Sum-intersective sets

We study additive intersective properties of sparse subsets of integers. In particular, we prove that for every set S with counting function o(log n) there exists a set A with lower asymptotic density 1/2 such that A + A is disjoint from S. We also show that this result is best possible.     

Concave programming for minimizing the zero-norm over polyhedral sets

Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zero-norm. This combinatorial optimization problem is NP-Hard and arises in various fields such as machine learning, pattern recognition, signal processing. One of the contributions of this paper is to propose two new smooth approximations of the zero-norm function, where the approximating functions are separable and concave. In this paper we first formally prove the equivalence between the approximating problems and the original nonsmooth problem. To this aim, we preliminarily state in a general setting theoretical conditions sufficient to guarantee the equivalence between pairs of problems. Moreover we also define an effective and efficient version of the Frank-Wolfe algorithm for the minimization of concave separable functions over polyhedral sets in which variables which are null at an iteration are eliminated for all the following ones, with significant savings in computational time, and we prove the global convergence of the method. Finally, we report the numerical results on test problems showing both the usefulness of the new concave formulations and the efficiency in terms of computational time of the implemented minimization algorithm.     

Solving the problem of packing equal and unequal circles in a circular container

In this paper we propose a Monotonic Basin Hopping approach and its population-based variant Population Basin Hopping to solve the problem of packing equal and unequal circles within a circular container with minimum radius. Extensive computational experiments have been performed both to analyze the problem at hand, and to choose in an appropriate way the parameter values for the proposed methods. Different improvements with respect to the best results reported in the literature have been detected.     

绕凸包主动流动控制的初步数值研究

基于程序可靠性校验,本文对绕凸包流动进行了数值研究,其中主要对不同吹／吸气速度影响进行了参数化研究,并根据结果对吹／吸气控制分离机理予以了解释,表明:吹吸气对附面层的吹断／吸除作用以及其对主流的气动堵塞作用是正确分析其影响分离机理的关键。     

Attractive forces between anisotropic inclusions in the membrane of a vesicle

The fluctuation-induced interaction between two rod-like, rigid inclusions in a fluid vesicle is studied by means of canonical ensemble Monte-Carlo simulations. The vesicle membrane is represented by a triangulated network of hard spheres. Five rigidly connected hard spheres form rod-like inclusions that can leap between sites of the triangular network. Their effective interaction potential is computed as a function of mutual distance and angle of the inclusions. On account of the hard-core potential among these, the nature of the potential is purely entropic. Special precaution is taken to reduce lattice artifacts and the influence of finite-size effects due to the spherical geometry. Our results show that the effective potential is attractive and short-range compared with the rod length L. Its well depth is of the order of , where is the bending modulus. Received 5 February 1999 and Received in final form 14 May 1999     

Docking of Atomic Clusters Through Nonlinear Optimization

The problem of molecular docking is defined as that of finding a minimum energy configuration of a pair of molecular structures (usually consisting of proteins, DNA or RNA fragments). It is often assumed that the two interacting structures can be considered as rigid bodies and that it is of interest to researchers to develop methods which enable to discover the potential binding sites. Many different models have been proposed in the literature for the definition of the potential energy between two molecular structures, most of which contain at least a term (known as Van Der Waals interaction) which accounts for pairwise attraction between atoms, a repulsion term and a term which takes into account electrostatic forces (Coulomb interaction). Some well known models, and in particular those used in rigid docking, are based on the assumption that the only terms which are relevant in the process of docking are pairwise interactions between atoms belonging to the two different parts of the structure. In this paper the problem of finding the lowest energy configuration of a pair of biomolecular structures, considered as rigid bodies, is defined and formulated as a global optimization problem. In terms of dimension of the search space this formulation is not 'high-dimensional', as there are only six degrees of freedom: 3 translation and 3 rotation parameters. However the energy surface of the docking problem is characterized by a huge number of local minima; moreover each function evaluation is quite expensive (interesting structures usually possess a few thousand atoms each). So there is a strong need both of local and of global optimization procedures. In this paper a local optimization technique, based upon standard non linear programming software and a penalized objective function, is introduced and its potential usefulness in the context of global optimization is outlined.