Some examples and basic properties of ultrametric spaces are briefly discussed.

Abstract A Composite Indicator (CI) is a useful tool to synthesize information on multidimensional phenomenon and make policy decisions. Multidimensional phenomena are often modeled by hierarchical latent structures that reconstruct relationships between variables. In this paper, we propose an exploratory, simultaneous model for building CI system analyze its several facets. The proposal, calle...

We first consider a cyclic φ-contraction map on a reflexive Banach space X and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic φ-contraction maps in reflexive Banach spaces in one of their works 2009 . In the second part of the paper, we will discuss the existence of best proximity points in the framework of more gene...

We present results from Monte Carlo simulations to test for ultrametricity and clustering properties in spin-glass models. By using a one-dimensional Ising spin glass with random power-law interactions where the universality class of the model can be tuned by changing the power-law exponent, we find signatures of ultrametric behavior both in the mean-field and non-mean-field universality classe...

High dimensional, sparsely populated data spaces have been characterized in terms of ultrametric topology. There are natural, not necessarily unique, tree or hierarchy structures defined by the ultrametric topology. Once such a structure is known, and can be defined, there are various implications including the feasibility of improved computational complexity for operations such as nearest neig...

Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitabl...