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Publication Metadata only A new family of random graphs for testing spatial segregation(Wiley, 2007) Priebe, Carey E.; Marchette, David J.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe authors discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. The authors address specifically the problem of testing. complete spatial randomness against spatial patterns of segregation or association between two or more classes of points on the plane. To this end, they use a particular type of parameterized random digraph called a proximity catch digraph (PCD) which is based on relative positions of the data points from various classes. The statistic employed is the relative density of the PCD, which is a U-statistic when scaled properly. The authors derive the limiting distribution of the relative, density, using the standard asymptotic theory of U-statistics. They evaluate the finite-sample performance of their test statistic by Monte Carlo simulations and assess its asymptotic performance via Pitman's asymptotic efficiency, thereby yielding the optimal parameters for testing. They further stress that their methodology remains valid for data in higher dimensions.Publication Metadata only A note on power bounded elements of von neumann algebras(Editura Acad Romane, 2014) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet A be a von Neumann algebra with predual A(*) and the unit element 1. An element a of A is said to be power bounded if sup(n >= 0) vertical bar vertical bar a(n)vertical bar vertical bar < infinity. In this note we show that, for any power bounded element a of A, theta = sigma(A, A(*)) - lim(n ->infinity)(1+a/2)(n) exists, theta is an idempotent and theta a = a theta = theta.Publication Metadata only A partial kite system of order n can be embedded in a kite system of order 8n+9(Charles Babbage Res Ctr, 2006) Lindner, Charles Curtis; Rodger, C.; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252In this paper, it is shown that a partial edge-disjoint decompostion of K-n into kites (that is, into copies of K-3 with a pendant edge attached) can be embedded in a complete edge-disjoint decompostion of K4t+9 into kites for all even t >= 2n. The proof requires first proving another interesting result, a generalization of an embeddding result on symmetric latin squares by L. D. Andersen, following a result by A. Cruse.Publication Metadata only A partial kite system of order n can be embedded in a kite system of order 8n+9(Charles Babbage Research Centre, 2006) Lindner, C.; Rodger, C.; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252In this paper, it is shown that a partial edge-disjoint decompostion of Kn into kites (that is, into copies of K3 with a pendant edge attached) can be embedded in a complete edge-disjoint decompostion of K4t+9 into kites for all even t ≥ 2n. The proof requires first proving another interesting result, a generalization of an embeddding result on symmetric latin squares by L. D. Andersen, following a result by A. Cruse.Publication Open Access Application of stochastic flows to the sticky Brownian motion equation(Multidisciplinary Digital Publishing Institute (MDPI), 2017) Hajri, Hatem; Arnaudon, Marc; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131We investigate the relationship between the levels of industry collaboration and entrepreneurial activities at universities and the employment choices of their science and engineering doctoral students. Using data from 176 U.S. universities over the period 1996-2005, we document that more interaction with industry at a university is typically associated with more of the university's doctoral students choosing industry employment. We also document a positive relationship between universities' licenses and startups and their graduates' post-doctoral study choices.Publication Metadata only Applications of bombieri-vinogradov type theorems to power-free integers(Ars Polona-Ruch, 2021) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803Studying a variant of a classical result of Walfisz on the number of representations of an integer as the sum of a prime number and a square-free integer with an extra additive constraint on the prime summand, we obtain an asymptotic formula for the number of representations of an integer N such that N - 1 is a prime number in the form p + N - p, where p is a prime number, N - p is square-free and p - 1 is cube-free. We improve the error term for the number of representations of an integer as the sum of a prime number and a k-free integer conditionally by assuming weaker forms of the Riemann hypothesis for Dirichlet L-functions. As a further application of our method, we find an asymptotic formula for the number of prime numbers p <= x such that p + 2y, 1 <= y <= 7, are all square-free. Our formula shows that a positive proportion of prime numbers leads to a longest possible progression of eight consecutive odd, square-free integers. A key ingredient in our approach is the Bombieri-Vinogradov theorem and its variant for sparse moduli due to Baier and Zhao which regulates the uniform distribution of prime numbers along certain short arithmetic progressions.Publication Metadata only Average r-rank artin conjecture(Polish Acad Sciences Inst Mathematics-IMPAN, 2016) Menici, Lorenzo; Department of Mathematics; Pehlivan, Cihan; Researcher; Department of Mathematics; College of Sciences; N/AN/APublication Metadata only Balanced and strongly balanced 4-kite designs(Utilitas Mathematica Publishing, 2013) Gionfriddo, Mario; Milazzo, Lorenzo; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ⋯, h, there exists a constant Ci such that dAi(x)= Ci for every vertex x, where AiS are the orbits of the automorphism group of G on its vertex-set and dAi(x) of a vertex is the number of blocks of containing x as an element of Ai. We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.Publication Metadata only Blow-up of solutions of coupled parabolic systems and hyperbolic equations(Springer, 2022) Kalantarova, Jamila; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655The problem of the blow-up of solutions of coupled systems of nonlinear parabolic and hyperbolic equations of second order is studied. The concavity method and its modifications are used to find sufficient conditions for the blow-up of solutions for an arbitrary positive initial energy of the problem.Publication Metadata only Cell-specific and post-hoc spatial clustering tests based on nearest neighbor contingency tables(Korean Statistical Soc, 2017) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ASpatial clustering patterns in a multi-class setting such as segregation and association between classes have important implications in various fields, e.g., in ecology, and can be tested using nearest neighbor contingency tables (NNCTs). a NNCT is constructed based on the types of the nearest neighbor (NN) pairs and their frequencies. We survey the cell-specific (or pairwise) and overall segregation tests based on NNCTs in literature and introduce new ones and determine their asymptotic distributions. We demonstrate that cell-specific tests enjoy asymptotic normality, while overall tests have chi-square distributions asymptotically. Some of the overall tests are confounded by the unstable generalized inverse of the rank-deficient covariance matrix. To overcome this problem, we propose rank-based corrections for the overall tests to stabilize their behavior. We also perform an extensive' Monte Carlo simulation study to compare the finite sample performance of the tests in terms of empirical size and power based on the asymptotic and Monte Carlo critical values and determine the tests that have the best size and power performance and are robust to differences in relative abundances (of the classes). in addition to the cell-specific tests, we discuss one(-class)-versus-rest type of tests as post-hoc,tests after a significant overall test. We also introduce the concepts of total, strong, and partial segregatioN/Association to differentiate different levels of these patterns. We compare the new tests with the existing NNCT-tests in literature with simulations and illustrate the tests on an ecological data set. (C) 2016 the Korean Statistical Society. Published by Elsevier B.V. all rights reserved.