Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

A Fractional Perspective to the Bond Graph Modelling of World Economies

Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Theory and measurement of social intelligence as a cognitive performance construct

Social intelligence

Algorithmic assistance to the optimization process in vehicle routing problems

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2013

Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Algorithmic Techniques in Gene Expression Processing. From Imputation to Visualization

The amount of biological data has grown exponentially in recent decades. Modern biotechnologies, such as microarrays and next-generation sequencing, are capable to produce massive amounts of biomedical data in a single experiment. As the amount of the data is rapidly growing there is an urgent need for reliable computational methods for analyzing and visualizing it. This thesis addresses this need by studying how to efficiently and reliably analyze and visualize high-dimensional data, especially that obtained from gene expression microarray experiments. First, we will study the ways to improve the quality of microarray data by replacing (imputing) the missing data entries with the estimated values for these entries. Missing value imputation is a method which is commonly used to make the original incomplete data complete, thus making it easier to be analyzed with statistical and computational methods. Our novel approach was to use curated external biological information as a guide for the missing value imputation. Secondly, we studied the effect of missing value imputation on the downstream data analysis methods like clustering. We compared multiple recent imputation algorithms against 8 publicly available microarray data sets. It was observed that the missing value imputation indeed is a rational way to improve the quality of biological data. The research revealed differences between the clustering results obtained with different imputation methods. On most data sets, the simple and fast k-NN imputation was good enough, but there were also needs for more advanced imputation methods, such as Bayesian Principal Component Algorithm (BPCA). Finally, we studied the visualization of biological network data. Biological interaction networks are examples of the outcome of multiple biological experiments such as using the gene microarray techniques. Such networks are typically very large and highly connected, thus there is a need for fast algorithms for producing visually pleasant layouts. A computationally efficient way to produce layouts of large biological interaction networks was developed. The algorithm uses multilevel optimization within the regular force directed graph layout algorithm.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

TU Graz: Course: 707.000 Web Science and Web Technology: Lecture 3: Network Theory and Terminology

In this class, we will discuss network theory fundamentals, including concepts such as diameter, distance, clustering coefficient and others. We will also discuss different types of networks, such as scale-free networks, random networks etc. Readings: Graph structure in the Web, A. Broder and R. Kumar and F. Maghoul and P. Raghavan and S. Rajagopalan and R. Stata and A. Tomkins and J. Wiener Computer Networks 33 309--320 (2000) [Web link, Alternative Link] Optional: The Structure and Function of Complex Networks, M.E.J. Newman, SIAM Review 45 167--256 (2003) [Web link] Original course at: http://kmi.tugraz.at/staff/markus/courses/SS2008/707.000_web-science/

Development of a semantic graph-based scene description

Software representations of scenes, i.e. the modelling of objects in space, are used in many application domains. Current modelling and scene description standards focus on visualisation dimensions, and are intrinsically limited by their dependence upon their semantic interpretation and contextual application by humans. In this paper we propose the need for an open, extensible and semantically rich modelling language, which facilitates a machine-readable semantic structure. We critically review existing standards and techniques, and highlight a need for a semantically focussed scene description language. Based on this defined need we propose a preliminary solution, based on hypergraph theory, and reflect on application domains.

Testing permutation properties through subpermutations

There has been great interest in deciding whether a combinatorial structure satisfies some property, or in estimating the value of some numerical function associated with this combinatorial structure, by considering only a randomly chosen substructure of sufficiently large, but constant size. These problems are called property testing and parameter testing, where a property or parameter is said to be testable if it can be estimated accurately in this way. The algorithmic appeal is evident, as, conditional on sampling, this leads to reliable constant-time randomized estimators. Our paper addresses property testing and parameter testing for permutations in a subpermutation perspective; more precisely, we investigate permutation properties and parameters that can be well approximated based on a randomly chosen subpermutation of much smaller size. In this context, we use a theory of convergence of permutation sequences developed by the present authors [C. Hoppen, Y. Kohayakawa, C.G. Moreira, R.M. Sampaio, Limits of permutation sequences through permutation regularity, Manuscript, 2010, 34pp.] to characterize testable permutation parameters along the lines of the work of Borgs et al. [C. Borgs, J. Chayes, L Lovasz, V.T. Sos, B. Szegedy, K. Vesztergombi, Graph limits and parameter testing, in: STOC`06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, ACM, New York, 2006, pp. 261-270.] in the case of graphs. Moreover, we obtain a permutation result in the direction of a famous result of Alon and Shapira [N. Alon, A. Shapira, A characterization of the (natural) graph properties testable with one-sided error, SIAM J. Comput. 37 (6) (2008) 1703-1727.] stating that every hereditary graph property is testable. (C) 2011 Elsevier B.V. All rights reserved.