interpreted in terms of cer...

There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called “Elementary Landscapes” and they have a number of special mathematical properties. The problems that are not elementary landscapes can be decomposed in a sum of elementary ...

Landscape theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of a special kind of landscapes called elementary landscapes. The decomposition of the objective function of a problem into its elementary components can be exploited to compute summary statistics. We present closed-form expressions for the fitness-distance corre...

Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixi...

We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they ar...

In the present investigation transient, G x/G/m queuing model with balking and reneging has been studied. The diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d. f.) for the number of customers in the system has been obtained. In special case, the steady state results that tally with those of Kimura and Ohsone have been e...

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of...

In the previous lecture we saw how to design locality sensitive hashing (LSH) for hamming and l1 distance, as a solution to the (c,R)-Near Neighbor problem. Whenever we use LSH for the nearest neighbor search, using some distance measure, the main task is to come up with a good elementary hashing function. This elementary hash function (H) is then used to create a composite hash function (G) fo...