Ultrametric approach to the genetic code and the genome is considered and developed. p-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be treated as p-adic ultrametric networks. Ultrametric modification of the Hamming distance is defined and noted how it can be useful. Ultrametric approach with p-a...

For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the distances in the probability space are separated and ununified when machine learning is introduced in the pattern recognition. There is still a problem that it ...

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

Let X be a metric space (we may allow +∞ as a value for some distances in X). We say that X has bounded geometry if, for each R > 0, there is a natural number N such that every ball of radius R in X contains at most N points. (In particular, X is discrete.) In this paper, we will consider bounded geometry metric spaces in this sense. Let X be such a space, and let `(X) denote the usual Hilbert ...

A recognition advantage for distinctive faces has been widely reported (e.g., Valentine, 1991). In such studies, distinctive faces produce more hits and fewer false alarms than typical faces. Although the finding is robust, the mechanism for this advantage has not been carefully explored. The choice of distractors in these studies does not guarantee equivalent target-distractor distances for ty...

The n-dimensional ternary Hamming space is Tn, where T = f0; 1; 2g. Three points in Tn form a line if they have in common excactly n 1 components. A subset of Tn is closed if, whenever it contains two points of a line, it contains also the third one. A generator is a set, whose closure is Tn. In this paper, we investigate several properties of closed sets and generators. Two alternative proofs ...

Objective Since the extreme lateral lumbar interbody fusion procedure was first reported by Ozgur in 2006, a large number of clinical studies have been published. Anatomical studies which explore methods to avoid visceral structures, such as the kidney, with this approach have not been examined in detail. We dissected the retroperitoneal space to analyze how the extreme lateral transpsoas appro...

In recent years it has become popular to study machine learning problems based on ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance comparisons such as d(A,B) < d(C,D). For many problems in machine learning and statistics it is unclear how to solve them in such a scenario. Up to now, the main approach...