In this article we develop the direct and inverse scattering theory of a discrete matrix Zakharov-Shabat system with solutions Un and W n. Contrary to the discretization scheme enacted by Ablowitz and Ladik, a central difference scheme is applied to the positional derivative term in the matrix Zakharov-Shabat system to arrive at a different discrete linear system. The major effect of the new di...

In this paper, we propose a distributed continuoustime linear dynamics for solving the localization problem based on signal angle-of-arrival information. We first formulate the AOA localization problem within the framework of formation graph theory, which is an extension of the classical graph theory by incorporating the positional information of the vertices. Solving the AOA localization probl...

In this study, a novel automatic nano-alignment system using machine vision coupled with a piezoelectric motor for motion control was developed. The analytical algorithm of this visionaided auto-alignment design makes use of inputs of real-time movement captured by CCD to obtain the corresponding output feedback. Through matrix transformation, the algorithm establishes the characteristic matrix...

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and interfraction positional uncertainty of tumour and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and efficient approach fo...

Signal search analysis is a general method to discover and characterize sequence motifs that are positionally correlated with a functional site (e.g. a transcription or translation start site). The method has played an instrumental role in the analysis of eukaryotic promoter elements. The signal search analysis server provides access to four different computer programs as well as to a large num...

The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorisation operations and the commutation...

In all multicellular organisms, development is influenced by the interactions between cells and their extracellular matrix (ECM). Information contained in the ECM provides the cell with temporal and positional clues, such as where it is, where it should be going, how old it is (in terms of cellular differentiation), and in some instances, when it is time for it to die (through apoptosis). It is...

An entropy game is played on a finite arena by two-and-a-half players: Despot, Tribune and non-deterministic People. Whenever Despot and Tribune decide on their actions, it leaves a set L of possible behaviors of People. Despot wants the entropy (growth rate) of L to be as small as possible, while Tribune wants to make it as large as possible. The main result is that the entropy game is determi...

This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) method their formation for reliable digital signal processing (DSP), transmission, data storage. The is obtained based on general positional (PNS) with conditions functions converting BNS a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, multivalued systems. G...

The article analyzes a linear mechanical system with large parameter at the vector of velocity forces and distributed delay in positional forces. With aid decomposition method, conditions are obtained under which problem stability analysis original second-order differential equations can be reduced to studying two auxiliary first-order subsystems. It should noted that one subsystems does not co...