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Item Open Access Capacity region of multi-resolution streaming in peer-to-peer networks(IEEE, 2013) Karagöz, B.; Yavuz, Semih; Ho, T.; Effros, M.Show more We consider multi-resolution streaming in fully-connected peer-to-peer networks, where transmission rates are constrained by arbitrarily specified upload capacities of the source and peers. We fully characterize the capacity region of rate vectors achievable with arbitrary coding, where an achievable rate vector describes a vector of throughputs of the different resolutions that can be supported by the network. We then prove that all rate vectors in the capacity region can be achieved using pure routing strategies. This shows that coding has no capacity advantage over routing in this scenario. © 2013 IEEE.Show more Item Open Access Capture resilient ElGamal signature protocols(Springer, 2006-11) Acan, Hüseyin; Kaya, Kamer; Selçuk, Ali AydınShow more One of the fundamental problems of public key cryptography is protecting the private key. Private keys are too long to be remembered by the user, and storing them in the device which performs the private key operation is insecure as long as the device is subject to capture. In this paper, we propose server-assisted protocols for the ElGamal signature scheme which make the system capture resilient in the sense that the security of the system is not compromised even if the signature device is captured. The protocols also have a key disabling feature which allows a user to disable the device's private key in case both the device and the password of the user are compromised simultaneously. © Springer-Verlag Berlin Heidelberg 2006.Show more Item Open Access A delayed consensus algorithm in networks of anticipatory agents(IEEE, 2016) Atay, Fatihcan M.; Irofti, D.Show more We introduce and analyze a delayed consensus algorithm as a model for interacting agents using anticipation of their neighbors' states to improve convergence to consensus. We derive a necessary and sufficient condition for the system to reach consensus. Furthermore, we explicitly calculate the dominant characteristic root of the consensus problem as a measure of the speed of convergence. The results show that the anticipatory algorithm can improve the speed of consensus, especially in networks with poor connectivity. Hence, anticipation can improve performance in networks if the delay parameter is chosen judiciously, otherwise the system might diverge as agents try to anticipate too aggressively into the future.Show more Item Open Access Entanglement and its operational measure(Springer, 2006) Klyachko, Alexander A.; Öztop, Barış; Shumovsky, Alexander S.Show more An operational representation of concurrence measuring the entanglement of bipartite systems by means of averages of basic observables is discussed. We prove the validity of this representation for bipartite systems with any dimension of a single-party Hilbert space. We show that Wigner-Yanase "skew" information gives a reasonable estimation of the amount of entanglement (in ebits) carried by mixed two-qubit states.Show more Item Open Access Extremely charged static dust distributions in general relativity(World Scientific, 1998) Gürses, Metin; Rainer, M.Show more Conformo static charged dust distributions are investigated in the framework of general relativity. Einstein’s equations reduce to a non-linear version of Poisson’s equation and Maxwell’s equations imply the equality of the charge and mass densities. An interior solution to the extreme Reissner-Nordström metric is given. Dust distributions con-centrated on regular surfaces are discussed and a complete solution is given for a spherical thin shell.Show more Item Open Access Fibre products of superelliptic curves and codes therefrom(IEEE, 1997) Stepanov, Serguei A.; Özbudak, FerruhShow more A method of constructing long geometric Goppa codes coming from fiber products of superelliptic curves is presented. A family of smooth projective curves with a lot of Fq-rational points are needed to produce a family of asymptotically good geometric Goppa codes. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Examples of such families are provided by modular curves, by Drinfeld modular curves, and by Artin-Schreier coverings of the projective line.Show more Item Open Access General entanglement(IOP, 2006) Klyachko, Alexander A.; Shumovsky, Alexander S.Show more The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.Show more Item Open Access Integrability of three dimensional gravity field equations(IOP Publishing Ltd, 2022-02-10) Gurses, MetinShow more We show that the tree dimensional Einstein vacuum feld equations with cosmological constant are integrable. Using the sl(2, R) valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the integrable nonlinear partial diferential equations. © 2021 Published under licence by IOP Publishing Ltd.Show more Item Open Access Integrable nonlocal reductions(Springer New York LLC, 2018) Gürses, Metin; Pekcan, A.Show more We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) and modified Korteweg-de Vries (mKdV) systems. We give soliton solutions of these nonlocal equations by using the Hirota method. We extend the nonlocal NLS equation to nonlocal Fordy-Kulish equations by utilizing the nonlocal reduction to the Fordy-Kulish system on symmetric spaces. We also consider the super AKNS system and then show that Ablowitz-Musslimani nonlocal reduction can be extended to super integrable equations. We obtain new nonlocal equations namely nonlocal super NLS and nonlocal super mKdV equations.Show more Item Open Access Nash equilibria for exchangeable team against team games and their mean field limit(IEEE, 2023-07-03) Sanjari, S.; Saldı, Naci; Yüksel, S.Show more We study stochastic mean-field games among finite number of teams each with large finite as well as infinite numbers of decision makers (DMs). We establish the existence of a Nash equilibrium (NE) and show that a NE exhibits exchangeability in the finite DM regime and symmetry in the infinite one. We establish the existence of a randomized NE that is exchangeable (not necessarily symmetric) among DMs within each team for a general class of exchangeable stochastic games. As the number of DMs within each team drives to infinity that is for the mean-field games among teams), using a de Finetti representation theorem, we establish the existence of a randomized NE that is symmetric (i.e., identical) among DMs within each team and also independently randomized. Finally, we establish that a NE for a class of mean-field games among teams (which is symmetric) constitutes an approximate NE for the corresponding pre-limit game among teams with mean-field interaction and large but finite number of DMs.Show more Item Open Access Numerical reconstruction of curves from their Jacobians(American Mathematical Society, 2021-08-21) Agostini, D.; Çelik, T. Ö.; Eken, Demir; Anni, Samuele; Karemaker, Valentijn; García, Elisa LorenzoShow more We approach the Torelli problem of recostructing a curve from its Jacobian from a computational point of view. Following Dubrovin, we design a machinery to solve this problem effectively, which builds on methods in numerical algebraic geometry. We verify this methods via numerical experiments with curves up to genus 7.Show more Item Open Access On erasure correction coding for streaming(IEEE, 2012) Tekin, Ömer Faruk; Ho, T.; Yao, H.; Jaggi, S.Show more We consider packet erasure correction coding for a streaming system where specific information needs to be decoded by specific deadlines, in order to ensure uninterrupted playback at the receiver. In our previous work [1], we gave a capacity-achieving code construction for the case of a fixed number of erasures. In this work, we consider a sliding window erasure pattern where the number of erasures within windows of size above some threshold is upper bounded by a fraction of the window size, modeling a constraint on burstiness of the channel. We lower bound the rates achievable by our previous code construction as a fraction of the capacity region, which approaches to one as the window size threshold and the initial playout delay increase simultaneously.Show more Item Open Access On existence of an x-integral for a semi-discrete chain of hyperbolic type(IOP, 2016) Zheltukhin, K.; Zheltukhina, NatalyaShow more A class of semi-discrete chains of the form t1x = f (x,t,t1,tx) is considered. For the given chains easily verifiable conditions for existence of x-integral of minimal order 4 are obtained.Show more Item Open Access On the geometric characterization of the extension property(The Belgian Mathematical Society, 2007) Goncharov, AlexanderShow more A geometric characterization of the extension property is given for Cantortype sets. The condition can also be done in terms of the rate of growth of certain sequences to the Robin constants of local parts of the set.Show more Item Open Access On the number of components of a complete intersection of real quadrics(Springer Basel, 2012) Degtyarev, Alex; Itenberg, Ilia; Kharlamov, Viatchesla; Itenberg, I.; Jöricke, B.; Passare, M.Show more Our main results concern complete intersections of three real quadrics. We prove that the maximal number B0 2 (N) of connected components that a regular complete intersection of three real quadrics in ℙN may have differs at most by one from the maximal number of ovals of the submaximal depth [(N −1)/2] of a real plane projective curve of degree d = N +1. As a consequence, we obtain a lower bound 1/4 N2 +O(N) and an upper bound 3/8 N2+O(N) for B0 2 (N). © Springer Science+Business Media, LLC 2012.Show more Item Open Access On the zeros of tails of power series(Springer, 2000) Ostrovskii, Iossif Vladimirovich; Havin, V. P.; Nikolski, N. K.Show more Let f(z)=∑k=0∞akzkf(z)=∑k=0∞akzk (1.1) be a power series with a positive radius of convergence. Let sn(z)=∑k=0nakzk,tn(z)=∑k=n+1∞akzksn(z)=∑k=0nakzk,tn(z)=∑k=n+1∞akzk be its nth section and nth tail, respectively.Show more Item Open Access Persistent perfect entanglement in atomic systems(IOP, 2004) Çakır, Özgür; Can, M. Ali; Klyachko, Alexander A.; Shumovsky, Alexander S.Show more It is shown that the system of an even number of three-level atoms in the Λ configuration in a cavity can evolve into a persistent maximum entangled state. The time of formation of such an entangled state is estimated.Show more Item Open Access Quantifying quantum information via uncertainties(OSA, 2007) Öztop, Barış; Klyachko, Alexander A.; Shumovsky, Alexander S.Show more We show, for a state ψ of a quantum system with the dynamic symmetry given by the Lie group G, total amount of quantum information and entanglement is provided by summarized uncertainty of basic observables.Show more Item Open Access Quantum marginal problem and N-representability(IOP, 2006) Klyachko, Alexander A.Show more A fermionic version of the quantum marginal problem was known from the early sixties as N-representability problem. In 1995 it was mentioned by the National Research Council of the USA as one of ten most prominent research challenges in quantum chemistry. In spite of this recognition the progress was very slow, until a couple of years ago the problem came into focus again, now in the framework of quantum information theory. In the paper I give a survey of the recent development.Show more Item Open Access Slopes of links and signature formulas(American Mathematical Society, 2021) Degtyarev, Alex I.; Florens, V.; Lecuona, A.G.; Vershik, A.M.; Buchstaber, V.M.; Malyutin, A.V.Show more We present a new invariant, called slope, of a colored link in an integral homology sphere and use this invariant to complete the signature formula for the splice of two links. We develop a number of ways of computing the slope and a few vanishing results. Besides, we discuss the concordance invariance of the slope and establish its close relation to the Conway polynomials, on the one hand, and to the Kojima-Yamasaki η-function (in the univariate case) and Cochran invariants, on the other hand. © 2021 by the American Mathematical Society.Show more