Analytical results for the plectonemic response of supercoiled DNA

The DNA molecule is modeled as an elastic rod with bending and twisting rigidities, subjected to external tension and twist applied at one end, the other end being clamped. We study the plectonemic equilibrium of such a rod, taking into account the impenetrability constraint. Numerical solutions of this boundary value problem have previously shown that purely elastic models can reproduce the supercoiling response of the DNA molecule. Using a variational approach, we derive analytical formulae for the elastic response of the filament, and extend former numerical results.     

Free-Edge and Ply Cracking Effect in Angle-Ply Laminated Composites Subjected to In-Plane Loads

This paper presents a semianalytical method for the prediction of interlaminar stresses and displacements near the free edges and ply cracks in general angle-ply laminates subjected to biaxial extensions and/or in plane shear deformation. The method is based on a state space representation of the three-dimensional equations of elasticity. Numerical solutions are obtained by using layer refinement in the through thickness direction and Fourier series expansion in the other directions. By this approach, an angle-ply laminate may be composed of an arbitrary number of monoclinic layers and each layer may have different material property and thickness. This method guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical results are compared with those obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularities near the free edges and ply cracks. Numerical solutions for antisymmetric laminates under extension and general laminates under shearing are new in the literature and can be used as benchmarks for validating new models.     

Algorithms in the W-Hierarchy

We show new upper bounds for problems in the W-hierarchy of fixed-parameter complexity. A crucial ingredient of our proofs is an extension to the W-RAM model, which permits more-powerful operations but remains equivalent to the original. We use the extended model to give new upper bounds for Subsetsum, Maximum Irredundant Set, and various problems concerning intersection of finite-state machines.     

Polynomial-Space Decidable Membership Problems for Recurrent Systems over Sets of Natural Numbers

A finite recurrent system over sets of natural numbers of dimension n is a pair composed of n n-ary functions over sets of natural numbers and an n-tuple of singleton sets of natural numbers. Every function is applied to the entries of the tuple and computes a set of natural numbers, that may also be empty. The results are composed into another tuple, and the process is started anew. Thus, a finite recurrent system defines an infinite sequence of n-tuples containing sets of natural numbers. The last entry of a generated n-tuple is called the output of a step, and the union of the output sets of all steps is the set defined by the finite recurrent system. Membership problems ask whether a given number is in a specified output set or in some output set. We study membership problems for special finite recurrent systems, whose functions are built from the set operations union, intersection and complementation and the arithmetical operations addition and multiplication. Sum and product of two sets of natural numbers are defined elementwise. We restrict the set of operations from which functions are built and determine the impact on the complexity of the membership problems. We focus on PSPACE-decidable membership problems and show completeness results for the complexity classes NL, NP and PSPACE.     

Dynamic Complexity Theory Revisited

Dynamic complexity investigates the required effort to maintain knowledge about a property of a structure under changing operations. This article introduces a refined notion of dynamic problems which takes the initial structure into account. It develops the basic structural complexity notions accordingly. It also shows that the dynamic version of the LOGCFL-complete problem D₂LREACH(acyclic) can be maintained with first-order updates.     

Truthful Approximation Mechanisms for Scheduling Selfish Related Machines

We consider the problem of scheduling jobs on related machines owned by selfish agents. We provide a 5-approximation deterministic truthful mechanism, the first deterministic truthful result for the problem. Previously, Archer and Tardos showed a 2-approximation randomized mechanism which is truthful in expectation only (a weaker notion of truthfulness). In case the number of machines is constant, we provide a deterministic Fully Polynomial-Time Approximation Scheme (FPTAS) and a suitable payment scheme that yields a truthful mechanism for the problem. This result, which is based on converting FPTAS to monotone FPTAS, improves a previous result of Auletta et al., who showed a (4 + ε)-approximation truthful mechanism.     

An approach to efficient business intelligent system for financial prediction

A concept of business intelligent system for financial prediction is considered in this paper. It provides data needed for fast, precise and good business decision support to all levels of management. The aim of the project is the development of a new online analytical processing oriented on case-based reasoning (CBR) where a previous experience for every new problem is taken into account. Methodological aspects have been tested in practice as a part of the management information system development project of “Novi Sad Fair”. A case study of an improved application of CBR in prediction of future payments is discussed in the paper. This paper is originally presented at The International Conference on Hybrid Information Technology 2006, at the special session on “Intelligent Information Systems for Financial Engineering”, November 2006 in Cheju Island, Korea.