Muhittin Mungan

Inversion method for content-based networks.

In this paper, we generalize a recently introduced expectation maximization (EM) method for graphs and apply it to content-based networks. The EM method provides a classification of the nodes of a graph, and allows one to infer relations between the different classes. Content-based networks are ideal models for graphs displaying any kind of community and/or multipartite structure. We show both numerically and analytically that the generalized EM method is able to recover the process that led to the generation of such networks. We also investigate the conditions under which our generalized EM method can recover the underlying content-based structure in the presence of randomness in the connections. Two entropies, S(q) and S(c), are defined to measure the quality of the node classification and to what extent the connectivity of a given network is content based. S(q) and S(c) are also useful in determining the number of classes for which the classification is optimal.

Inelastic collisions of three particles on a line as a two-dimensional billiard

Abstract We study the inelastic collisions of three particles on a line. We show that this system is a two dimensional billiard in a semi-enclosed space with unconventional reflection laws. Using this geometric language, we describe completely the dynamics of this system. We find that the asymptotic behavior changes when the coefficient of restitution becomes smaller than a critical value r c . For r > r c , the system can be understood in terms of a conventional billiard in an infinite wedge. For r ≤ r c , this is no longer true and the asymptotic behavior is richer. We also investigate the question of triple collisions and find that they are regularizable only for certain values of r .

The Information Coded in the Yeast Response Elements Accounts for Most of the Topological Properties of Its Transcriptional Regulation Network.

The regulation of gene expression in a cell relies to a major extent on transcription factors, proteins which recognize and bind the DNA at specific binding sites (response elements) within promoter regions associated with each gene. We present an information theoretic approach to modeling transcriptional regulatory networks, in terms of a simple “sequence-matching” rule and the statistics of the occurrence of binding sequences of given specificity in random promoter regions. The crucial biological input is the distribution of the amount of information coded in these cognate response elements and the length distribution of the promoter regions. We provide an analysis of the transcriptional regulatory network of yeast Saccharomyces cerevisiae, which we extract from the available databases, with respect to the degree distributions, clustering coefficient, degree correlations, rich-club coefficient and the k-core structure. We find that these topological features are in remarkable agreement with those predicted by our model, on the basis of the amount of information coded in the interaction between the transcription factors and response elements.

Analytical solution of a stochastic content-based network model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.

Bulk and surface structure of the clean and adsorbate-covered decagonal Al-Co-Ni quasicrystal

We review our Al adsorption experiments on the tenfold-symmetry surface of the decagonal Al–Co–Ni quasicrystal and present computational simulations of adsorption on a structural model based on a fundamental Al–Co cluster with 20 A diameter, symmetry , and 8 A periodicity. This cluster is the building unit of τ2-Al13Co4, from which, by a sequence of minor changes, the structures of the phases in the stability region of decagonal Al–Co–Ni can be derived. The model used for the decagonal Al70Co15Ni15 is an idealized model with a two-layer periodicity (4 A) and no chemical or structural disorder. We find that the bulk and surface properties of this model are in good agreement with experiments. Our molecular-dynamics simulations of Al adsorption reproduce the experimental results and show that by varying the thermal relaxation rates of the adsorbed layer, a variety of different surface morphologies can be achieved. We also present our recent experiments on dissociative adsorption of oxygen on the decagonal surface.

Deposition of atoms on a quasicrystalline substrate : Molecular dynamics study in three dimensions

We study the three-dimensional structure formation when atoms are deposited onto a substrate with a decagonal quasicrystalline order. Molecular-dynamicscalculations show that the adsorbate layer consists of ordered nano-scale domains with orientations determined by the underlying substrate symmetry. Depending on the relative strength of the interactions of adsorbate atoms with each other and with the substrate atoms, different morphologies are observed ranging from layer-by-layer growth to cluster formation. We also find that the film thickness likewise affects the overall structure of the growing film: Depending on the relative strength of the interaction between adsorbate atoms, a structural transition of the configuration of the adsorbate layers closest to the substrate can occur as the number of deposited layers increases.

Predicting abundances of plants and pollinators using a simple compartmental mutualistic model.

Key gaps to be filled in population and community ecology are predicting the strength of species interactions and linking pattern with process to understand species coexistence and their relative abundances. In the case of mutualistic webs, like plant–pollinator networks, advances in understanding species abundances are currently limited, mainly owing to the lack of methodological tools to deal with the intrinsic complexity of mutualisms. Here, we propose an aggregation method leading to a simple compartmental mutualistic population model that captures both qualitatively and quantitatively the size-segregated populations observed in a Mediterranean community of nectar-producing plant species and nectar-searching animal species. We analyse the issue of optimal aggregation level and its connection with the trade-off between realism and overparametrization. We show that aggregation of both plants and pollinators into five size classes or compartments leads to a robust model with only two tunable parameters. Moreover, if, in each compartment, (i) the interaction coefficients fulfil the condition of weak mutualism and (ii) the mutualism is facultative for at least one party of the compartment, then the interactions between different compartments are sufficient to guarantee global stability of the equilibrium population.

Subthreshold behavior and avalanches in an exactly solvable charge density wave system

We present a toy charge density wave (CDW) model in 1d exhibiting a depinning transition with threshold force and configurations that are explicit. Due to the periodic boundary conditions imposed, the threshold configuration has a set of topological defects whose location and number depend on the realization of the random phases. Approaching the threshold, these defects are relocated by avalanches whose size dependence on the external driving force F is described by a record-breaking process. We find that the depinning transition in this model is a critical phenomenon, with the cumulative avalanche size diverging near the threshold as . The exact avalanche size distributions and their dependence on the control parameter are obtained. Remarkably, the scaling exponents associated with the critical behavior depend on 1) the initial conditions and 2) the relationship between the system size and the pinning strength.

Determining pair interactions from structural correlations

We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the statistical properties of the potential landscape. Understanding this relation facilitates quantitative studies of magnetic flux line interactions in type II superconductors, using structural information available from Lorentz microscope images or Bitter decorations. Previous work by some of us supported the conjecture that the relationship between pair correlations and interactions in pinned flux line ensembles is analogous to the corresponding relationship in the theory of simple liquids. The present paper aims at a more thorough understanding of this relation. We report the results of numerical simulations and present a theory for the low density behavior of the pair correlation function which agrees well with our simulations and captures features observed in experiments. In particular, we find that the resulting description goes beyond the conjectured classical liquid type relation and we remark on the differences.

q-oscillators, the q-epsilon tensor and quantum groups

Abstract Considering a multi-dimensional q -oscillator invariant under the (non-quantum) group U ( n ), we construct a q -deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this q -epsilon tensor is shown to yield the quantum group SL q ( n ) and establishes the relationship of the U( n ) invariant q -oscillator to quantum groups and quantum group related oscillators. Furthermore the q -epsilon tensor provides the connection between SL q ( n ) and the volume element of the quantum hyperplane.