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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
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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 Open Access Estimates of the coverage of parameter space by Latin hypercube and orthogonal array-based sampling(Elsevier, 2018) Donovan, D.; Burrage, K.; Burrage, P.; McCourt, T. A.; Thompson, B.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432In this paper we use counting arguments to prove that the expected percentage coverage of a d dimensional parameter space of size n when performing k trials with either Latin Hypercube sampling or Orthogonal Array-based Latin Hypercube sampling is the same. We then extend these results to an experimental design setting by projecting onto a t < d dimensional subspace. These results are confirmed by simulations. The theory presented has both theoretical and practical significance in modelling and simulation science when sampling over high dimensional spaces.Publication Open Access Computation of pseudospectral abscissa for large-scale nonlinear eigenvalue problems(Oxford University Press (OUP), 2017) Meerbergen, Karl; Michiels, Wim; Van Beeumen, Roel; Department of Mathematics; Mengi, Emre; Faculty Member; Department of Mathematics; College of Sciences; 113760We present an algorithm to compute the pseudospectral abscissa for a nonlinear eigenvalue problem. The algorithm relies on global under-estimator and over-estimator functions for the eigenvalue and singular value functions involved. These global models follow from eigenvalue perturbation theory. The algorithm has three particular features. First, it converges to the globally rightmost point of the pseudospectrum, and it is immune to nonsmoothness. The global convergence assertion is under the assumption that a global lower bound is available for the second derivative of a singular value function depending on one parameter. It may not be easy to deduce such a lower bound analytically, but assigning large negative values works robustly in practice. Second, it is applicable to large-scale problems since the dominant cost per iteration stems from computing the smallest singular value and associated singular vectors, for which efficient iterative solvers can be used. Furthermore, a significant increase in computational efficiency can be obtained by subspace acceleration, that is, by restricting the domains of the linear maps associated with the matrices involved to small but suitable subspaces, and solving the resulting reduced problems. Occasional restarts of these subspaces further enhance the efficiency for large-scale problems. Finally, in contrast to existing iterative approaches based on constructing low-rank perturbations and rightmost eigenvalue computations, the algorithm relies on computing only singular values of complex matrices. Hence, the algorithm does not require solutions of nonlinear eigenvalue problems, thereby further increasing efficiency and reliability. This work is accompanied by a robust implementation of the algorithm that is publicly available.Publication Open Access Infinitesimal Chow dilogarithm(American Mathematical Society (AMS), 2021) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871Let C2 be a smooth and projective curve over the ring of dual numbers of a field k. Given non-zero rational functions f, g, and h on C2, we define an invariant ?(f ? g ? h) ? k. This is an analog of the real analytic Chow dilogarithm and the extension to non-linear cycles of the additive dilogarithm of [Algebra Number Theory 3 (2009), pp. 1.34]. Using this construction we state and prove an infinitesimal version of the strong reciprocity conjecture of Goncharov [J. Amer. Math. Soc. 18 (2005), pp. 1.60] with an explicit formula for the homotopy map. Also using ?, we define an infinitesimal regulator on algebraic cycles of weight two which generalizes Park's construction in the case of cycles with modulus [Amer. J. Math. 131 (2009), pp. 257-276].Publication Open Access Asymptotic H-Plateau problem in H-3(Mathematical Sciences Publishers (MSP), 2016) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of SciencesWe show that for any Jordan curve Gamma in S-infinity(2) (H-3) with at least one smooth point, there exists an embedded H-plane P-H in H-3 with partial derivative P-infinity(H) = Gamma for any H is an element of [0, 1).Publication Open Access Modeling the interplay between HDV and HBV in chronic HDV/HBV patients(Multidisciplinary Digital Publishing Institute (MDPI), 2022) Mhlanga, A.; Zakh, R.; Churkin, A.; Reinharz, V.; Glenn, J.S.; Etzion, O.; Cotler, S.J.; Barash, D.; Dahari H.; Yurtaydın, Süleyman Cihan; Faculty Member; School of Medicine; 189330Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions.Publication Open Access HMI-PRED 2.0: a biologist-oriented web application for prediction of host-microbe protein-protein interaction by interface mimicry(Oxford University Press (OUP), 2022) Lim, H., Tsai, C.J.; Nussinov, R.; Department of Computer Engineering; Department of Chemical and Biological Engineering; Keskin, Özlem; Gürsoy, Attila; Faculty Member; Department of Computer Engineering; Department of Chemical and Biological Engineering; College of Engineering; 26605; 8745HMI-PRED 2.0 is a publicly available web service for the prediction of host-microbe protein-protein interaction by interface mimicry that is intended to be used without extensive computational experience. A microbial protein structure is screened against a database covering the entire available structural space of complexes of known human proteins.Publication Open Access Nonsmooth algorithms for minimizing the largest eigenvalue with applications to inner numerical radius(Oxford University Press (OUP), 2020) Department of Mathematics; Mengi, Emre; Kangal, Fatih; Faculty Member; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 113760; N/ANonsmoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be globally convergent unaffected by nonsmoothness. One of these algorithms models the eigenvalue function with a piece-wise quadratic function and is effective in dealing with nonconvex problems. The other algorithm projects the Hermitian matrix into subspaces formed of eigenvectors and is effective in dealing with large-scale problems. We generalize the latter slightly to cope with nonsmoothness. For both algorithms we analyze the rate of convergence in the nonsmooth setting, when the largest eigenvalue is multiple at the minimizer and zero is strictly in the interior of the generalized Clarke derivative, and prove that both algorithms converge rapidly. The algorithms are applied to, and the deduced results are illustrated on the computation of the inner numerical radius, the modulus of the point on the boundary of the field of values closest to the origin, which carries significance for instance for the numerical solution of a symmetric definite generalized eigenvalue problem and the iterative solution of a saddle point linear system.Publication Open Access Market selection and the information content of prices(Wiley, 2021) Ekmekçi, Mehmet; Department of Economics; Atakan, Alp Enver; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; 39383We study information aggregation when n bidders choose, based on their private information, between two concurrent common-value auctions. There are k(s) identical objects on sale through a uniform-price auction in market s and there are an additional k(r) objects on auction in market r, which is identical to market s except for a positive reserve price. The reserve price in market r implies that information is not aggregated in this market. Moreover, if the object-to-bidder ratio in market s exceeds a certain cutoff, then information is not aggregated in market s either. Conversely, if the object-to-bidder ratio is less than this cutoff, then information is aggregated in market s as the market grows arbitrarily large. Our results demonstrate how frictions in one market can disrupt information aggregation in a linked, frictionless market because of the pattern of market selection by imperfectly informed bidders.Publication Open Access Generic uniqueness of area minimizing disks for extreme curves(Johns Hopkins University (JHU) Press, 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of SciencesWe show that for a generic nullhomotopic simple closed curve Γ in the boundary of a compact, orientable, mean convex 3-manifold M with H2(M, Z) = 0, there is a unique area minimizing disk D embedded in M with ∂D = Γ. We also show that the same is true for nullhomologous curves in the absolutely area minimizing surface case.