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.
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.
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.
37373998
On The Combinatorics Of Multi-Restricted Numbers
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.
44866557
A Multiple-Criterion Model for Machine Scheduling
We consider a scheduling problem involving a single processor being utilized by two or more customers. Traditionally, such scenarios are modeled by assuming that each customer has the same criterion. In practice, this assumption may not hold. Instead of using a single criterion, we examine the implications of minimizing an aggregate scheduling objective function in which jobs belonging to different customers are evaluated based on their individual criteria. We examine three basic scheduling criteria: minimizing makespan, minimizing maximum lateness, and minimizing total weighted completion time. Although determining a minimum-cost schedule according to any one of these criteria is polynomially solvable, we demonstrate that when minimizing a mix of these criteria, the problem becomes NP-hard.
43104862
Program Derivation in Type Theory: A Partitioning Problem
Abstract Martin-Lof's type theory is a theory in which one can write both specifications and programs. By interpreting propositions as types, predicate logic is available when formulating a specification. The rules of type theory are formulated as tactics which makes a “top down” construction of programs possible. These ideas are illustrated by a formal derivation of a program for a partitioning problem.
16236446
Image Classification and Querying Using Composite Region Templates
The tremendous growth in digital imagery is driving the need for more sophisticated methods for automatic image analysis, cataloging, and searching. We present a method for classifying and querying images based on the spatial orderings of regions or objects using composite region templates (CRTs). The CRTs capture the spatial information statistically and provide a robust way to measure similarity in the presence of region insertions, deletions, substitutions, replications, and relocations. The CRTs can be used for classifying and annotating images by assigning symbols to the regions or objects and by extracting symbol strings from spatial scans of the images. The symbol strings can be decoded using a library of annotated CRTs to automatically label and classify the images. The CRTs can also be used for searching by sketch or example by measuring image similarity based on relative counts of the CRTs.
16384039
Experimenting with object navigation in parallel object databases
This paper addresses the problem of selecting the best object navigation strategy for a query to be run in parallel, when considering multiple alternative strategies. This is done by performing experiments with three pointer-based join algorithms, running simple and complex queries in a parallel ODMG-compliant object database system. We believe our results provide insights into how physical properties of queries impact on the performance of different joins operators in a parallel environment.
14058785
ImpACT: An Alternative to Technology Readiness Levels for Commercial-Off-The-Shelf (COTS) Software
The use of Technology Readiness Levels (TRLs) as a tool in assessing acquisition and development program risk has steadily increased over the past several years. There is considerable evidence to support the utility of using TRLs as part of a risk assessment, but there are some difficulties in using TRLs with software, especially Commercial-Off-The-Shelf (COTS) software technology and products. These difficulties take several forms, including “blurring-together” various aspects of COTS technology/product readiness; the absence of some important aspects of readiness; COTS product “decay;” and no mechanism to account for changes in the relative importance of the contributors to technology/product readiness over time. This paper briefly examines these issues, and proposes an alternate methodology—ImpACT—for assessing COTS software technology and product readiness which considers these factors.