40354027
Minimal trees of given search number
Abstract A recurrence relation and asymptotic estimate for the number of minimal trees of given search number are derived. In addition, a language for describing these trees and structures within them is developed. Their automorphisms groups are also discussed.
30784259
Semilattice-based dualities
The paper discusses “regularisation” of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities.
5633682
On the Unimodality and Combinatorics of Bessel Numbers
The Bessel numbers are reparametrized coefficients of Bessel polynomials. The paper investigates the analogies between Stirling numbers and Bessel numbers. A generating function for the Bessel numbers is obtained, and a proof of their unimodality is given. Stirling numbers and Bessel numbers are applied to the enumeration of orbit decompositions of various powers of permutation representations.
45241521
Association Schemes, Superschemes, and Relations Invariant Under Permutation Groups
Abstract An association scheme is the associated scheme of a superscheme iff it is a permutation group scheme. The group and its action are recovered from the Bose-Mesner superalgebra of the superscheme, which is a 'quantised' version of a Krasner (relation) algebra of the second kind.
5110411
Quasigroups and quandles
Abstract Two connexions between quasigroups and quandles are established. In one direction, Joyce's homogeneous quandle construction is shown to yield a quasigroup isotopic to the loop constructed by Scimemi on the set of o-commutators of a group automorphism o. In the other direction, the universal multiplication group construction of quasigroup theory is extended to quandles. The group of a knot becomes the universal right multiplication group of the knot quandle.
37373998
On The Combinatorics Of Multi-Restricted Numbers
1926668
Exploring "Multiple Worlds" in Parallel
We examine computing alternative solutions to a problem in parallel to improve response time.Problems with exploring multiple alternatives in parallel include (1) side-effects and (2) combinatorial ...
17816721
Triangle Guarding
We consider the problem of triangle guarding ( -guarding) a simple, 2D polygon Q. A polygon Q is -guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards to lie in Q and Q has a transparent boundary then the vertices of the convex hull of Q (CH (Q)) form the minimum set of -guards. We examine two other variations of the problem. In the first, the guards may be placed within a transparent border surrounding Q. For this variation, we describe a polynomial time algorithm, related to the classic algorithm for finding min-link separators, that finds a minimum set of -guards. In the second, we consider the case where Q’s boundary is opaque and show that, as in the traditional art gallery problem, finding a minimum set of vertex -guards is NP-hard. Transparent Fences Given simple polygons P and Q with Q contained in P , where |Q|+ |P | = n, what is the minimum number and placement of guards in P needed to -guard Q, assuming that both Q and P have transparent boundaries? Our algorithm for this problem is inspired by an algorithm for finding min-link separators between two convex polygons, one contained in the other [1]. The following basic lemmas motivate using this approach. Define legal regions to be regions of the outer polygon P , that are not contained in the interior of CH (Q) (Figure 1).
16418860
Integrated spatial and feature image query
Abstract. We present a new system for querying for images by regions and their spatial and feature attributes. The system enables the user to find the images that contain arrangements of regions similar to those diagrammed in a query image. By indexing the attributes of regions, such as sizes, locations and visual features, a wide variety of complex joint spatial and feature queries are efficiently computed. In order to demonstrate the utility of the system, we develop a process for the extracting color regions from photographic images. We demonstrate that integrated spatial and feature querying using color regions improves image search capabilities over non-spatial content-based image retrieval methods.
6489448
ABC: a hypermedia system for artifact-based collaboration
Abstract : Our project is studying the process by which groups of individuals work together to build large, complex structures of ideas, and we are developing a distributed hypermedia system to support the process. This description includes a brief overview of the system, but emphasizes three components: a hypermedia data management system or graph server, a set of browsers for working with graph objects, and a set of applications for working with data contents of graph nodes. A number of research issues are raised and discussed in context, including: composite objects; anchored links; scaling up for large applications; partitioning the hypermedia graph; consistency and completeness across subgraphs; and an open, extensible architecture for applications.
18320669
Operator and parameter adaptation in genetic algorithms
Abstract Genetic Algorithms are a class of powerful, robust search techniques based on genetic inheritance and the Darwinian metaphor of “Natural Selection”. These algorithms maintain a finite memory of individual points on the search landscape known as the “population”. Members of the population are usually represented as strings written over some fixed alphabet, each of which has a scalar value attached to it reflecting its quality or “fitness”. The search may be seen as the iterative application of a number of operators, such as selection, recombination and mutation, to the population with the aim of producing progressively fitter individuals.These operators are usually static, that is to say that their mechanisms, parameters, and probability of application are fixed at the beginning and constant throughout the run of the algorithm. However, there is an increasing body of evidence that not only is there no single choice of operators which is optimal for all problems, but that in fact the optimal choice of operators for a given problem will be time-variant i.e. it will depend on such factors as the degree of convergence of the population. Based on theoretical and practical approaches, a number of authors have proposed methods of adaptively controlling one or more of the operators, usually invoking some kind of “meta-learning” algorithm, in order to try and improve the performance of the Genetic Algorithm as a function optimiser.In this paper we describe the background to these approaches, and suggest a framework for their classification, based on the learning strategy used to control them, and what facets of the algorithm are susceptible to adaptation. We then review a number of significant pieces of work within the context of this setting, and draw some conclusions about the relative merits of various approaches and promising directions for future work.