DNA may be represented by sequences of four symbols, but it is often useful to convert those symbols into real or complex numbers for further analysis. Several mapping schemes have been used in the past, but most of them seem to be unrelated to any intrinsic characteristic of DNA. The objective of this work was to study a mapping scheme that is directly related to DNA characteristics, and that ...

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we ...

Nearest neighbor classification methods are a useful and a relatively straightforward to implement classification technique. However, despite such appeal, they still suffer from the curse of dimensionality. Additionally, the nature of the data sets may not be wholly applicable to the model assumed in the nearest neighbor methods. As such there have been many proposed optimizations. Two such opt...

Given a set S of n sites (points), and a distance measure d, the nearest neighbor searching problem is to build a data structure so that given a query point q, the site nearest to q can be found quickly. This paper gives a data structure for this problem; the data structure is built using the distance function as a “black box”. The structure is able to speed up nearest neighbor searching in a v...

The reliable detection of an object of interest in an input image with arbitrary background clutter and occlusion has to a large extent remained an elusive goal in computer vision. Traditional model-based approaches are inappropriate for a multi-class object detection task primarily due to difficulties in modeling arbitrary object classes. Instead, we develop a detection framework whose core co...

K-nearest neighbor classification algorithm is one of the most basic algorithms in machine learning, which determines sample's category by similarity between samples. In this paper, we propose a quantum with Hamming distance. algorithm, computation firstly utilized to obtain distance parallel. Then, core sub-algorithm for searching minimum unordered integer sequence presented find out Based on ...

We prove a variety of new correlation inequalities which bound intermediate distance correlations from below by long distance correlations. Typical is the following which holds for spin 1/2 nearest neighbor Ising ferromagnets: