Computational Biology

Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species

The Effect of Turbid Water in the Optical Path of a Photographic System on the Modulation Transfer Function of That System

Various levels of a turbid suspension were introduced into a specially constructed tank and photographs of a variable transmittance sinusoidal object containing a step tablet were taken. The resulting images were processed and measured on a micro-densitometer to obtain the modulation transfer functions of the system. Results indicate that with increasing turbidity there is a speed loss, increased flare or reduced contrast, and decreasing modulation transfer functions. The increasing flare is not the only factor causing the demodulation of the underwater images

ON COMPUTING A BUY/COPY POLICY USING THE PITT-KRAFT MODEL

The Pitt-Kraft model of buying versus photocopying results in a small, but complex, nonlinear program. This paper identifies a Kuhn-Tucker point and demonstrates that for certain parameter values it is not optimal. A policy generation procedure is presented; the purpose is to prevent convergence of a primal algorithm to this inferior policy, which satisfies the Kuhn-Tucker optimality conditions

Quadratic Binary Programming Models in Computational Biology

In this paper we formulate four problems in computational molecular biology as 0-1 quadratic programs. These problems are all NP-hard and the current solution methods used in practice consist of heuristics or approximation algorithms tailored to each problem. Using test problems from scientific databases, we address the question, “Can a general-purpose solver obtain good answers in reasonable time?” In addition, we use the latest heuristics as incumbent solutions to address the question, “Can a general-purpose solver confirm optimality or find an improved solution in reasonable time?” Our computational experiments compare four different reformulation methods: three forms of linearization and one form of quadratic convexification

Inverting graphs of rectangular matrices

AbstractThis paper addresses the question of determining the class of rectangular matrices having a given graph as a row or column graph. We also determine equivalent conditions on a given pair of graphs in order for them to be the row and column graphs of some rectangular matrix. In connection with these graph inversion problems we discuss the concept of minimal inverses. This concept turns out to have two different forms in the case of one-graph inversion. For the two-graph case we present a method of determining when an inverse is minimal. Finally we apply the two-graph theorem to a class of energy related matrices

AN EXACT UPDATE FOR HARRIS' TREAD

The purpose of this note is to show how Harris' TREAD value can be computed without approximation

CONVERGENCE OF COLUMN GENERATION FOR SEMI-INFINITE PROGRAMS IN THE PRESENCE OF EQUALITY CONSTRAINTS

A convergence theorem is presented for the standard column generation algorithm which embodies GLM. The primary extension of earlier published theorems is the allowance of equality constraints. A related stability theorem is introduced to demonstrate robustness

SEARCHING ONE MULTIPLIER IN GLM

A unified approach is developed for one-dimensional GLM. The major result is a convergence theorem for interval reduction. Comparative analysis of bisection, linear interpolation and tangential approximation reveals the relative advantages of tangential approximation