Stefan Balev

A dynamic programming based reduction procedure for the multidimensional 0–1 knapsack problem

Abstract This paper presents a preprocessing procedure for the 0–1 multidimensional knapsack problem. First, a non-increasing sequence of upper bounds is generated by solving LP-relaxations. Then, a non-decreasing sequence of lower bounds is built using dynamic programming. The comparison of the two sequences allows either to prove that the best feasible solution obtained is optimal, or to fix a subset of variables to their optimal values. In addition, a heuristic solution is obtained. Computational experiments with a set of large-scale instances show the efficiency of our reduction scheme. Particularly, it is shown that our approach allows to reduce the CPU time of a leading commercial software.

Protein Threading: From Mathematical Models to Parallel Implementations

This paper presents a new network-flow formulation for the problem of predicting 3D protein structures using threading. Several integer-programming models based on this formulation are proposed and compared. These models allow for an efficient decomposition and for the application of a parallel branch-and-cut algorithm, significantly reducing the running time. The efficiency of our approach has been confirmed by extensive computational experiments.

Lagrangian approaches for a class of matching problems in computational biology

This paper presents efficient algorithms for solving the problem of aligning a protein structure template to a query amino-acid sequence, known as protein threading problem. We consider the problem as a special case of graph matching problem. We give formal graph and integer programming models of the problem. After studying the properties of these models, we propose two kinds of Lagrangian relaxation for solving them. We present experimental results on real-life instances showing the efficiency of our approaches.

A Model of Road Network and Buildings Extension Co-evolution☆

Abstract Urban morphology tries to understand the spatial structure of cities. It searches to identify the patterns and underlying substructures but also the process of city development. Our contribution follows this last direction, we model the co-evolution of the road network and the buildings. Our goal is triple: to combine cellular automata simplicity with city irregularities, to enable the road network and buildings co-evolution and to respect temporal coherence. These objectives lead us to propose a simulation model based on a geographic automata system. Several kinds of models already exist, but they usually concentrate only on the evolution of the road network or only on the population density. The originality of our work consists in the dynamic of co-evolution of the city, we propose a city morphogenesis model.

A Study of Protein Structure Using Amino Acid Interaction Networks

Proteins are biological macromolecules participating in the large majority of processes which govern organisms. The roles played by proteins are varied and complex. Certain proteins, called enzymes, act as catalysts and increase several orders of magnitude, with a remarkable specificity, the speed of multiple chemical reactions essential to the organism survival. Proteins are also used for storage and transport of small molecules or ions, control the passage of molecules through the cell membranes, etc. Hormones, which transmit information and allow the regulation of complex cellular processes, are also proteins. Genome sequencing projects generate an ever increasing number of protein sequences. For example, the Human Genome Project has identified over 30,000 genes which may encode about 100,000 proteins. One of the first tasks when annotating a new genome is to assign functions to the proteins produced by the genes. To fully understand the biological functions of proteins, the knowledge of their structure is essential. In their natural environment, proteins adopt a native compact three-dimensional form. This process is called folding and is not fully understood. The process is a result of interactions between the proteins amino acids which form chemical bonds. In this paper we identify some of the properties of the network of interacting amino acids. We believe that understanding these networks can help to better understand the folding process. There exist different classifications of proteins according to their structure, such as CATH (Orengo, 1997) and SCOP (Murzin.1995). Proteins from the same class have similar structures and most often, similar functions. In this paper we show that structure classes can also be defined in the terms of the properties of amino acid networks.

4 – Networking, Networks and Dynamic Graphs

Networks cannot be confined within a single field of research. The concepts associated with them have considerably changed over time, and continue to do so today. This makes it difficult to give a single clear definition of a network. Networks are also the location of processes and so are embedded in time, and their structure can change; these are the observations on which our approach is based. Throughout this chapter, we will attempt to shed light on these scientific objects by accepting the bias inherently present in the desire to produce mathematical and computational models for studying networks with NetLogo.