Man-Keung Siu

On the cycle structure of some nonlinear shift register sequences

The cycle structure of a nonlinear shift register is the subject of interest in several recent papers. This paper investigates the cycle structure of the “connection” of two shift registers, thereby constructing two classes of nonlinear feedback logics which generate sequences of maximal length. The relationship between the present theory and results in other works is also indicated.

Proof and pedagogy in ancient China: Examples from Liu Hui's commentary on JIU ZHANG SUAN SHU

Through the discussion of several examples from Liu Huis commentary on the ancient Chinese mathematical classics JIU ZHANG SUAN SHU this article attempts to illustrate the pedagogical implications embodied therein, mainly the aspects of proof in ancient Chinese mathematics and more generally the role of proofs in mathematics.

Two-dimensional binary arrays with good autocorrelation

Calabro and Wolf (1968) Inform. Contr. 11 ) investigate the autocorrelation properties of certain periodic two-dimensional arrays. This note points out a relationship between periodic p × q -arrays with two-level autocorrelation and difference sets in the group C ( p ) × C ( q ), where C ( n ) denote the cyclic group of order n . This observation enables us to construct several families of such arrays, some of which are perfect.

Adaptive File Allocation in Star Computer Network

In this paper, we study the allocation of files in a star network. Unlike previous algorithms which assume that files are independently accessed and independently assigned, the interaction of files during the processing of queries is directly incorporated into our cost model. We present an adaptive algorithm, which is much faster than existing algorithms on file allocation, obtains solutions which are on the average only 0.1 percent away from the optimal solutions, and possesses many desirable properties such as the satisfaction of some necessary and sufficient conditions for file allocation.

On models of information retrieval processes

Abstract A model called the binary independence model is presented as a generalization of a few models which have applied to the analyses of a clustered search process, some indexing strategies and a relevance feedback process. This model, together with the Swets model, the linked-2-Poisson model, the 2-Poisson model, the binary limited-dependence model, the tree dependence model, the binary dependence model and the non-binary independent model are compared and contrasted. Despite the fact that these models are intended for different applications, three aspects of modelling are identified, based on which, these models are compared. The three aspects are the class concept, the distribution of similarities and the relation between a matching function and its retrieval effectiveness. As results of the comparison between the models, more insight into the models is gained and a set of guidelines are suggested to help a system designer to choose a model.

A generalized counter scheme

Abstract The transposition heuristic is a common method used to improve the performance of accessing records in a linked list. After the list has reached a steady state for the transposition heuristic, we begin to keep a frequency count for each record. A method of re-arranging the records, called the generalized counter scheme, is introduced and is shown to be optimal among all possible methods of re-arrangement based on the counts. The scheme is applicable even when the count is small. The usual counter scheme is also shown to be optimal for any finite count.

Effective Automatic Indexing Using Term Addition and Deletion

In mformaUon retrieval indexing is the task consisting of the assignment to stored records and mcommg mformatton requests of content ~dent~fiers capable of representing record or query content If the mdexmg is performed automatically and the records are wntten documents, an mmal set of index terms might be chosen by taking words extracted from document roles or abstracts, this mmal term assignment might then be improved by addmg related terms chosen from a thesaurus, by deletmg extraneous or marginal terms, and by replacing smgle terms by term combmaaons and phrases. In the present study formal proofs are given of the retrieval effectiveness under well-defined condmons of mdexmg policies based on the use of single terms, term additions and deletions, and term combmaaons or phrases.

History of mathematics and its relation to mathematical education

This article elaborates on the following aspects of the role played by the history of mathematics in mathematical education: (1) content of curriculum, (2) standard of rigour, (3) interrelation among topics, (4) understanding of subject matter, (5) cultural viewpoint, (6) confidence in doing mathematics.

Nonexistence of certain perfect arrays

Abstract Perfect binary arrays are equivalent to Menon difference sets in certain groups. This note proves a theorem on the Menon difference set and interprets its consequences on the nonexistence of certain perfect arrays.

Proof in the Western and Eastern Traditions: Implications for Mathematics Education

As one of the three panellists on the topic of proof within the Western and the Eastern cultural traditions, the author focuses on the ‘algorithmic’ and ‘dialectic’ aspects of doing mathematics with some illustrative examples taken from both the Western and Eastern worlds. The author argues that both mathematical traditions incorporate and use both aspects in constructing proofs.