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Publication Metadata only A characterization of heaviness in terms of relative symplectic cohomology(Wiley, 2024) Mak, Cheuk Yu; Sun, Yuhan; Department of Mathematics; Varolgüneş, Umut; Department of Mathematics; College of SciencesFor a compact subset K$K$ of a closed symplectic manifold (M,omega)$(M, \omega)$, we prove that K$K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.Publication Metadata only A characterization of the closed unital ideals of the Fourier-Stieltjes algebra B(G) of a locally compact amenable group G(Elsevier, 2003) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet G be a locally compact amenable group, B(G) its Fourier–Stieltjes algebra and I be a closed ideal of it. In this paper we prove the following result: The ideal I has a unit element iff it is principal. This is the noncommutative version of the Glicksberg–Host–Parreau Theorem. The paper also contains an abstract version of this theorem.Publication Metadata only A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties(Elsevier, 1998) Elishakoff, I; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AStructural uncertainties are modelled using stochastic and interval methods to quantify the uncertainties in the response quantities. Through a suitable discretization, stochastic and interval finite element methods are constructed. A comparison of these methods is illustrated using a shear frame with uncertain stiffness properties.Publication Metadata only A direct method for the inversion of physical systems(Institute of Physics (IOP) Publishing, 1994) Caudill, Lester F.; Rabitz, Herschel; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.Publication Metadata only A long-range dependent workload model for packet data traffic(Inst Operations Research Management Sciences, 2004) Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131We consider a probabilistic model for workload input into a telecommunication system. It captures the dynamics of packet generation in data traffic as well as accounting for long-range dependence and self-similarity exhibited by real traces. The workload is found by aggregating the number of packets, or their sizes, generated by the arriving sessions. The arrival time, duration, and packet-generation process of a session are all governed by a Poisson random measure. We consider Pareto-distributed session holding times where the packets are generated according to a compound Poisson process. For this particular model, we show that the workload process is long-range dependent and fractional Brownian motion is obtained as a heavy-traffic limit. This yields a fast synthesis algorithm for generating packet data traffic as well as approximating fractional Brownian motion.Publication Metadata only A new correlation coefficient for bivariate time-series data(Elsevier Science Bv, 2014) Erdem, Orhan; Varlı, Yusuf; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of SciencesThe correlation in time series has received considerable attention in the literature. Its use has attained an important role in the social sciences and finance. For example, pair trading in finance is concerned with the correlation between stock prices, returns, etc. In general, Pearson's correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use. Here, we introduce a new correlation coefficient which takes into account the lag difference of data points. We investigate the properties of this new correlation coefficient. We demonstrate that it is more appropriate for showing the direction of the covariation of the two variables overtime. We also compare the performance of the new correlation coefficient with Pearson's correlation coefficient and Detrended Cross-Correlation Analysis (DCCA) via simulated examples. (C) 2014 Elsevier B.V. All rights reserved.Publication Metadata only A note on the algebra of p-adic multi-zeta values(International Press of Boston, 2015) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871We prove that the algebra of p-adic multi-zeta values, as defined in [4] or [2], are contained in another algebra which is defined explicitly in terms of series. The main idea is to truncate certain series, expand them in terms of series all of which are divergent except one, and then take the limit of the convergent one. The main result is Theorem 3.12.Publication Metadata only A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation(Elsevier, 1998) Micaletti, RC; Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AA method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions, This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.Publication Open Access A stochastic representation for mean curvature type geometric flows(Institute of Mathematical Statistics (IMS), 2003) Touzi, N.; Department of Mathematics; Soner, Halil Mete; Faculty Member; Department of Mathematics; College of Administrative Sciences and EconomicsA smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved by studying the squared distance function to Gamma(t). For the codimension k mean curvature flow, the state process is dX(t) = root2P dW(t), where W(t) is a d-dimensional Brownian motion, and the control P is any projection matrix onto a (d - k)-dimensional plane. Smooth solutions of the inverse mean curvature flow and a discussion of non smooth solutions are also given.Publication Metadata only A stochastic representation for the level set equations(Taylor & Francis Inc, 2002) Touzi, Nizar; Department of Mathematics; Soner, Halil Mete; Faculty Member; Department of Mathematics; College of Sciences; N/AA Feynman-Kac representation is proved for geometric partial differential equations. This representation is in terms of a stochastic target problem. In this problem the controller tries to steer a controlled process into a given target by judicial choices of controls. The sublevel sets of the unique level set solution of the geometric equation is shown to coincide with the reachability sets of the target problem whose target is the sublevel set of the final data.