Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let S=(s_1,s_2,..., s_m) and T = (t_1,t_2,..., t_n) be vectors of non-negative integers with sum_{i=1}^{m} s_i = sum_{j=1}^n t_j. Let B(S,T) be the number of m*n matrices over {0,1} with j-th row sum equal to s_j for 1 <= j <= m and k-th column sum equal to t_k for 1 <= k <= n. Equivalently, B(S,T) is the number of bipartite graphs with m vertices in one part with degrees given by S, and n vertices in the other part with degrees given by T. Most research on the asymptotics of B(S,T) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.Comment: Multiple minor adjustments. Accepted by JCT-

Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Human-computer interaction closes the digital divide: a multicultural, intergenerational ICT case study

Ethnic and racial tensions are aggravated by social inequities. The media unwittingly feeds this dilema. Look at how often we are directed to the internet for further information. While exploring the internet may be easier for some computer users, others demonstrate a complete avoidance for this type of knowledge exchange. Misunderstandings that occur between cultural communities may be exacerbated by the digital divide through lack of access, for whatever reason, causing a meaningful gap in cultural differences, and henceforth leading to serious communication breakdowns. This paper argues for more research on measuring the effectiveness of increased opportunities for Web-mediated cross-cultural/intergenerational knowledge sharing that is designed to overcome the ever widening digital divide

Towards a complete inventory of stratospheric dust particles, with implications for their classification

Several investigators have recently proposed classification schemes for stratospheric dust particles [1-3]. In addition, extraterrestrial materials within stratospheric dust collections may be used as a measure of micrometeorite flux [4]. However, little attention has been given to the problems of the stratospheric collection as a whole. Some of these problems include: (a) determination of accurate particle abundances at a given point in time; (b) the extent of bias in the particle selection process; (c) the variation of particle shape and chemistry with size; (d) the efficacy of proposed classification schemes and (e) an accurate determination of physical parameters associated with the particle collection process (e.g. minimum particle size collected, collection efficiency, variation of particle density with time). We present here preliminary results from SEM, EDS and, where appropriate, XRD analysis of all of the particles from a collection surface which sampled the stratosphere between 18 and 20km in altitude. Determinations of particle densities from this study may then be used to refine models of the behavior of particles in the stratosphere [5]

Planning effective HCI to enhance access to educational applications

Information and communications technologies (ICT) are widely believed to offer new options for Web-mediated courseware design. Multimedia and online courseware development accentuates a belief that highly graphical (or visual) delivery media will meet the individualised instructional requirements of diverse student cohorts. While most electronic courseware may allow the user to proceed at their own pace, two assumptions are commonly made by courseware designers. Firstly, to facilitate learning, all users are assumed capable of assimilating the graphical content with their current experiential knowledge. There is little or no consideration of different cognitive styles. Understanding learner attributes is essential to increasing accessibility to computerised information. Secondly, learning is assumed rather than demonstrated. To deal with this issue, data analysis techniques can be used to differentiate between what an individual knows from what they do not. This paper presents two research projects that demonstrate the importance of awareness for the human-dimension of human-computer interaction (HCI) in designing effective online experiential learning for special education

Human-computer interaction: GUI raises targets for computer literacy

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The metamorphosis of e-learning

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