The exact distribution of the maximum, minimum and the range of multinomial/dirichlet and multivariate hypergeometric frequencies

The exact distribution of the maximum and minimum frequencies of Multinomial/Dirichlet and Multivariate Hypergeometric distributions of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact Multinomial/Dirichlet and Multivariate Hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

Scheduling of a parallel computation-bound application and sequential applications executing concurrently on a cluster - a case study

Studies have shown that most of the computers in a non-dedicated cluster are often idle or lightly loaded. The underutilized computers in a non-dedicated cluster can be employed to execute parallel applications. The aim of this study is to learn how concurrent execution of a computation-bound and sequential applications influence their execution performance and cluster utilization. The result of the study has demonstrated that a computation-bound parallel application benefits from load balancing, and at the same time sequential applications suffer only an insignificant slowdown of execution. Overall, the utilization of a non-dedicated cluster is improved.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

A computation trust model with trust network in multi-agent systems

Trust is a fundamental issue in multi-agent systems, especially when they are applied in e-commence. The computational models of trust play an important role in determining who and how to interact in open and dynamic environments. To this end, a computation trust model is proposed in which the confidence information based on direct prior interactions with the target agent and the reputation information from trust network are used. In this way, agents can autonomously deal with deception and identify trustworthy parties in multi-agent systems. The ontological property of trust is also considered in the model. A case study is provided to show the effectiveness of the proposed model.

Minimum span frequency assignment problem on triangular lattices

This paper considers the Minimum Span Frequency Assignment Problem with Interference Graph on Triangular Grid (MSFAP-TG), a special case of the Minimum Span Frequency/Channel Assignment (MSFAP) for cellular systems and optical networks. The MSFAP-TG is interesting in its own right and thus worth studying. In this paper, we propose strong integer programming formulations for the MSFAP-TG and present polyhedral results on these formulations. In solving the MSFAP-TG, we implement these integer programs to obtain exact solutions. We also develop a heuristic for obtaining feasible solutions and upper bounds for the problems. With the use of these upper bounds, and a simple lower bound, the computation time of the exact algorithm can be improved substantially. The heuristic turns out to be quite good in terms of the quality of upper bounds and is extremely efficient in computation time. Last of all, we present new concepts for tackling large scale MSFAP-TGs.

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Scheduling of a parallel computation-bound application and sequential applications executing concurrently on a cluster - a case study.

Studies have shown that most of the computers in a non-dedicated cluster are often idle or lightly loaded. The underutilized computers in a non-dedicated cluster can be employed to execute parallel applications. The aim of this study is to learn how concurrent execution of a computation-bound and sequential applications influence their execution performance and cluster utilization. The result of the study has demonstrated that a computation-bound parallel application benefits from load balancing, and at the same time sequential applications suffer only an insignificant slowdown of execution. Overall, the utilization of a non-dedicated cluster is improved.

Symbolic computation and perfect fluids in general relativity

Focuses on two areas within the field of general relativity. Firstly, the history and implications of the long-standing conjecture that general relativistic, shear-free perfect fluids which obey a barotropic equation of state p = p(w) such that w + p = 0, are either non-expanding or non-rotating. Secondly the application of the computer algebra system Maple to the area of tetrad formalisms in general relativity.

Fast computation of trimmed means

We present two methods of calculating trimmed means without sorting the data in O(n) time. The existing method implemented in major statistical packages relies on sorting, which takes O(n log n) time. The proposed algorithm is based on the quickselect algorithm for calculating order statistics with O(n) expected running time. It is an order of magnitude faster than the existing method for large data sets.

Data-driven computation of contact dynamics during two-point manipulation of deformable objects

This study represents a preliminary step towards data-driven computation of contact dynamics during manipulation of deformable objects at two points of contact. A modeling approach is proposed that characterizes the individual interaction at both points and the mutual effects of the two interactions on each other via a set of parameters. Both global as well as local coordinate systems are tested for encoding the contact mechanics. Artificial neural networks are trained on simulated data to capture the object behavior. A comparison of test data with the output of the trained system reveals a mean squared error percentage between 1% and 3% for simple interactions.