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.     

Stream Classification System Based on Susceptibility to Algal Growth in Response to Nutrients

We developed a stream classification system that is based on stream’s susceptibility to algal growth using a two-step approach. The model portrays algal biomass as a result of stream’s response to nutrient concentrations and the response is governed by various stream factors. In the first step, a nutrient-chlorophyll a relationship was developed to characterize nutrient’s effects on algal biomass. Residuals of the relationship were attributed to stream’s susceptibility to algal growth in response to nutrients and referred to as “observed” susceptibility. In the second step, conditions of other contributing factors were used to explain the variation in the residuals and the developed relationship was used to generate “predicted” susceptibility. Existing data compiled from various monitoring projects of Illinois streams and rivers were used to illustrate the approach. Streams were classified into three (high, medium, and low) categories based on their observed and predicted susceptibility values, respectively. With the available data, the model showed a 40-50% success rate for classifying the streams based on three observed and predicted susceptibility categories. Model entropy also was calculated for selecting the best model. The results show the important role of both nutrients and other contributing factors in explaining the variation of algal biomass. The study also suggests ways to fine tune the model and improve its accuracy, which would make the presented model a more viable tool for stream classification for establishing nutrient criteria to prevent surface streams from eutrophication.     

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.     

Computing Minimal Multi-Homogeneous Bezout Numbers Is Hard

The multi-homogeneous Bezout number is a bound for the number of solutions of a system of multi-homogeneous polynomial equations, in a suitable product of projective spaces. Given an arbitrary, not necessarily multi-homogeneous, system, one can ask for the optimal multi-homogenization that would minimize the Bezout number. In this paper it is proved that the problem of computing, or even estimating, the optimal multi-homogeneous Bezout number is actually NP-hard. In terms of approximation theory for combinatorial optimization, the problem of computing the best multi-homogeneous structure does not belong to APX, unless P = NP. Moreover, polynomial-time algorithms for estimating the minimal multi-homogeneous Bezout number up to a fixed factor cannot exist even in a randomized setting, unless BPP ⫆ NP.