2022 - 2023 Program

Title : Current methods for solving the Helmholtz equation           Link to Video

Speaker:  Abderrahmane BENDALI, Emeritus Professor, University of Toulouse, Mathematical institute of Toulouse, INSA Toulouse.

Abstract: Numerical simulation of wave propagation problems is of vital importance in several domains of science and technology. The talk first presents how this simulation can be reduced to the numerical solution of the Helmholtz equation. Some simple examples then highlight the serious difficulties facing this task. Some current methods for efficiently solving the Helmholtz equation are then presented. 

Title : Generalized Variance Functions For Exponential Families and Applications. Link to video

Speaker:  Afif Masmoudi. Sfax University, College of Science. Tunisia.

Abstract: In this talk, we present the notion of generalized variance for exponential families in a d-dimensional linear space. Under some conditions, we prove that the generalized variance characterizes the multinomial, poisson gaussian, negative multinomial models.

We also introduce the glm regression for Tweedie distributions. We illustrate the obtained results by applying simulation studies and some applications. 

Title : An iterative method for the solution of the Maxwell equations in very large domains. Link to video

Speaker:  Sébastien Tordeux, Pau University, France.

Abstract: Solving the Maxwell system by classical methods faces on very large domains a major difficulty. It involves a linear system which is impossible to invert by a LU method, when it exceeds 20 million degrees of freedom. An iterative method based on domain decomposition can overcome this issue.  Variational domain decomposition methods benefit from a strong theoretical framework but are rather difficult to implement in a HPC context. In this talk, we will show that iterative Trefftz methods can be an excellent alternative because they do not require any matrix inversion. Numerical simulations involving a billion of unknowns will illustrate the performance of the iterative Trefftz solver. 

Title : New gradient system approach to solve some degenerate parabolic problems. Application to an electroporation model in cell-biology. Link to video

Speaker: Zakaria Belhachmi, University of Haute Alsace, France.

Abstract: We present a gradient system approach based on the identification of a gradient system structure to some degenerate parabolic equations. Such structure, called j-gradient, allows us to solve the PDEs system in the framework of the well established gradient systems theory to study these PDEs classes and to perform their numerical approximation and analysis. The application of the approach to a model in cell biology shows the interest of having such tools in an abstract and general form to make the study less problem dependant. 

Title : Topological sholl descriptors for neuronal classification and clustering. Link to video

Speaker: Sadok Kallel, American University of Sharjah, United Arab Emirates.

Abstract: Variations in neuronal morphology among cell classes, brain regions, and animal species are thought to underlie known heterogeneities in neuronal function. Thus, accurate quantitative descriptions and classification of large sets of neurons is important for functional characterization. However, unbiased computational methods to classify groups of neurons are currently scarce. We present an unbiased method to study neuronal morphologies which assigns to each Neuron an invariant depending on distance from the soma, and taking values in suitable metric spaces. Such descriptors can include tortuosity, branching pattern, “energy”, wiring, etc. Using detection and metric learning algorithms, we can then provide efficient clustering and classification schemes for neurons. This is joint work with Reem Khalil, Ahmad Farhat and Pawel Dlotko.

Title: Invasion percolation and scaling limits.       Link to slides      Link to video

Speaker:  Nicolas Broutin, Sorbonne Université , France.

Abstract: I will explain how the exploration of graphs using Prim's algorithm, or invasion percolation, yields intuitive approaches to some scaling limits the classical multiplicative coalescent processes related to random graphs. This is based on joint work with J.-F. Marckert. 

Title : Singular limit solutions for a 2-dimensional semilinear elliptic system of Liouville type in some general case adding singular sources.  Link to video    Link to slides

Speaker:  Sami Baraket. El Imam University. Riyadh, Kingdom of Saudi Arabia.

Abstract: We consider some semilinear elliptic system with exponential nonlinearity in dimension 2 with  singular sources of Dirac masses . In particular, we construct solutions such that the set of blow up points may intercept. Many cases occur. We will discuss the case where the commun concentration point will be the commun Dirac mass in the two equations of the system.

Title : On the minimal prime graphs. (Link to video).

Speaker:  Youssef Boudabbous. University  de  La Reunion,  Laboratory of Informatic and Mathematics

Abstract: The first part of this talk concerns the description of the 1-minimal and 2-minimal prime graphs (A. Cournier and P. Ille, 1998) and that of the 3-minimal triangle-free prime graphs (M. Alzohairi and Y. B., 2014). In the the second part, we present the recent description of the 3-minimal prime graphs (F. Alrusaini, M. Alzohairi, M. Bouaziz, and Y. B., 2022). Finally, in the third part, we give a recursive procedure to construct the minimal prime graphs. More precisely, given an integer k, with k ≥ 3, we give a method for constructing the k-minimal prime graphs from the (k −1)-minimal prime graphs. Notice that this last part consists in the presentation in the particular case of graphs of a recent result on minimal prime digraphs (M. Alzohairi, M. Bouaziz, and Y. B., 2022).

Title : Title: Subgraph Statistics in Series-Parallel Graphs and Related Graph Structures. (Link to video).

Speaker:  Michael Drmota,  Institut für Diskrete Mathematik und Geometrie, TU Wien. Austria.

Abstract:  Series-parallel graphs can be characterized in several ways. For example, they can be generated by a successive series-parallel extension of a forest, or they are precisely those graphs with no K_4 as a minor.

The main purpose of this talk is to establish asymptotic properties of the subgraph counting problem in random series-parallel graphs, where we assume that every series-parallel graph G with n vertices appears equally likely.

Let H be a fixed connected series-parallel graph. The main result says that the number of occurrences of H (as a subgraph) in a random series-parallel graph of size n follows asymptotically a normal limiting distribution with linear expectation and variance.

Actually the same result holds for so-called sub-critical graph classes.

The main ingredient in the proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations.

This is joint work with Lander Ramos and Juanjo Ru\'e.

Title :   Convexity properties of the Mittag-Leffler random variable. (Link to video).

Speaker:  Thomas Simon. Lille University.

Abstract: The Mittag-Leffler random variable is defined by its moment generating function which is the classical Mittag-Leffler function $E_a(x)$ with parameter $a \in (0,1)$. We will present some convexity properties for this random variable, which appears in different domains. We will establish a link between the log-concavity of the density and the reciprocal convexity of $E_a(x)$. We will exhibit a peacock related to the dimension $d = 2(1-a)$ of the underlying Bessel process. Finally, we will show some subadditivity and log-concavity properties of $E_a(x)$ for all $a > 0$, in connection with a neoclassical inequality on the generalized binomial coefficients.

Title: Distributions and Moments: Characterizations, Limit Theorems, Inference (link to video)

Link to slides

Speaker: Jordan  M. Stoyanov  (stoyanovj@gmail.com). Bulgarian Academy of Sciences, Sofia, Bulgaria - Shandong University, Jinan, China - Formerly at Newcastle University, UK

Bio: Jordan Stoyanov is a Honorary Professor at the Bulgarian Academy of Sciences, Professor at Shandong University, (China), and formerly a Professor at Newcastle University (UK). He is a Fellow of the Institute of Mathematical Statistics,  the International Statistical Institute, the Bernoulli Society, and the London Mathematical Society. He is Associate Editor in several journals in probability and statistics,  and his interests are in Probability and Stochastic Processes, with Applications. He wrote 5 books, with several editions in different languages, and one of them is the well-known: "Counterexamples in Probability". 

Abstract: The discussion will be on statistical/probability distributions, continuous or discrete, onedimensional and multidimensional, and the role of their moments, finite or not. In particular, assume that we deal with a distribution having finite all moments of positive integer orders. Any such a distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In the latter case there are infinitely many distributions of any kind, discrete and continuous, all with the same moments.

    Example: Given is a normally distributed r.v. Z ~ N(0,1). Then Z  is M-determinate,  Z^2 (being chi-square) is M-determinate, however Z^3 is M-indeterminate. Moreover, the transformation X = exp (Z), the LogNormal, is M-indeterminate. Then, a little surprisingly, the fourth power, Z^4, is M-determinate, while the product of four independent copies of Z turns out to be  M-indeterminate.  

    A description of the current state of arts in this area will be presented. It includes a variety of checkable conditions which are either sufficient or necessary for uniqueness or for non-uniqueness (Cramer, Carleman, Hardy, Krein, Lin, rate of growth of moments).  Besides the moments, we can efficiently exploit the cumulants/semi-invariants to establish non-conventional limit theorems.  The uniqueness, or M-determinacy, is an important and useful property from both theoretical and  applied point of view. In particular, the M-determinacy is an essential requirement for the validity of a fundamental limit theorem (Frechet-Shohat). However, to use moments in the case of M-indeterminacy is quite `risky’, exposed to big errors.  It will be shown how to solve statistical inference problems in terms of the moments.   If time permits, some challenging open questions will be outlined.

Title : Interacting Urn Models ( Video, slides)

Speaker:  Neeraja Sahasrabudhe ( Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohali), India.

Abstract: An interacting urn model is a random process involving N urns such that the reinforcement in each urn depends on all the urns or on a non-trivial subset of the given set of N urns. In this talk, we will discuss some recent developments in the area. In particular, I will talk about asymptotic behaviour of two-colour urns with graph based interactions.

Bio: Dr. Neeraja Sahasrabudhe is currently working as an Assistant Professor at the Department of Mathematical Sciences of Indian Institute of Science Education and Research Mohali. Prior to joining IISER Mohali, she spent a few years as a postdoctoral researcher at the Indian Statistical Institute and at the Indian Institute of Technology Bombay. She finished her PhD from the University of Padova, Italy. Her research interests are mainly in the areas of random processes with reinforcement. In particular, she works on urn models, consensus on networks, stochastic approximation and preferential attachment random graphs.

Speaker:   Anita Behme, Technische Universitat Dresden, Germany.

Title:  Invariant distributions of Lévy-type processes and related questions. (Video Link)

Abstract:  We establish a distributional equation as a criterion for invariant measures of Markov processes associated to Lévy-type operators. It is obtained via a characterization of infinitesimally invariant measures of the associated generators. Particular focus is put on the one-dimensional case where the distributional equation becomes a Volterra-Fredholm integral equation, and on Lévy-type processes solving stochastic differential equations. The results are compared to other methods of determining invariant measures, applied on several examples and an outlook on possible applications in Monte Carlo simulations is presented.

Bio:  Anita Behme earns the Chair of Applied Stochastics at TU Dresden and is full professor there. She was an invited professor at several Universities in Germany and US. Her research interest is in probability theory and stochastic processes.

Title :   Numerical splitting schemes for stochastic differential equations with Locally Lipschitz drift.

Speaker:  Massimiliano Tamborrino, Warwick University, England.

Abstract: In this talk, we construct and analyse explicit numerical splitting methods for a class of semilinear multivariate stochastic differential equations (SDEs) with additive noise, where the drift is allowed to grow polynomially and satisfies a global one-sided Lipschitz condition. The methods are proved to be mean-square convergent of order 1, and to preserve important structural properties of the SDE. First, the numerical schemes hypoelliptic in every iteration step: that is, the noise, entering only in some of the components, propagate to the other components via the drift, as for the theoretical model. Second, they are geometrically ergodic and have asymptotically bounded second moments. Third, they preserve oscillatory dynamics, such as amplitudes, frequencies and phases of oscillations, even for large time steps. Our results are illustrated on the stochastic FitzHugh-Nagumo model (a well-known neuronal model describing the generation of spikes of single neurons at the intracellular level) and compared with known mean-square convergent tamed/truncated variants of the Euler-Maruyama method. The capability of the proposed splitting methods to preserve the afore mentioned properties makes them applicable within different statistical inference procedures. In contrast, known Euler-Maruyama type methods commonly fail in preserving such properties, yielding ill-conditioned likelihood-based estimation tools or computationally infeasible simulation-based inference algorithms, as illustrated in the talk. 

Title :   A Hybrid Volatility and Deep Learning Model for Forecasting Bitcoin Volatility, 

Speaker:  Dr Farhat Iqbal, Imam Abdurrahman Bin Faisal University, KSA.

Abstract: When compared to the characteristics of traditional asset classes, such as equities and commodities, Bitcoin price movements are commonly described as highly nonlinear and volatile across economic periods. Given the difficulty in quantifying and modeling Bitcoin's price volatility, such behaviors pose a challenge from a risk management perspective. To forecast Bitcoin's realized volatility, we propose hybrid analytical techniques that combine the non-stationary properties of Generalized Autoregressive Conditional Heteroskedasticity models with the nonlinear modeling capabilities of deep learning algorithms, such as Long Short Term Memory, Gated Recurrent Unit, and Bidirectional LSTM algorithms with single, double, and triple layer network architectures. In-sample and out-of-sample forecasting results indicate that such hybrid models can generate accurate price volatility forecasts for Bitcoin.