Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

Parametric multiple sequence alignment and phylogeny construction

Bounds are given on the size of the parameter-space decomposition induced by multiple sequence alignment problems where phylogenetic information may be given or inferred. It is shown that many of the usual formulations of these problems fall within the same integer parametric framework, implying that the number of distinct optima obtained as the parameters are varied across their ranges is polynomially bounded in the length and number of sequences.     

Optimized prefactored compact schemes

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we describe a strategy for developing high-order accurate prefactored compact schemes, requiring very small stencil support. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes. The prefactorization strategy splits the central implicit schemes into forward and backward biased operators. Using Fourier analysis, we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components. This ensures that when the forward and backward stencils are added, the original central compact scheme is recovered. To extend the resolution characteristic of the schemes, an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh. The resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth- and eighth-order compact schemes making them more suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. The efficiency, accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems.     

Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

Computational analysis of native and modified oligofructosides

This paper presents a quantum chemical calculation of native (2–7 fructoside residues) and chemically modified (2–4 fructoside residues) levan molecule models. A levan modification was carried out by oxidation and the following reduction or hyrdazonation of the fructoside rings. The conformational particularity and reaction ability was studied for the native and for the modified levan molecules.     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

Homogenization of two-phase flow: high contrast of phase permeabilityHomogénéisation d'écoulement diphasique : grand contraste de perméabilité d'une phase

The steady-state two-phase flow non-linear equation is considered in the case when one of phases has low effective permeability in some periodic set, while on the complementary set it is high; the second phase has no contrast of permeabilities in different zones. A homogenization procedure gives the homogenized model with macroscopic effective permeability of the second phase depending on the gradient and on the second order derivatives of the macroscopic pressure of the first phase. This effect cannot be obtained by classical (one small parameter) homogenization. To cite this article: G.P. Panasenko, G. Virnovsky, C. R. Mecanique 331 (2003).     

Normative KGP agents

We extend the logical model of agency known as the KGP model, to support agents with normative concepts, based on the roles an agent plays and the obligations and prohibitions that result from playing these roles. The proposed framework illustrates how the resulting normative concepts, including the roles, can evolve dynamically during the lifetime of the agent. Furthermore, we illustrate how these concepts can be combined with the existing capabilities of KGP agents in order to plan for their goals, react to changes in the environment, and interact with other agents. Our approach gives an executable specification of normative concepts that can be used directly for prototyping applications. Fariba Sadri is a senior lecturer at Imperial College London, from where she received her PhD. Her earlier work concentrated on integrity of deductive databases and temporal reasoning, in particular using the event calculus. In more recent years her work has been on agent technologies and multi-agent systems. She has worked on logic-based agent models, reasoning, dynamic belief revision, and inter-agent communication and negotiation for resources. She was co-awarded an EPSRC grant for research into logic-based multi-agents and was co-investigator in the EU SOCS project. Kostas Stathis is a senior lecturer at Royal Holloway, University of London and he holds a PhD from Imperial College London. His research interests are in the area of computational intelligence in general and in the intersection of computational logic and cognitive systems for social computing applications in particular. His research interests include: representation of human-computer (or computer-computer) interaction as a game; cognitive & autonomous agents; artificial agent societies; agent communication; programmable agents and agent platforms. He is a co-investigator of the EU ArguGRID project and was a co-investigator of the EU SOCS project. Francesca Toni is a senior lecturer at Imperial College London, from where she received her PhD. Her earlier work focused on abductive reasoning. In more recent years, she focused on argumentation, agent models and multi-agent systems. She has worked on computational logic-based agent models, agent reasoning, dynamic belief revision, and inter-agent communication and negotiation for resources. She has been co-ordinator of the EU SOCS project, which developed the KGP model of agency, and is coordinator of the EU ArguGRID project, on the application of argumentative agents within grid systems.