Perceptions of online tutorials for distance learning in mathematics and computing

We report on student and staff perceptions of synchronous online teaching and learning sessions in mathematics and computing. The study is based on two surveys of students and tutors conducted 5 years apart, and focusses on the educational experience as well as societal and accessibility dimensions. Key conclusions are that both staff and students value online sessions, to supplement face-to-face sessions, mainly for their convenience, but interaction within the sessions is limited. Students find the recording of sessions particularly helpful in their studies.

On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Resolução de problemas no cenário da matemática discreta

Pós-graduação em Educação Matemática - IGCE

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Constructing and Deconstructing Latin Trades

This paper discusses existence results for latin trades and provides a Glueing Construction which is subsequently used to construct all latin trades of finite order greater than three.

Classification of normal swallowing and oropharyngeal dysphagia using wavelet

Oropharyngeal dysphagia is characterized by any alteration in swallowing dynamics which may lead to malnutrition and aspiration pneumonia. Early diagnosis is crucial for the prognosis of patients with dysphagia, and the best method for swallowing dynamics assessment is swallowing videofluoroscopy, an exam performed with X-rays. Because it exposes patients to radiation, videofluoroscopy should not be performed frequently nor should it be prolonged. This study presents a non-invasive method for the pre-diagnosis of dysphagia based on the analysis of the swallowing acoustics, where the discrete wavelet transform plays an important role to increase sensitivity and specificity in the identification of dysphagic patients. (C) 2008 Elsevier Inc. All rights reserved.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.

Trades and Graphs

The trade spectrum of a simple graph G is defined to be the set of all t for which it is possible to assemble together t copies of G into a simple graph H, and then disassemble H into t entirely different copies of G. Trade spectra of graphs have applications to intersection problems, and defining sets, of G-designs. In this investigation, we give several constructions, both for specific families of graphs, and for graphs in general.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2

In this paper necessary and sufficient conditions for a vector to be the fine structure of a balanced ternary design with block size 3, index 3 and rho(2) = 1 and 2 are determined with one unresolved case.