Synch. vs. link: the interplay of structure and dynamics in complex networks, 12th March 2008
Stefano Boccaletti (CNR- Istituto dei Sistemi Complessi, Firence, Italy The Embassy of Italy in Israel, Tel Aviv, Israel)
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Some aspects of Lévy-type partial-integral differential equations, 10th March 2008
Emmanuel Chasseigne (Laboratoire de Mathématiques et Physique Théorique, Université F. Rabelais, France)
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Kleptography: Using Cryptography Against Cryptography, 7th March 2008
Moti Yung (Columbia University and Google)
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Signcryption or How to Kill Two Birds in One Stone, 7th March 2008
Yuliang Zheng (University of North Carolina at Charlotte)
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On the relativistic heat equation, 6th March 2008
Salvador Moll (Departament de Tecnologia, Universitat Pompeu Fabra, España)
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Mathematical models for solids and fluids, 3rd March 2008
Peicheng Zhu (Fachbereich Mathematik, Tech. Univ. Darmstadt, Darmstadt, Deutschland)
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Finite element approximations in a non-Lipchitz domain, 29th February 2008
The finite element method has been widely analyzed in its different forms for all kind of partial differential equations. However, as far as we know, all analyses are restricted to the case of polygonal or smooth domains and no results have been obtained for the case in which the domain is non Lipschitz, with the exception of the well known fracture problems. In this talk we present convergence results for a model problem in a plane domain with an external cusp. Several difficulties arise in this problem because many of the results on Sobolev spaces, which are fundamental in the analysis of partial differential equations in variational form, do not apply.
Gabriel Acosta Rodriguez. (Profesor Asociado, Universidad de Buenos Aires y Universidad de General Sarmiento, Argentina).
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Tropical discriminants, 28th February 2008
The theory of A-discriminants is a far going generalization of the discriminant of a univariate polynomial, proposed in the late 80's by Gel'fand, Kapranov and Zelevinsky, who also described many of their combinatorial properties. We present a new approach to this theory using tropical geometry.
Alicia Dickenstein (Departamento de Matemáticas, Universidad de Buenos Aires, Argentina).
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Una panorámica de la Geometría Tropical, 15th February 2008
Mª Jesús de la Puente (Profesora titular, Universidad Complutense de Madrid).
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The numerical inversion of the Laplace transform with applications to evolution problems, 15th February 2008
Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting there a potential behavior are considered (sectorial Laplace transforms). A spectral order, parallelizable method for their numerical inversion is proposed. The method takes into account the available information about the errors arising in the evaluations.
The application of the Laplace transform and the proposed inversion algorithm to integrate in time evolution equations is considered.
María López (Contratada Juan de la Cierva, Universidad Autónoma de Madrid).
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Direct numerical methods for mixed-integer optimal control problems, 15th February 2008
Optimal control problems involving time-dependent decisions from a finite set have gained much interest lately, as they occur in practical applications with a high potential for optimization. Typical examples are the choice of gears in transport or separation processes involving valves to switch inflow/outflow locations between trays or columns. We present relaxation and convexification based rounding strategies for direct methods of optimal control such that the resulting trajectory fulfills constraints and reaches the objective function value of any (and in particular the optimal) relaxed solution up to a certain tolerance. We show that this tolerance depends on the control discretization grid, in other words, that the rounded solution will be arbitrarily close to the relaxed one, if only the underlying grid is chosen fine enough. This is even true for a finite number of switches, and holds for the linear as well as for the nonlinear case, involving path and control constraints. Examples will be supplied to illustrate the procedure.
Sebastian Sager (Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany).
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Numerical Solution of the Exterior Helmholtz Equation, 15th February 2008
Professor of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Schreiber Building, room 321 The Helmholtz equation is an elliptic partial differential. For large wavenumbers it is no longer positive definite. When used for scattering about a body one needs to impose a Sommerfeld radiation condition for well-posedness. This makes the solution complex and the equation is no longer self-adjoint.
The solution of this problem involves three steps. First, one must choose a discretization of the equation in the interior. It is known that the grid must increase faster than linear in the wavenumber. We shall briefly discuss one approach to gain high resolution. Second, one must choose the artificial boundary condition to approximate the Sommerfeld radiation condition. We will describe several possibilities depending on the shape of the outer artificial surface. Finally, one must solve the resultant system of linear equations. The discretrization leads to a matrix which is nonpositive, nonsymmetrc and has a large condition number. We will use a Krylov space method to solve this system. However, for efficiency a preconditioner is necessary. We present a preconditioner based on a complex wave number and discuss its total efficiency. We will also make some remarks on the inverse scattering problem.
Eli Turkel (Professor of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Israel).
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Computing in the dark using algebraic geometry, 13th February 2008
CWI Amsterdam & Mathematical Institute, Leiden University Secure computation focuses on multi-lateral security, i.e., secure cooperation among mutually distrusting parties or parties with conflicting interests. It was proved (EUROCRYPT 2000) by Cramer, Damgaard and Maurer that information-theoretically secure multi-party computation can be realized from mathematical devices called linear secret sharing schemes with (strong) multiplication. It was shown (CRYPTO 2006) by Chen and Cramer that such devices can be constructed using algebraic function fields. This is the first non-trivial connection between secure computation and algebraic geometry.
In this talk we briefly introduce the concept of secure computation, and discuss some of the mathematical details behind this result. Moreover, we will present some recent extensions and novel remarkable applications.
Ronald Cramer (Professor, Matematical Institute, Leiden University).
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Optimal Control of Power Generating Kite Systems: Real-Time Optimization vs. Robust Periodic Optimal Control, 5th February 2008
The talk reports on recent progress in modelling and optimization techniques for optimal feedback control, whose developments were motivated by a new technology: Wind power generating large scale kite systems, currently investigated by academics and companies in Europe and the US in order to meet the tight Kyoto CO2 emission limits. This technology is based on the idea to let kites fly very fast in a crosswind direction and exploit the enormous forces by slowly pulling out the cable and driving a generator at the ground, periodically interrupted by retracting the cable while reducing the cable force. One of the main problems to make the technology work is feedback control of this highly unstable and nonlinear system. We discuss first how real-time optimization in the framework of Nonlinear Model Predictive Control with simultaneous parameter estimation can address this problem, and discuss the ingredients for fast online optimization algorithms: direct multiple shooting, real-time iterations, online active set strategies.
As a second approach we present a newly developed method to simultaneously optimize a reference trajectory along with a linear periodic feedback controller in order to robustly stabilize the kite systems. The method is based on the optimization of the solution of periodic Lyapunov differential equations which describe the uncertainty due to disturbances like e.g. wind. One unexpected result with possibly high impact in practice is the discovery of open-loop stable kite orbits, i.e. the possibility to generate stable periodic attractors just by a smart choice of periodic inputs of this nonlinear and unstable system.
Finally, the status of real world implementation of the project is illustrated by pictures and videos from the collaboration partners.
Joint work with Boris Houska, Hans Joachim Ferreau, Andreas Ilzhoefer, and Hans Georg Bock.
Moritz Diehl (Professor for Optimization in Engineering, Electrical Engineering Department, K.U. Leuven, Belgium).
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Accurate solution of global field interpolations for particle simulations, 5th February 2008
Often particle methods represent a given field as a sum of basis functions, such as Gaussians. The general problem of finding a set of basis functions and their weights such that the field is accurately represented corresponds to a problem of radial basis function interpolation. It is well-known that when the basis function has global support, the quality of the interpolation can be very good, often exhibiting high-order convergence. However, in practice there are difficulties associated with solving a large, dense and ill-conditioned system. It is possible to avoid the problem using compact support basis functions, but with a compromise in the accuracy of interpolation.
We are investigating some new methods for performing accurate field interpolations with global basis functions. We show excellent results using a preconditioned iterative solution method, where convergence to machine precision can be achieved in a handful of iterations. Other methods under investigation will also be discussed.
This work is in collaboration with Louis F. Rossi, University of Delaware.
Lorena Barba (Department of Mathematics, University of Bristol, United Kingdom).
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Fast and strongly localized observation for the Schrödinger equation, 31 January 2008
Marius Tucsnak (Professeur à l'Université Henri Poincaré-Nancy 1).
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Runge-Kutta convolution quadrature methods for linear Volterra equtions, 31 January 2008
César Palencia (Catedrático Dpto. de Matemática Aplicada Universidad de Valladolid).
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Mathematical modeling of Network Seminar Series, 22th January 2008
An Optimal Median Estimation Algorithm for Streaming data and its usage for Estimating Internet Link Delays from Active Measurements.
Yuval Shavitt (School of Electrical Engineering, The Iby and Aladar Fleischman Faculty of Engineering).
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Financial Seminar Series, 21th January 2008
Unveiling volatility of financial markets: memories, extreme times, estimation and other privacies.
Josep Perelló (Departament de Física Fonamental, Universitat de Barcelona).
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Tropical geometry Seminar Series, 10-11th January 2008
Tropical curves, Ilia Itenber (Professeur, IRMA, Université Louis Pasteur).
Recursive formulas for Welschinger invariants, Ilia Itenberg (Professeur, IRMA, Université Louis Pasteur).
Geometric Constructions in Tropical Geometry, Luis Tabera (Imdea Mathematics).
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Controllability of parabolic equations with nonsmooth coefficients in the principal part, 9th January 2008
Jérôme Le Rousseau (INRIA Paris-Rocquencourt, Université de Provence).
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Hardy inequalities in twisted waveguides, 29th November 2007
David Krejcirik (Department of Theoretical Physics, Nuclear Physics Institute).
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Existence and continuity of global attractors for a class of non local evolution equations, 29th November 2007
Antonio L. Pereira (Instituto de Matemática e Estatística-USP).
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Creating materials with desired refraction coefficient, 29th November 2007
A. G. Ramm (Mathematics Department, Kansas State University).
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Secure Multiparty Computation for Linear Algebra Functions, 19th November 2007
Carles Padró de la Universitat Politécnica de Catalunya.
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On a Lie--Poisson system and its Lie algebra, 24th October 2007
Arieh Iserles (Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge).
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Chaos and the formation of binary objects in the Kuiper-belt, 24th October 2007
David Farrelly (Department of Chemistry, Utah State University).
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Simulaciones numéricas en la industria del petróleo utilizando elementos finitos hp, 10th September 2007
David Pardo Zubiaur (Universidad de Texas en Austin, Austin, Texas, EEUU).
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