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Yayın Enabling cooperation, resource allocation and receiver selection across cells: complementary fractional frequency reuse(IEEE, 2013) Bakşi, Saygın; Kaya, Onur; Bıyıkoğlu, TürkerFor a multi-cell multiple access channel, we develop a comprehensive cooperative communication framework: we propose a novel complementary fractional frequency reuse (FFR) strategy tailored specifically for pairwise user cooperation, also taking into account cell sectoring. This strategy allows the cell edge users not only to pool their resources and cooperate across cells, but also to choose the best receiver. We divide the users into cooperating inner and outer user pairs, and assign each pair orthogonal resources using OFDMA. We employ pairwise bidirectional cooperation based on block Markov superposition encoding among user pairs. We derive the achievable rates, while taking into account the geometry dependent interference at the users and the receiver. We find the jointly optimal power allocation, partner selection and receiver selection strategies that maximize the sum rate of the system. We then propose a heuristic matching algorithm, which operates based only on user and receiver locations. We compare the performance of our proposed strategies with several non-cooperative models, and demonstrate that the sum rate can nearly be doubled, while using the same resources.Yayın Network synchronization: Spectral versus statistical properties(Elsevier B.V., 2006-12) Atay, Fatihcan Mehmet; Bıyıkoğlu, Türker; Jost, JürgenWe consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.Yayın Discovering cis-regulatory modules by optimizing barbecues(Elsevier Science Bv, 2009-05-28) Mosig, Axel; Bıyıkoğlu, Türker; Prohaska, Sonja J.; Stadler, Peter F.Gene expression in eukaryotic cells is regulated by a complex network of interactions, in which transcription factors and their binding sites on the genomic DNA play a determining role. As transcription factors rarely, if ever, act in isolation, binding sites of interacting factors are typically arranged in close proximity forming so-called cis-regulatory modules. Even when the individual binding sites are known, module discovery remains a hard combinatorial problem, which we formalize here as the Best Barbecue Problem. It asks for simultaneously stabbing a maximum number of differently colored intervals from K arrangements of colored intervals. This geometric problem turns out to be an elementary, yet previously unstudied combinatorial optimization problem of detecting common edges in a family of hypergraphs, a decision version of which we show here to be NP-complete. Due to its relevance in biological applications, we propose algorithmic variations that are suitable for the analysis of real data sets comprising either many sequences or many binding sites. Being based on set systems induced by interval arrangements, our problem setting generalizes to discovering patterns of co-localized itemsets in non-sequential objects that consist of corresponding arrangements or induce set systems of co-localized items. In fact, our optimization problem is a generalization of the popular concept of frequent itemset mining.Yayın Preface(Springer Verlag, 2007) Bıyıkoğlu, Türker; Leydold, Josef; Stadler, Peter F.[No abstract available]Yayın Dendrimers are the unique chemical trees with maximum spectral radius(Univ Kragujevac, 2012) Bıyıkoğlu, Türker; Leydold, JosefIt is shown that dendrimers have maximum spectral radius and maximum Collatz-Sinogowitz index among all chemical trees of given size. The result is also generalized for the class of chemical trees with prescribed number of pendant vertices.Yayın Optimal and near-optimal partner selection algorithms in cooperative OFDMA(IEEE, 2012) Bakşi, Saygın; Kaya, Onur; Bıyıkoğlu, TürkerWe obtain the jointly optimal power allocation and partner selection policies, that maximize the sum rate of a cooperative OFDMA system with mutually cooperating pairs of users. We show that the power allocation and partner selection steps can be performed sequentially, and the latter step can be formulated as a maximum weighted matching problem on an undirected graph, which can be solved in polynomial time. We further propose practical algorithms, and compare their performances to the optimal matching algorithm, and demonstrate that very simple and low complexity algorithms based on user-user and user-receiver distances may provide near-optimum rate performance. Moreover, we observe that algorithms that achieve superior sum-rate performance, surprisingly pair the cell edge users, with the strong users near the base station.Yayın Cryptanalysis of Fridrich's chaotic image encryption(World Scientific Publishing, 2010-05) Solak, Ercan; Çokal, Cahit; Yıldız, Olcay Taner; Bıyıkoğlu, TürkerWe cryptanalyze Fridrich's chaotic image encryption algorithm. We show that the algebraic weaknesses of the algorithm make it vulnerable against chosen-ciphertext attacks. We propose an attack that reveals the secret permutation that is used to shuffle the pixels of a round input. We demonstrate the effectiveness of our attack with examples and simulation results. We also show that our proposed attack can be generalized to other well-known chaotic image encryption algorithms.Yayın Algebraic connectivity and degree sequences of trees(Elsevier Science Inc, 2009-01-15) Bıyıkoğlu, Türker; Leydold, JosefWe investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on non-pendant vertices starting at the characteristic set of the Fiedler vector.Yayın Graphs with given degree sequence and maximal spectral radius(Electronic Journal of Combinatorics, 2008-09-15) Bıyıkoğlu, Türker; Leydold, JosefWe describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is non-increasing with respect to an ordering of the vertices induced by breadth-first search. For trees the resulting structure is uniquely determined up to isomorphism. We also show that the largest spectral radius in such classes of trees is strictly monotone with respect to majorization.Yayın Four-cycled graphs with topological applications(Birkhauser Verlag AG, 2012-03) Bıyıkoğlu, Türker; Civan, YusufWe call a simple graph G a 4-cycled graph if either it has no edges or every edge of it is contained in an induced 4-cycle of G. Our interest on 4-cycled graphs is motivated by the fact that their clique complexes play an important role in the simple-homotopy theory of simplicial complexes. We prove that the minimal simple models within the category of flag simplicial complexes are exactly the clique complexes of some 4-cycled graphs. We further provide structural properties of 4-cycled graphs and describe constructions yielding such graphs. We characterize 4-cycled cographs, and 4-cycled graphs arising from finite chessboards. We introduce a family of inductively constructed graphs, the external extensions, related to an arbitrary graph, and determine the homotopy type of the independence complexes of external extensions of some graphs.
