The combinatorics of binary arrays

This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin

A Survey of Hadamard Difference Sets

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic according to the properties of the underlying group. Difference sets are important in design theory because they are equivalent to symmetric (v, k, λ) designs with a regular automorphism group [L]

Binary matrices of optimal autocorrelations as alignment marks

We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of dimensions up to 7 by 7 and optimal diagonally-symmetric matrices of 8 by 8 and 9 by 9 were found by exhaustive searches.Comment: 8 pages, 6 figures and 1 tabl

The merit factor of binary arrays derived from the quadratic character

We calculate the asymptotic merit factor, under all cyclic rotations of rows and columns, of two families of binary two-dimensional arrays derived from the quadratic character. The arrays in these families have size p x q, where p and q are not necessarily distinct odd primes, and can be considered as two-dimensional generalisations of a Legendre sequence. The asymptotic values of the merit factor of the two families are generally different, although the maximum asymptotic merit factor, taken over all cyclic rotations of rows and columns, equals 36/13 for both families. These are the first non-trivial theoretical results for the asymptotic merit factor of families of truly two-dimensional binary arrays.Comment: minor correction

Papers on predicative constructions : Proceedings of the workshop on secundary predication, October 16-17, 2000, Berlin

This volume presents a collection of papers touching on various issues concerning the syntax and semantics of predicative constructions. A hot topic in the study of predicative copula constructions, with direct implications for the treatment of he (how many he's do we need?), and wider implications for the theories of predication, event-based semantics and aspect, is the nature and source of the situation argument. Closer examination of copula-less predications is becoming increasingly relevant to all these issues, as is clearly illustrated by the present collection

A study of spatial data models and their application to selecting information from pictorial databases

People have always used visual techniques to locate information in the space surrounding them. However with the advent of powerful computer systems and user-friendly interfaces it has become possible to extend such techniques to stored pictorial information. Pictorial database systems have in the past primarily used mathematical or textual search techniques to locate specific pictures contained within such databases. However these techniques have largely relied upon complex combinations of numeric and textual queries in order to find the required pictures. Such techniques restrict users of pictorial databases to expressing what is in essence a visual query in a numeric or character based form. What is required is the ability to express such queries in a form that more closely matches the user's visual memory or perception of the picture required. It is suggested in this thesis that spatial techniques of search are important and that two of the most important attributes of a picture are the spatial positions and the spatial relationships of objects contained within such pictures. It is further suggested that a database management system which allows users to indicate the nature of their query by visually placing iconic representations of objects on an interface in spatially appropriate positions, is a feasible method by which pictures might be found from a pictorial database. This thesis undertakes a detailed study of spatial techniques using a combination of historical evidence, psychological conclusions and practical examples to demonstrate that the spatial metaphor is an important concept and that pictures can be readily found by visually specifying the spatial positions and relationships between objects contained within them

Awaiting the support of the written description: defining the technical contribution in the emergence of early English patent law

PhDTechnology had made but tentative advances under the aegis of oral communication with merely sporadic demands for a recognisably modern patent system until the late 1700s. Fixity of craft knowledge had a problematic upbringing with guilds propagating stasis under a collectivist encirclement of skills. Emancipation from this feudalistic overhang was associated with mysteries often not tethered to a location; untied by sole-trading sometimes immigrant artisans including apothecaries, applied mathematicians and surgical practitioners, with the use of notebooks to question, record, and faithfully witness explanation and clinical experiences. These vernacular descriptions revealed an inheritable imperative to forego secrecy. Meanwhile, government attempts to administer the phenomenon of invention becoming a democratic asset required that the introducer, as well as the originator, be rewarded. The highly-skilled responded to this security, London’s allure creating a polyglot conurbation, yet one where the utility of early formats of inventive output required but vague commitments to public education. Having finally exposed the inadequacies of oral information-transfer, the parallels of the advent of printing presses and the reach of faith, stimulated access to learned communications. Later, scientific literacy created a new appreciation of vulgar knowledge; this elevation also uncovering novel entrepreneurial chattels; individual property in everyday techniques. The jigsaw next required key visionaries: those who were technologically adept while simultaneously demanding written instruments to stipulate inventive space. The reaction of the Commons was to legislate against monopolies, a response insufficient to foster patents for invention. The mosaic of language initiated a still later seismic shift in the description of scientific phenomena. Publication became the arc of progress through which new fraternities held sway as intellectual networks demanded the utensil of the hypothesis to interpret advances. Contemporaneously, the early adoption of some broad patents provided a realisation whereby, discriminating that which was truly momentous required disclosure of a full written description, the most significant part of which was to become the applicant’s patent specification.Staff Development Fund of Athlone Institute of Technology, Athlone, Irelan