Abstracts of theses in mathematics

summary:Zhukavets, Natalia: Close 2-groups. Smolíková, Petra: Simple colorings and simple homomorphisms. Růžička, Pavel: Cofinal chains in module theory and representations of distributive lattices. Janečková, Hana: Time series with changing parameters. Večeř, Jan: Stochastic calculus in econometrics. Sváček, Petr: Finite element method for a problem with nonlinear boundary conditions. Dušek, Zdeněk: Harmonic analysis in Riemannian geometry. Śmídek, Michal: Measurability of sets of points of differentiability of functions Banach spaces. Klapka, Štěpán: Markov models in signalling systems. Hykšová, Magdalena: Karel Rychlík (1885-1968). Maxová, Jana: On oriented covers and decompositions of Eulerian graphs. Murtinová, Eva: Separation axioms in dense subsets. Franěk, Petr: Some problems of recursive methods in time series analysis. Čížek, Martin: The mathematical analysis of components of the risk in the insurance of persons. Mrkvička, Tomáš: Models of random sets and their statistical analysis

Temporal Networks

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

The effectiveness of a computer-supported intervention targeting phonological recoding and orthographic processing for children with word reading impairment

This research designed, developed, trialled, and evaluated a reading intervention targeting phonological recoding and orthographic processing for children with persistent reading impairment. Eight otherwise typically developing Year 2 participants with reading delay despite previous intervention, were randomly assigned to two groups in a single subject multiple-treatment cross-over design study. The results of group and individual analyses indicated that all participants made significant gains on measures of nonword reading with trends for gains in word reading

Computational complexity of digraph decomposition and the congruence extension property for algebras

The strong direct product is one of the standard graph products. In 1992, Feigenbaum and Schaffer presented a polynomial-time algorithm to find the unique prime factorization of connected graphs under the strong direct product. In this paper, we show that weakly connected directed graphs have unique prime factorizations with respect to the strong direct product, and we give a polynomial-time algorithm to find the prime factorizations of such digraphs. This is an extension of Feigenbaum and Schaffer\u27s work on factoring undirected graphs under the strong direct product and Imrich\u27s work on factoring undirected graphs with respect to the weak direct product. We also investigate the problem of determining whether an algebra has the congruence extension property. We prove that this problem is complete for polynomial time

The Structure of Information Pathways in a Social Communication Network

Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail communication among the faculty and staff of a large university over a two-year period. We formulate a temporal notion of "distance" in the underlying social network by measuring the minimum time required for information to spread from one node to another -- a concept that draws on the notion of vector-clocks from the study of distributed computing systems. We find that such temporal measures provide structural insights that are not apparent from analyses of the pure social network topology. In particular, we define the network backbone to be the subgraph consisting of edges on which information has the potential to flow the quickest. We find that the backbone is a sparse graph with a concentration of both highly embedded edges and long-range bridges -- a finding that sheds new light on the relationship between tie strength and connectivity in social networks.Comment: 9 pages, 10 figures, to appear in Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'08), August 24-27, 2008, Las Vegas, Nevada, US

Exploratory Analysis in Learning Analytics

This article summarizes the methods, observations, challenges and implications for exploratory analysis drawn from two learning analytics research projects. The cases include an analysis of a games-based virtual performance assessment and an analysis of data from 52,000 students over a 5-year period at a large Australian university. The complex datasets were analyzed and iteratively modeled with a variety of computationally intensive methods to provide the most effective outcomes for learning assessment, performance management and learner tracking. The article presents the research contexts, the tools and methods used in the exploratory phases of analysis, the major findings and the implications for learning analytics research methods