Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π=(u ₁,…,u _k ) of vertices of a graph G is the set of vertices x that minimize (maximize) the remoteness ∑ _i d(x,u _i ). Two algorithms for median graphs G of complexity O(n idim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes.     

Balancing task allocation in multi-robot systems using K-means clustering and auction based mechanisms

This paper aims to solve the balanced multi-robot task allocation problem. Multi-robot systems are becoming more and more significant in industrial, commercial and scientific applications. Effectively allocating tasks to multi-robots i.e. utilizing all robots in a cost effective manner becomes a tedious process. The current attempts made by the researchers concentrate only on minimizing the distance between the robots and the tasks, and not much importance is given to the balancing of work loads among robots. It is also found from the literature that the multi-robot system is analogous to Multiple Travelling Salesman Problem (MTSP). This paper attempts to develop mechanism to address the above two issues with objective of minimizing the distance travelled by ‘m’ robots and balancing the work load between ‘m’ robots equally. The proposed approach has two fold, first develops a mathematical model for balanced multi-robot task allocation problem, and secondly proposes a methodology to solve the model in three stages. Stage I groups the ‘N’ tasks into ‘n’ clusters of tasks using K-means clustering technique with the objective of minimizing the distance between the tasks, stage II calculates the travel cost of robot and clusters combination, stage III allocates the robot to the clusters in order to utilise all robot in a cost effective manner.     

Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications

Nonpolynomial quintic spline functions are used to develop a numerical algorithm for computing an approximation to the solution of a system of second order boundary value problems associated with heat transfer. We show that the approximate solutions obtained by our algorithm are better than those produced by other spline and domain decomposition methods. A comparison of our algorithm with nonpolynomial quadratic spline method is discussed with the help of two numerical examples.     

Collusion set detection using graph clustering

Many mal-practices in stock market trading—e.g., circular trading and price manipulation—use the modus operandi of collusion. Informally, a set of traders is a candidate collusion set when they have “heavy trading” among themselves, as compared to their trading with others. We formalize the problem of detection of collusion sets, if any, in the given trading database. We show that naïve approaches are inefficient for real-life situations. We adapt and apply two well-known graph clustering algorithms for this problem. We also propose a new graph clustering algorithm, specifically tailored for detecting collusion sets. A novel feature of our approach is the use of Dempster–Schafer theory of evidence to combine the candidate collusion sets detected by individual algorithms. Treating individual experiments as evidence, this approach allows us to quantify the confidence (or belief) in the candidate collusion sets. We present detailed simulation experiments to demonstrate effectiveness of the proposed algorithms.     

A DEM‐based parallel computing hydrodynamic and transport model

The sudden and accidental water pollution response system (SAWPRS) for Yangtze River in central China required to develop a hydrodynamic and transport model, which is readily available and capable of simulating a large river system within GIS environment. This study facilitates such effort by developing a parallel computing method based on digital elevation model (DEM) using overlapping domain decomposition approach (ODDA) and message passing interface (MPI) protocol. The hydrodynamic and transport model was redesigned using finite volume method for hydrodynamic and transport model dispersion, the SIMPLEC method for solving the flow field, and the pressure weighted interpolating method for the flow field modification. This modelling approach was verified in two experiments using different sets of computer clusters. The model output was evaluated against the measured data collected for the year 1998 for Wanzhou, an upstream river segment of Yangtze River. The relative error was found to be less than 10%. The performance of parallel computation was found excellent as evident from the cost efficiency values greater than 0.81 in both experiments and increased computation speed while increasing the number of computer clusters. Overall, the parallel computing modelling system developed here was found to meet all requirements of SAWPRS. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust classification of EEG signal for brain-computer interface.

We report the implementation of a text input application (speller) based on the P300 event related potential. We obtain high accuracies by using an SVM classifier and a novel feature. These techniques enable us to maintain fast performance without sacrificing the accuracy, thus making the speller usable in an online mode. In order to further improve the usability, we perform various studies on the data with a view to minimizing the training time required. We present data collected from nine healthy subjects, along with the high accuracies (of the order of 95% or more) measured online. We show that the training time can be further reduced by a factor of two from its current value of about 20 min. High accuracy, fast learning, and online performance make this P300 speller a potential communication tool for severely disabled individuals, who have lost all other means of communication and are otherwise cut off from the world, provided their disability does not interfere with the performance of the speller.     

Knowledge representation using fuzzy Petri nets-revisited

In the paper by S. Chen et al. (see ibid., vol.2, no.3, p.311-19, 1990), the authors proposed an algorithm which determines whether there exists an antecedent-consequence relationship from a fuzzy proposition d _s to proposition d_j and if the degree of truth of proposition d_s is given, then the degree of truth of proposition d_j can be evaluated. The fuzzy reasoning algorithm proposed by S. Chen et al. (1990) was found not to be working with all types of data. We propose: (1) a modified form of the algorithm, and (2) a concept of hierarchical fuzzy Petri nets for data abstraction     

Mathematical modelling of an aquatic ecosystem I

This paper presents a mathematicfa1 model of an aquatic ecosystem. The model differs from previous models in that it incorporates characteristics of specific phyla of phytaplankton and zooplankton, inter and intra-phyla interaction and limiting nutrient processing by decomposers.     

Minimization of interfaces and interconnections in a digital system satisfying concurrency constraints

The problem of minimizing the number of links and buses in a digital system subject to a given set of concurrency constraints among data transfers is studied. The notion of the transfer graph (TG) is introduced which depicts the data transfer paths and concurrency requirements in the system, A very simple node labelling procedure is applied on the nodes of the TG, which enables one to make a direct assignment of transfers to buses without going through any elaborate computational steps.     

The Use of Legendre Polynomial Expansions in Solving Optimal Control Problems in the Space l 2

A method for solving a class of general deterministic optimal control problems is presented here. The method consists of relating the functions involved in the problem to sequences and then converting the problem to one which deals with these sequences alone. The function-sequence correspondence is defined by representing each function by its Legendre polynomial expansion and then relating the function to the sequence of coefficients in this expansion. After this is done, the problem is converted to one in l ²; by determining the equivalents in l ²; of differentiation, inner multiplication, and multiplication.

The resulting problem in l ²; is a non-linear programming problem which consists of an infinite array of equations, inequalities, and expressions, each of which involves infinite polynomial expressions. To solve a problem of this type it must be approximated by a finite non-linear programming problem. After this is done various methods can bo used for solving the final problem.