Veranstaltungen
- Mittwoch, 04.10.2023, 10:00 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Pedro Pérez-Aros, Universidad de O'Higgins, Chile:
Coderivative-based semi-Newton method in nonsmooth difference programming
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
In this presentation, we explore a new category of challenging nonsmooth optimization problems. These problems involve the difference between generally nonconvex functions as their objective. We introduce an innovative Newton-type algorithm designed for solving such problems. This algorithm leverages advanced tools from variational analysis and is based on the concept of the coderivative generated second-order subdifferential (generalized Hessian). We discuss the algorithm's well-posedness properties, establishing its viability under broad conditions. Additionally, we analyze its convergence rates, incorporating assumptions such as the Kurdyka-Lojasiewicz condition. The talk ends with some numerical experiments which ilustrate the performance of our development.
Veranstalter
WIAS Berlin
- Mittwoch, 04.10.2023, 10:00 Uhr (WIAS-ESH)
- Seminar Interacting Random Systems
Tiffany Y.Y. Lo, Uppsala University, Sweden:
The expected degree distribution in duplication divergence models
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We study the degree distribution of a randomly chosen vertex in a duplication-divergence graph, paying particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2016), relies heavily on the analysis of related birth-catastrophe processes. This is joint work with A. D. Barbour.
Veranstalter
WIAS Berlin
- Mittwoch, 04.10.2023, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Subhro Ghosh, National University of Singapore:
Rigidity phenomena in strongly correlated random point fields and the emergence of forbidden regions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
The aim of this talk is to give an introduction to recent results concerning rigidity properties of random point fields, focussing in particular on the associated phenomenon of forbidden regions. Rigidity phenomena pertain to the emergence of singularities in strongly correlated point processes (e.g. those related to random matrices, Coulomb gases, zeros of random polynomials and random sections of line bundles), wherein local conservation laws have been shown to hold true. This includes, e.g., local conservation laws for mass or centre of mass, conditioned on the environment (ie the configuration of points outside a given domain). Such rigidity phenomena have been shown to be closely related to the emergence of novel `forbidden regions' in the spatial distribution of points conditioned on important classes of rare events. In particular, spatial holes (i.e. vacant domains) of macroscopic size (at the scale of the droplet) in strongly rigid point fields have been shown to enforce the emergence of complementary holes (of comparable scale) in other parts of the space.Based in part on the following joint works. [1] Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues, with Y. Peres, Duke Math. J., 166(10), 1789-1858 [2] Gaussian complex zeros on the hole event: the emergence of a forbidden region, with A. Nishry, Comm. Pure Appl. Math. 72(1), 3-62 [3] Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles, with U. Gangopadhyay, K.A. Tan, Comm. Pure Appl. Math., to appear [4] Forbidden regions for random zeros on Riemann surfaces, with T.C. Dinh, H. Wu, near completion
Veranstalter
WIAS Berlin - Mittwoch, 04.10.2023, 14:00 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Dorothee Knees, Universität Kassel:
Regularity results for a static relaxed micromorphic model
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
The relaxed micromorphic model is a generalized continuum model allowing to describe for instance size effects of microstructured solids. The state of the solid subject to external loads is characterized by the displacement field u : R3 ⊃ Ω → R3 and the microdistortion tensor P : Ω → R 3x3. The corresponding system of partial differential equations consists of the system of linear elasticity that is coupled with a system of Maxwell type for the distortion tensor P. We will discuss the regularity of weak solutions under different assumptions on the smoothness of the domain. The main ingredients for the proofs are the Helmholtz decomposition and refined difference quotient arguments based on generalized inner variations in combination with a Piola-type transformation. This is ongoing joint work with Patrizio Neff (Duisburg-Essen) and Sebastian Owczarek (Warsaw).
Weitere Informationen
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
- Mittwoch, 04.10.2023, 15:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Reinhard Scholz, Leibniz-Institut für Polymerforschung Dresden:
Simulation amphiphiler Polymernetzwerke
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
Polymere bestehen aus langen Ketten chemisch identischer oder ähnlicher Monomere. In biologischen Systemen kommen solche Systeme u.a. als Proteine und Energiespeicher vor, sowie als Träger der Erbinformation. Für die Wechselwirkung mit Lösungsmittelmolekülen spielen spezielle biologische Funktionen keine wesentliche Rolle, was eine vergröberte statistische Beschreibung ermöglicht, in der nur noch zwischen den Monomeren des Polymers und den Lösungsmittelmolekülen unterschieden wird. Amphiphile Polymere bestehen aus mindestens zwei Arten von Teilketten, die unterschiedlich mit einem Lösungsmittel wechselwirken können. Die Synthese solcher Systeme erfolgt in einem guten Ko-Lösungsmittel für alle Bestandteile. Anschließend kann ein anderes Lösungsmittel gewählt werden, das nur eine Komponente gut löst, während eine andere Komponente nicht gelöst wird, so dass Strukturen auf einer Nanometerskala entstehen. Im Rahmen der DFG-geförderten Forschergruppe 2811 Ädaptive Polymergele mit kontrollierter Netzwerkstruktur" werden gezielt amphiphile Netzwerke aus Sternpolymeren aufgebaut. Die mit experimentellen Methoden gefundenen Eigenschaften werden mit theoretischen Modellen und Simulationen interpretiert. In diesem Vortrag wird insbesondere auf das Quellverhalten solcher Netzwerke und auf die Strukturbildung im selektiven Lösungsmittel eingegangen.
Weitere Informationen
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin