Ομιλητής : Αλέκος Βίδρας (Πανεπιστήμιο Κύπρου).

Ημερομηνία, ώρα : Παρασκευή 25 Οκτωβρίου 2024, 13:00

Τοποθεσία : Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Ανακατασκευάζοντας τις ολόμορφες στο χωρίο Ω ⊆ ℂ συναρτήσεις από τις τιμές των στο υποσύνολο M θετικού μέτρου του συνόρου ∂Ω.”.

Περίληψη : “Αρχείο pdf “

Ομιλητής : Prof. Antoine Chaillet (L2S-CentraleSupélec and Université Paris-Saclay,  Institut Universitaire de France) https://l2s.centralesupelec.fr/en/u/chaillet-antoine/

Μέρος, ώρα : Τρίτη 22 Οκτωβρίου 2024, 13:30στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Stability and robustness of nonlinear time-delay systems: recent results and open questions”

Περίληψη : “The input-to-state stability (ISS) property offers an interesting framework to study both stability and robustness of nonlinear systems. While this concept is now well developed in a finite-dimensional context, several important questions remain open when working with infinite-dimensional systems. This presentation will focus on a particular class of such systems, namely time-delay systems. We will review fundamental results to study ISS of time-delay systems, particularly through the tool of Lyapunov-Krasovskii functionals (LKF).

We will also report some recent results related to the possibility of deriving stability properties based on a LKF whose dissipation is merely in terms of the current value of the solution’s norm (point-wise dissipation). We will also list a series of open questions in the field and describe the partial answers obtained so far, with the secrete hope that some attendees will come up with novel ideas to tackle them!”

Ομιλητής : κ. Lehel Banjai.

Μέρος, ώρα : Τρίτη 18.10.2024, στις 10:45 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Numerical methods for the fractional Helmholtz equation.”

Περίληψη : “In this talk we consider the Helmholtz equation where the usual Laplacian is replaced by a non-local variant: the spectral fractional Laplacian. The thus obtained fractional Helmholtz equation has applications to geophysical electromagnetics, but in this talk we focus on the development and analysis of efficient numerical methods. We describe and analyse two possible approaches. Firstly, a direct contour integral method discretised by a sinc quadrature combined with an hp-finite element method. Secondly a tensor product hp-finite element method applied to an equivalent local problem in a spatially extended domain. In both cases we show that the cost is equivalent to solving a single standard Helmholtz equation and a fractional Poisson problem. The talk ends with numerical experiments showing exponential convergence of both approaches.”

Ομιλητής : κ. Γεώργιος Μπαρμπαλιάς.

Μέρος, ώρα : Τρίτη 16.07.2024, στις 11:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Computable one-way functions on the reals.”

Περίληψη : “

A major open problem in computational complexity is the existence of a one-way function, namely a function from strings to strings which is computationally easy to compute but hard to invert. Levin (2023) formulated the notion of one-way functions from reals (infinite bit-sequences) to reals in terms of computability, and asked whether partial computable one- way functions exist. We give a strong positive answer using the hardness of the halting problem and exhibiting a total computable one-way function.

This is joint work with Xiaoyan Zhang.

Preprint: http://arxiv.org/abs/2406.15817

”

Ομιλητής : κ. Jasper Rou.

Μέρος, ώρα : Παρασκευή 14.06.2024, στις 13:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Convergence of time-stepping Deep Gradient Flow Methods.”

Περίληψη : “In this research, we consider the convergence of neural network algorithms for partial differential equations (PDE). More specifically, we consider a Time-stepping Deep Gradient Flow method, where the PDE is solved by discretizing it in time and writing it as the solution of minimizing a variational problem. A neural network approximation is then trained to solve this minimization using stochastic gradient descent. This method reduces the training time compared to for instance the Deep Galerkin Method. We prove two things.

First, that there exists a neural network converging to the solution of the PDE. This proof consists of three parts: 1) convergence of the time stepping; 2) equivalence of the solution of the discretized PDE and the minimizer of the variational formulation and 3) the approximation of the minimizer by a neural network by using a version of the universal approximation theorem. Second, we prove that when training the network we converge to the correct solution. This proof consists of two parts:

1) as the number of neurons goes to infinity we converge to some gradient flow and 2) as the training time goes to infinity this gradient flow converges to the solution.”

Ομιλητής : κ. Στέφανος Θεοδωρακόπουλος.

Μέρος, ώρα : Παρασκευή 31.05.2024, στις 13:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Θέματα σε οπισθόδρομες στοχαστικές διαφορικές εξισώσεις τύπου μέσου πεδίου και McKean-Vlasov, και οπισθόδρομη διάδοση του χάους (Topics on mean-field and McKean-Vlasov backward stochastic differential equations, and the backward propagation of chaos).”

Περίληψη : “First we shall present a version of the McKean-Vlasov and mean-field BSDEs in a general setting, and the notion of backward propagation of chaos. We will then discuss some of the technical difficulties that had to be overcome in order to establish the limit theorems and see some of their immediate corollaries and rates of convergence. Finally, we will introduce the concept of stability with respect to the data for the backward propagation of chaos, and state the intermediate results that allowed us to prove its validity under a natural framework.”

Ομιλητής : κ. Daniel Schmidt (Monash University, Australia).

Μέρος, ώρα : Παρασκευή 29.03.2024, στις 13:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Prevalidated ridge regression as a highly-efficient drop-in replacement for logistic regression for high-dimensional data”

Περίληψη : “Linear models are widely used in classification and are particularly effective for high-dimensional data where linear decision boundaries/separating hyperplanes are often effective for separating classes, even for complex data. A recent example of a technique effectively utilising linear classifiers is the ROCKET family of classifiers for time series classification. One reason that the ROCKET family is so fast is due to its use of a linear classifier based around standard squared-error ridge regression. Fitting a linear model based on squared-error is significantly faster and more stable than fitting a standard regularised multinomial logistic regression based on logarithmic-loss (i.e., regularised maximum likelihood), as in the latter case the solutions can only be found via a numerical search.

While fast, one drawback of using squared-error ridge-regression is that it is unable to produce probabilistic predictions. I will demonstrate some very recent work on how to use regular ridge-regression to train L2-regularized multinomial logistic regression models for very large numbers of features, including choosing a suitable degree of regularization, with a time complexity that is no greater than single ordinary least-squares fit. This in contrast to logistic regression, which requires a full refit for every value of regularisation parameter considered, and every fold used for cross-validation. Using our new approach allows for models based on linear classifier technology to provide well calibrated probabilistic predictions with minimal additional computational overhead. If time permits, I will also discuss some thoughts on when such linear classifiers would be expected to perform well.”

Ομιλητής : κ. Νικόλαος Παλληκαράκης (ΣΕΜΦΕ)

Μέρος, ώρα : Παρασκευή 22.03.2024, στις 13:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Solving Inverse Problems with Supervised Machine Learning Models”

Περίληψη : “The latest years, machine learning has been one of the main directions in the numerical solution of inverse problems, aiming to face the ill-posed nature of these problems. In this talk, we delve into the numerical solution of inverse problems and specifically inverse eigenvalue and inverse source problems, from a machine learning perspective.

In the first part, we focus on the inverse Sturm-Liouville eigenvalue problem for symmetric potentials and the inverse transmission eigenvalue problem for spherically symmetric refractive indices. We present the main ideas behind supervised machine learning regression and briefly discuss the basic properties of the algorithms we implement, which are k-Nearest Neighbours (kNN), Random Forests (RF) and Neural Networks (MLP). Afterwards, we numerically solve the direct problems using well known methods, in order to produce the spectral data which in turn are used for training the machine learning models. We consider examples of inverse problems and compare the performance of each model to predict the unknown potentials and refractive indices respectively, from a given small set of the lowest eigenvalues.

In the second part, we pose the inverse problem, to predict the number of sources inside a dielectric cylinder. Using classification Neural Networks, we show that this problem is solved with high accuracy. Our experiments validate the efficiency of these machine learning models for numerically tackling such inverse problems, providing a proof-of-concept for their applicability in this field.”

Ομιλητής : κ. Ιωάννης Τζουάνας (Bielefeld University) / https://ekvv.uni-bielefeld.de/pers_publ/publ/PersonDetail.jsp?personId=309525527&lang=EN

Μέρος, ώρα : Τρίτη 09/01/2024, στις 13:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Ergodic Mean-Field Games of Singular Control with Regime-Switching”

Περίληψη : “This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion. The mean-field interaction is of scalar type and it is given through the stationary distribution of the population. Via a constructive approach, we prove the existence and uniqueness of the stationary mean-field equilibrium. Furthermore, we show that this realizes a symmetric εN-Nash equilibrium for a suitable ergodic N-player game with singular controls. The proof hinges on the characterization of the optimal solution to the representative player’s ergodic singular stochastic control problem with regime switching, which is of independent interest and appears here for the first time. This talk is based on the joint work with Jodi Dianetti and Giorgio Ferrari.”

Ομιλητής : Μιχάλης Τσατσόμοιρος ( Washington State University https://www.math.wsu.edu/faculty/tsat/ )

Μέρος, ώρα : Παρασκευή 03/11/2023, στις 13:45 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : “Rank One Perturbations for Cone Reachability and Holdability”

Περίληψη : “A choice of feedback control in a linear control system is proposed in order for the trajectory to eventually enter the nonnegative orthant and remain therein for all time thereafter. This is achieved by imposing the strong Perron-Frobenius property and involves altering the eigenvalues, as well as the left eigenvectors via rank one perturbations.”

Ομιλητής : Prof. Michael Ruzhansky (Ghent University and Queen Mary University of London, http://ruzhansky.org)

Μέρος, ώρα : Τετάρτη 04/10/2023, στις 15:00 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.

Τίτλος : Very weak solutions to PDEs with singularities

Περίληψη : “In this talk we will review the notion of very weak solutions, introduced for dealing with PDEs with very strong singularities in coefficients or data.”

Ομιλητής : Prof. Mihir Kumar Chakraborty (https://sites.google.com/site/mihirkchakraborty/

Μέρος, ώρα : Παρασκευή 29/09, στις 13:30 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Reflections on BSDEs

Περίληψη : “We consider backward stochastic differential equations (BSDEs) and reflected BSDEs in the genereality that will allow a unified study of certain discrete-time and continuous-time control problems on random time horizons. We provide well-posedness results for the BSDEs and reflected BSDEs with optional obstacle process in case of appropriately weighted square-integrable data. This is based on joint work with Dylan Possamaï.

Ομιλητής : Prof. Mihir Kumar Chakraborty (https://sites.google.com/site/mihirkchakraborty/

Μέρος, ώρα : Παρασκευή 12/05, στις 13:35 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Some Aspects of Mathematical Pluralism.

Περίληψη : “In this talk I will provide examples of plurality in mathematics caused because of both the internal as well as external reasons. Thus it will be argued that culture, being understood in a wider sense, plays a significant role in the creation and development of mathematical notions. Recent research called ” Mathematical practices” and “Proof events” may also have justification from this perspective of multiplicity. As a result, from the angles of content and method current uniformity all over the world needs a critical review.”

Ομιλητής : Natalia Kopteva (U. Limerick, https://staff.ul.ie/natalia/)

Μέρος, ώρα : Παρασκευή 05/05, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : A posteriori error estimates for singularly perturbed equations.

Περίληψη : “Solutions of singularly perturbed partial differential equations typically exhibit sharp boundary and interior layers, as well as corner singularities. To obtain reliable numerical approximations of such solutions in an efficient way, one may want to use meshes that are adapted to solution singularities using a posteriori error estimates.

In this talk, we shall discuss residual-type a posteriori error estimates singularly perturbed reaction-diffusion equations and singularly perturbed convection-diffusion equations. The error constants in the considered estimates are independent of the diameters of mesh elements and of the small perturbation parameter. Some earlier results will be reviewed [1], with the main focus on the more recent preprint [2], and a very brief discussion of [3].”

References:

[1] A. Demlow & N. Kopteva, Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems, Numer. Math., 133 (2016), 707-742

[2] N. Kopteva, R. Rankin, Pointwise a posteriori error estimates for discontinuous Galerkin methods for singularly perturbed reaction-diffusion equations, preprint, 2022.

[3] A. Demlow, S. Franz and N. Kopteva, Maximum norm a posteriori error estimates for convection-diffusion problems, IMA J. Numer. Anal., (2023), published online 20-Feb-2023.

Ομιλητής : Κωνσταντίνος Δαρειώτης (School of Mathematics, U. Leeds, https://eps.leeds.ac.uk/maths/staff/6172/dr-konstantinos-dareiotis)

Μέρος, ώρα : Παρασκευή 28/04, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Regularisation of differential equations by multiplicative fractional noises.

Περίληψη : “In this talk, we consider differential equations perturbed by multiplicative fractional Brownian noise. Depending on the value of the Hurst parameter $H$, the resulting equation is pathwise viewed as an ordinary ($H>1$), Young  ($H \in (1/2, 1)$) or rough  ($H \in (1/3, 1/2)$) differential equation. In all three regimes we show regularisation by noise phenomena by proving the strongest kind of well-posedness for equations with irregular drifts: strong existence and path-by-path uniqueness. In the Young and smooth regime $H>1/2$ the condition on the drift coefficient is optimal in the sense that it agrees with the one known for the additive case. In the rough regime $H\in(1/3,1/2)$ we assume positive but arbitrarily small drift regularity for strong  well-posedness, while for distributional drift we obtain weak existence. This is a joint work with Máté Gerencsér.”

Ομιλητής : Dominik Schmid (U Bonn & Princeton)

Μέρος, ώρα : Τετάρτη 13/07, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Mixing times for the TASEP on the circle.

Περίληψη : “The exclusion process is one of the best-studied examples of an interacting particle system. In this talk, we consider simple exclusion processes on finite graphs. We give an overview over some recent results on the mixing time of the totally asymmetric simple exclusion process (TASEP). In particular, we provide bounds on the mixing time of the TASEP on the circle, using a connection to periodic last passage percolation.
This talk is based on joint work with Allan Sly (Princeton).”

Ομιλητής : Peter Markowich (distinguished Professor of Applied Mathematics and Computational Science, King Abdullah University of Science and Technology)
https://www.kaust.edu.sa/en/study/faculty/peter-markowich

Μέρος, ώρα : Τρίτη 14/06, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : EMERGENCE OF BIOLOGICAL TRANSPORTATION NETWORKS AS A SELF-REGULATED DIFFUSION PROCESS.

Περίληψη : “We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal L2-gradient flow for the symmetric tensor valued diffusivity D of abroad class of entropy dissipations associated with a purely diffusive model. The introduction of a prescribed electric potential leads to the Fokker-Planck equation, for whose entropy dissipations we also investigate the formal L2-gradient flow. We derive an integral formula for the second variation of the dissipation functional, proving convexity (in dependence of diffusivity tensor) for a quadratic entropy density modeling Joule heating. Finally, we couple in the Poisson equation for the electric potential obtaining the Poisson-Nernst-Planck system. The formal gradient flow of the associated entropy loss functional is derived, giving an evolution equation for D coupled with two auxiliary elliptic PDEs.”

Ομιλητής : Αλεξάνδρα Χρονοπούλου (Alexandra Chronopoulou, https://stat.illinois.edu/directory/profile/achronop)

Μέρος, ώρα : Παρασκευή 03/06, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Discrete-time Approximation of Rough Volatility Models .

Περίληψη : ““Rough” volatility models (RVM) have been introduced to describe the anti-persistent behavior of the volatility of financial assets. These are models in which the stock follows a geometric Brownian motion, with volatility described by a fractional Ornstein–Uhlenbeck process with Hurst parameter less than 1/2. In the first part of this talk, we will introduce a new framework for the estimation of the volatility process of an asset using low frequency daily option trading entries. We will apply this method to S&P 500 data and obtain estimates of the Hurst parameter that motivate the need for RVM. In the second part of the talk, we will establish the weak convergence of a novel Donsker-type scheme for RVM, which leads naturally to a Binomial tree for option pricing”

Ομιλητής : Διονύσης Θεοδόσης – Παλιμέρης (Πολυτεχνείο Κρήτης)

Μέρος, ώρα : Παρασκευή 27/5, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : Cruise Controllers and Fluid-like Traffic Models.

Περίληψη : “In this talk, we will focus on Control Lyapunov function methodologies for the design of families of cruise controllers for the safe operation of autonomous vehicles and we will discuss the new principle of vehicle nudging, whereby autonomous vehicles may “push” other vehicles in front of them, which may increase traffic flow and capacity. The Control Lyapunov functions are based on measures of the energy of the system with the kinetic energy expressed in ways similar to Newtonian or relativistic mechanics. Moreover, we will present the macroscopic models that correspond to the derived control laws, obtaining fluid-like models that consist of a conservation equation and a momentum equation with pressure and viscous terms. Finally, we will show that, by selecting appropriately the parameters of the feedback laws, we can determine the physical macroscopic fluid characteristics, i.e. we get free hand to create an artificial fluid that approximates the emerging traffic flow.”

Ομιλητής : Dylan Possamai (ETH Zürich), https://sites.google.com/site/possamaidylan/

Μέρος, ώρα : Τετάρτη 06 Απριλίου 2022 & ώρα 13:35, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.

Τίτλος : Non-asymptotic convergence rates for mean-field games: weak formulation and McKean–Vlasov BSDEs.

Περίληψη : “This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control, and interactions through the joint distribution of players’ states and controls. We provide first a new characterisation of mean-field equilibria as arising from solutions to a novel kind of McKean–Vlasov back- ward stochastic differential equations, for which we provide a well-posedness theory. We incidentally obtain there unusual existence and uniqueness results for mean-field equilibria, which do not require short-time horizon, separability assumptions on the coefficients, nor Lasry and Lions’s monotonicity conditions, but rather smallness conditions on the terminal reward. We then take advantage of this characterisation to provide non-asymptotic rates of convergence for the value functions and the Nash-equilibria of the N-player version to their mean-field counterparts, for general open-loop equilibria. This relies on new back- ward propagation of chaos results, which are of independent interest. This is a joint work with Ludovic Tangpi.”

Ομιλητής : Anupreet Porwal (University of Washington, Seattle).

Μέρος, ώρα : Παρασκευή 28 Ιανουαρίου 2022 & ώρα 18:08, μέσω WebEx.

Τίτλος : Laplace Power-expected-posterior priors for generalized linear models with applications to logistic regression.

Περίληψη : “Power-expected-posterior (PEP) methodology, which borrows ideas from the literature on power priors, expected-posterior priors and unit information priors, provides a systematic way to construct objective priors. The basic idea is to use imaginary training samples to update a non-informative prior into a minimally-informative prior. In this work, we develop a novel definition of PEP priors for generalised linear models that relies on a Laplace expansion of the likelihood of the imaginary training sample. This approach has various computational, practical and theoretical advantages over previous proposals for non-informative priors for generalised linear models. We place a special emphasis on logistic regression models, where sample separation presents particular challenges to alternative methodologies. We investigate both asymptotic and finite-sample properties of the procedures, showing that is both asymptotic and intrinsic consistent, and that its performance is at least competitive and, in some settings, superior to that of alternative approaches in the literature”

Ομιλητής : Κώστας Παπαφιτσώρος (Weierstrass Institute, Berlin)

Μέρος, ώρα : Τρίτη 21 Δεκεμβρίου 2021 & ώρα 14:05, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.

Τίτλος : Ανακατασκευή ψηφιακής εικόνας με μεθόδους ολικής κύμανσης.

Περίληψη : “Στην ομιλία αυτή αρχικά θα δώσουμε μία εισαγωγή στην ανακατασκευή ψηφιακών εικόνων με ελαχιστικές μεθόδους χρησιμοποιώντας συναρτησιοειδή κανονικοποίησης τύπου ολικής κύμανσης (Total Variation) πρώτης και δεύτερης τάξης. Θα εξετάσουμε τη δομή των λύσεων τέτοιων ελαχιστικών προβλημάτων από θεωρητική σκοπιά και θα συζητήσουμε τα αντίστοιχα πλεονεκτήματα αλλά και τους περιορισμούς που προκύπτουν στην ποιότητα των ανακατασκευασμένων εικόνων. Θα αναλύσουμε το ρόλο των παραμέτρων κανονικοποίησης (regularisation parameters) και θα εισάγουμε ένα ελαχιστικό πρόβλημα δύο επιπέδων (bilevel minimisation) που υπολογίζει αυτόματα τέτοιες παραμέτρους.  Οι υπολογιζόμενες παράμετροι κανονικοποίησης είναι χωρικά εξαρτημένες, κάτι που έχει ως αποτέλεσμα  την καλύτερη ανακατασκευή των λεπτομέρειων της εικόνας. Σαν εφαρμογή, θα παρουσιάσουμε αριθμητικά αποτελέσματα στην αποθορυβοποίηση και στην ανακατασκευή εικόνων μαγνητικής τομογραφίας.“

Ομιλητής : Γεωργία Καραλή (Παν. Κρήτης)

Μέρος, ώρα : 09/11/2021 – Το Σεμινάριο θα πραγματοποιηθεί διαδικτυακά, μέσω Zoom. Μπορείτε να συνδεθείτε ακολουθώντας τον σύνδεσμο : https://us06web.zoom.us/j/85349831604?pwd=Ulg2TWpHZURyR09WejIxbEVUVFRwUT09

Τίτλος : Στοχαστική διεπιφανειακή κίνηση και ιδιότητες εξισώσεων αντίδρασης – διάχυσης σε προβλήματα αλλαγής φάσης

Περίληψη : “Εξετάζουμε πρόσφατα αποτελέσματα σχετικά με την κίνηση της στοχαστικής διεπιφανειακής κίνησης για συγκεκριμένες στοχαστικές διαφορικές εξισώσεις αντίδρασης-διάχυσης από προβλήματα αλλαγής φάσης, καθώς και τα αντίστοιχα διεπιφανειακά τους όρια για χωρική διάσταση ένα, δύο ή τρία. Στη μονοδιάστατη περίπτωση, η στοχαστική δυναμική των διεπιφανειών δίνεται ουσιαστικά από μια πεπερασμένων διαστάσεων ντετερμινιστική “αργή” πολλαπλότητα. Εάν ο θόρυβος είναι αρκετά μικρός, η στοχαστική δυναμική δίνεται από τη διαδικασία Wiener που προβάλλεται κατάλληλα στην “αργή” πολλαπλότητα. Στη γενική κίνηση της στοχαστικής διεπιφανειακής κίνησης, όπου η “αργή” πολλαπλότητα είναι απειροδιάστατη, η δυναμική στο όριο δίνεται από ένα πρόβλημα στοχαστικού ελευθέρου συνόρου. Επίσης, γίνεται μελέτη της ύπαρξης, της ομαλότητας και της πυκνότητας των στοχαστικών λύσεων.“

Ομιλητής : Nίκος Γεωργίου (University of Sussex, http://www.sussex.ac.uk/profiles/329373)

Μέρος, ώρα : Παρασκευή 13 Μαρτίου 2020 & ώρα 13:05, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.

Τίτλος : Order of the variance for discrete Hammersley processes.

Περίληψη : “We discuss the order of the variance on a lattice analogue of the Hammersley process, for which the environment on each site has independent, Bernoulli distributed values.
The last passage time is the maximum number of Bernoulli points that can be collected on a piecewise linear path, where each segment has strictly positive but finite slope.
This model is an exactly solvable example of the KPZ class, but only in certain directions, as the shape function exhibits two flat edges. We study the order of the variance in directions that fall in the flat edge, in directions that approximate the edge of the flat edge, and in directions in the strictly concave section of the shape for the i.i.d. model and for the associated equilibrium model with boundaries. If time permitting, we will discuss the shape function and variance in some inhomogeneous models as well.
This is an exposition of several works with Janosch Ortmann, Elnur Emrah and Federico Ciech”

Ομιλητής: Μπουρνέτας Αποστόλης (ΕΚΠΑ).

Μέρος, ώρα : Παρασκευή 06 Μαρτίου 2020 & ώρα 13:05, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.

Τίτλος : Προσαρμοστική βελτιστοποίηση για στοχαστικά συστήματα υπό ελλιπή πληροφόρηση: Το πρόβλημα multi-armedbandit με περιορισμούς.

Περίληψη : “Το μοντέλο multi-armed bandit είναι ένα γενικό πλαίσιο βελτιστοποίησης στοχαστικών συστημάτων υπό ελλιπή πληροφόρηση. Αναφέρεται σε ένα σύνολο στατιστικών πληθυσμών από τους οποίους οι διαδοχικές παρατηρήσεις ακολουθούν πλήρως ή εν μέρει άγνωστες κατανομές. Σε κάθε βήμα ένας αποφασίζων επιλέγει ένα πληθυσμό από τον οποίον παίρνει μια παρατήρηση. Οι παρατηρήσεις θεωρούνται ως κέρδος ή αμοιβή για τον αποφασίζοντα, που επομένως θέλει να μεγιστοποιήσει τη συνολική αναμενόμενη αμοιβή του κάτω από κατάλληλα ορισμένα κριτήρια. Το πρόβλημα εντοπίζεται στην εύρεση πολιτικών επιλογής πληθυσμών που συνδυάζουν αποτελεσματικά την εκμάθηση των άγνωστων κατανομών των αμοιβών και τη συγκέντρωση μεγάλων αμοιβών.

Το παραπάνω γενικό πλαίσιο μπορεί να χρησιμοποιηθεί για την εύρεση προσαρμοστικά βέλτιστων λύσεων σε μεγάλη πλειάδα στοχαστικών συστημάτων υπό ελλιπή πληροφόρηση. Στην ομιλία θα γίνει μια εισαγωγή στα κριτήρια βελτιστοποίησης μέσω ελαχιστοποίησης της απώλειας λόγω ελλιπούς πληροφόρησης (regret) και θα συζητηθεί η περίπτωση όπου η λήψη παρατηρήσεων από κάθε πληθυσμό επιφέρει ένα διαφορετικό κόστος και υπάρχει ένας περιορισμός στο συνολικό κόστος δειγματοληψίας.”

Ομιλητής: Ιωάννης Εμμανουήλ (ΕΚΠΑ).

Μέρος, ώρα : Παρασκευή 28 Φεβρουαρίου 2020 & ώρα 13:05, στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών, κτ. Ε΄, 2ος όροφος.

Τίτλος : Ομάδες με ομολογική διάσταση 1.

Περίληψη : “Αφού πρώτα διατυπώσουμε το πρόβλημα του (συν-)ομολογικού χαρακτηρισμού των ελεύθερων ομάδων, θα περιγράψουμε προσπάθειες που έχουν καταβληθεί για την κατανόηση της δομής των πεπερασμένα παραγόμενων ομάδων με ομολογική διάσταση 1. Οι προσπάθειες αυτές εμπλέκουν τεχνικές από τη συνδυαστική θεωρία ομάδων και τη θεωρία των αλγεβρών τελεστών, καθώς επίσης και τεχνικές συνολοθεωρητικού χαρακτήρα.

Ομιλητής: Καθηγητής κος Γίδας Βασίλης ( Brown University, https://www.brown.edu/academics/applied-mathematics/basilis-gidas ).

Μέρος, ώρα : Παρασκευή, 21 Φεβρουαρίου 2020, 13:05, Αίθουσα Σεμιναρίων, Τομέα Μαθηματικών, ΣΕΜΦΕ (Κτίριο Ε, 2ος Όροφος)

Τίτλος : Towards a Syntactic/Probabilistic Framework for Vision/Speech Recognition and Biological Processes.

Περίληψη : “The goal of computer vision is to build “intelligent” machines that interpret scenes, in the sense of recognizing objects or other structures in a scene, and provide succinct descriptions of context, actions, and intentions. In computer speech the goal is similar – “interpret” or recognize speech. In the past few decades, important advances have been made in concrete applications such as industrial inspection, medical imagery, remote sensing, animation, robotics, and airline reservation. Such applications have motivated the development of powerful statistical/mathematical tools such as statistical learning theory and Monte Carlo optimization and simulation algorithms. But a coherent conceptual and mathematical framework for high-level vision and speech recognition tasks, is missing. The same is the case for complex biological processes such as protein folding or the collective behavior of genes, proteins and cells. In this talk we will present a probabilistic syntactic/grammatical framework, reminiscent to Chomsky’s grammatical systems in linguistics, for studying vision/speech recognition tasks as well as biological processes. The framework will be motivated by isolating some key sources of difficulty in vision/speech systems which exhibit regularities from local to global – regularities which can be modeled only by syntactic/grammatical rules. The framework will be used to define a finite automata representation of genes (analogous to the grammatical representation of languages) and a statistical algorithmic procedure for finding genes in the human genome.”

Ομιλητής: Καθηγητής κος Ψαρράκος Παναγιώτης ( (http://www.math.ntua.gr/~ppsarr ).

Μέρος, ώρα : Παρασκευή, 24 Ιανουαρίου 2020, 13:35, Αίθουσα Σεμιναρίων, Τομέα Μαθηματικών, ΣΕΜΦΕ (Κτίριο Ε, 2ος Όροφος)

Τίτλος : Travelling from matrices to matrix polynomials

Περίληψη : “The study of matrix polynomials of higher degree has attracted considerable attention in recent decades. The interest has been motivated by a wide range of applications of polynomial eigenvalue problems in areas such as differential equations, systems theory, control theory, mechanics and vibrations. In this presentation, we will see how results of the standard matrix theory, concerning Jordan structure, pseudospectra, eigenvalue condition numbers, spectral distance problems, numerical ranges and (entrywise) nonnegative matrices, have been extended to the setting of matrix polynomials in a natural way. In particular, basic matrix theory can be viewed as the study of a special case of matrix polynomials of first degree.”

Ομιλητής: Γκουνταρούλης Δήμος

Μέρος, ώρα : Παρασκευή, 10 Ιανουαρίου 2020, 13:35, Αίθουσα Σεμιναρίων, Τομέα Μαθηματικών, ΣΕΜΦΕ (Κτίριο Ε, 2ος Όροφος)

Τίτλος : Topological Aspects of the Human Genome

Περίληψη : The 3D organization of the genome plays an important role in controlling gene expression. Very recently a new method of Oligopaint labeling and optical imaging permitted to determine positions of subsequent 30kb-large portions of chromatin fibers with 50 nm accuracy (B. Bintu et al. Science 362, 2018). We analysed the topology of deposited chromatin tracings. To simulate the effect of a limited precision of the determination of the centroid position of sequential 30kb-long chromatin blocks, we introduced method-specific tracing errors to positions of every vertex and we produced 10 independent tracings. All individual polygonal curves determined by cartesian coordinates of individual tracings were closed using the stochastic closure method and were analysed using knot invariants.We analysed 4727 deposited tracings of the same 2Mb-large chromosome regions of chromosome 21 of Oligopaint-stained IMR90 cells. The tracings behaved similarly to random walks with a moderate size. Nearly 50% of tracings were knotted and the frequency of forming a given knot was inversely correlated with its complexity.It is far from certain that the corresponding, traced 2Mb long chromatin fibres were indeed knotted. The reason of this uncertainty lies in the 50nm large errors in the determination of spatial positions of centroids of sequential 30 kb- large chromatin portions. However, when we applied error-mimicking perturbations applied to unknotted polygonal chains, we observed that several of deposited tracings that were robustly unknotted. It still unclear whether chromatin can be knotted. However, in all these cases where tracing errors were unable to change the topology of analysed tracings, we could conclude that traced 2MB long chromatin fibers were unknotted.

Affiliations:

• Center for Integrative Genomics , University of Lausanne, Switzerland
• SIB,  Swiss Institute of Bioinformatics, Lausanne, Switzerland
• Baylor College of Medicine, Houston Texas, USA
• Rice University, Houston Texas, USA