ISMMA SEMINAR

• Tuesday, November 26, 2024, 11:00 AM:
  Random multiple-fragmentation and flow of particles on a surface – Dr. Oana-Valeria Lupașcu-Stamate (ISMMA)
  

Abstract: We investigate stochastic fragmentation processes for particles with spatial position. The mathematical problem models the time evolution of a system of particles which move on an Euclidean surface driven by a given force (e.g., gravitational, fluid interaction, repulsion/attraction), and split in fragments with smaller masses and velocities. We establish a multiple-fragmentation process and we solve the corresponding stochastic integro-differential equation. Finally, we present several numerical simulations of such processes. These results are obtained jointly with Lucian Beznea (Bucharest) and Ioan R. Ionescu (Paris).

• Tuesday, April 16, 2024, 10:00 AM:
  Numerical solution to the Dirichlet problem for linear parabolic SPDEs based on averaging over characteristics – Dr. Vasile Nicolae Stanciulescu
  

Abstract: We consider SPDEs with deterministic coefficients which are smooth up to some order of regularity. We establish some theoretical results in terms of existence, uniqueness and regularity of the classical solution to the considered problem. Then, we provide the probabilistic representations (the averaging-over-characteristics formulas) of its solution. We, thereafter, construct numerical methods for it. The methods are based on the averaging-over-characteristics formula and the weak sense numerical integration of ordinary stochastic differential equations in bounded domains. Their orders of convergence in the mean-square sense and in the sense of almost sure convergence are obtained. The Monte Carlo technique is used in practical realization of the methods. Results of some numerical experiments are presented. The results are in agreement with the theoretical findings.

• Thursday, March 14, 2024, 11:00 AM:
  Existence and boundedness of solutions to singular anisotropic elliptic equations – Dr. Florica Cârstea (University of Sydney, Australia)
  

Abstract: In this talk, we present new results on the existence and uniform boundedness of solutions for a general class of Dirichlet anisotropic elliptic problems … [download abstract].

• Tuesday, March 5, 2024, 10:00 AM:
  Optimal control problems for a phase field model for tumor growth – Prof. Dr. Pierluigi Colli (University of Pavia, Italy)
  

Abstract: A class of distributed optimal control problems, with deep quench approach and sparsity, is considered for a tumor growth model, which is of Cahn-Hilliard type and includes a term for chemotaxis. The evolution of the tumor fraction is governed by a pointwise inclusion involving the subdifferential of a double obstacle potential. The control and state variables are nonlinearly coupled and the cost functional contains a nondifferentiable term like the L1-norm in order to include sparsity effects. The so-called “deep quench approach” enables us to approximate the convex part of the double obstacle potential by functions of logarithmic type from the interior of the domain. This approximation is used to derive first-order optimality conditions also for the double obstacle case, by obtaining a variational inequality in terms of the associated adjoint state variables. Moreover, the sparsity results for the optimal controls are discussed. The talk reports on a joint research project with Andrea Signori and Juergen Sprekels.

• Thursday, February 15, 2024, 10:00 AM:
  Diffusion models and their applications in computer vision – CS Dr. Bogdan Alexe (ISMMA)
  

Abstract: Diffusion models are a new class of generative models that have shown outstanding performance in generating high-quality images, video, sound, text, etc. They are named for their similarity to the natural diffusion process in physics, which describes how molecules move from high-concentration to low-concentration areas. In the context of machine learning, diffusion models generate new data by reversing a diffusion process, i.e., information loss due to noise intervention. The main idea here is to add random noise to data and then undo the process to get the original data distribution from the noisy data. The famous DALL-E 2 (from OpenAI), Midjourney, and open-source Stable Diffusion that create realistic images based on the user’s text input are all examples of diffusion models. In this talk I will explain how these diffusion models work and present some common applications in computer vision.

• Tuesday, December 19, 2023, 10:00 AM:
  A probabilistic numerical approach to the inverse Cauchy problem – CSIII Dr. Andreea Grecu (ISMMA)
  

Abstract: We introduce a probabilistic numerical approach for the reconstruction of the unknown boundary data of the steady state heat equation in a bounded domain in ℝ^d, having discrete measurements inside the domain and on a part of the boundary. We shall provide theoretical results which reveal that our approach is designed to spectrally approximate the inverse operator that we deal with. Finally, a parallel algorithm shall be presented together with numerical experiments. This is based on a joint work with Iulian Cîmpean and Liviu Marin.

• Thursday, November 23, 2023, 10:00 AM:
  Isolated singularities for nonlinear elliptic equations with Hardy potential – CSIII Dr. Maria Fărcășeanu (ISMMA)
  

Abstract: In this talk, we present results regarding the existence and behaviour near zero of solutions for some nonlinear elliptic equations with singular potentials. This is joint work with Florica Cîrstea. The presentation is partially supported by CNCS-UEFISCDI Grant No. PN-III-P1-1.1-PD-2021-0037.

• Tuesday, May 9, 2023, 10:00 AM:
  Radial Efficiency Measures and Nonparametric Envelopment Estimators – CS Dr. Luiza Badin (ISMMA)
  

Abstract: The technical efficiency of economic producers can be interpreted as their ability to convert specific inputs of production process into desired outputs. The efficient production frontier can be defined as the locus of the maximal level of output that can be produced using a given level of input. If prices of inputs are available, one can consider a cost frontier determined by the minimal cost of producing a desired level of output. The technical efficiency of a particular producer is then determined by an appropriate measure of the distance between the geometrical point in the input-output space, that characterizes the producer, and the optimal frontier, where optimality is defined in terms of various economic assumptions.
In practice, the attainable set and the shape of its boundaries are unknown, therefore the efficiency of a given producer is unknown. All these unknown quantities must be estimated based on a sample of observed producers. From a statistical point of view, this problem is related to the problem of estimating the support of a multivariate random variable, subject to various shape constraints induced by corresponding economic assumptions.
In this presentation we summarize and discuss the most important statistical results available in the literature on nonparametric efficiency estimation.

• Thursday, May 4, 2023, 10:00 AM:
  Soluții periodice în timp pentru interacțiunea unui fluid Newtonian cu o membrană elastică – Drd. Claudiu Mîndrilă (Charles Univ., Prague)
  

Abstract: Considerăm un domeniu 3D mărginit și neted care conține un fluid Newtonian care verifică ecuațiile Navier-Stokes. O parte a frontierei domeniului are atașată o membrană elastică plată care se poate mișca doar în direcție normală , iar viteza membranei este egală cu cea a fluidului de pe frontieră. Sistemul conține și o forțare externă care este presupusă perodică în timp. Arătăm că acest sistem admite (cel puțin) o soluție slabă periodică în timp dacă magnitudinea forțelor (în normă L^2) și a volumului domeniului în timp este mărginită de o anumită constantă ce depinde doar de domeniu, perioada mișcării, constante de material.
Rezultatele au fost obținut în colaborare cu S. Schwarzacher (Univ. Uppsala).

Referințe:

• 1. Time-Periodic Weak Solutions for an Incompressible Newtonian Fluid Interacting with an Elastic Plate, with S. Schwarzacher, SIAM Journal on Math. Analysis, Vol. 54, Issue 4, (2022). D.O.I.: https://doi.org/10.1137/21M1458946 disponibil   și la https://arxiv.org/abs/2111.06239v2
  2. Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions, with  S. Schwarzacher,  disponibil   și la https://arxiv.org/abs/2303.13625

• Thursday, April 6, 2023, 10:00 AM:
  On some nonlinear PDE’s with relevance in economics – CSI Dr. Gabriel Eduard Vîlcu (ISMMA)
  

Abstract: The Monge-Ampère equation is a nonlinear second-order partial differential equation that arises in a natural way in differential geometry and has applications to production models in economics. On the other hand, the constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations (called the CES system). We construct the exact solutions for the Monge-Ampère equation and CES system under some special conditions. Several open problems are also discussed.

• Tuesday, March 28, 2023, 10:00 AM:
  Principii de maximum pentru P-funcții și aplicații – Dr. Cristian Enache (American University of Sharjah, Emiratele Arabe Unite)
  

Abstract: În această prezentare vom analiza o serie de rezultate privind principiile de maxim pentru P-funcții și aplicațiile lor în studiul ecuațiilor cu derivate parțiale. Mai precis, vom arăta cum pot fi folosite astfel de principii de maxim în probleme de interes fizic sau geometric, pentru a obține diferite estimări a priori, inegalități izoperimetrice, rezultate de simetrie, rezultate de convexitate, forma unor frontiere libere și rezultate de tip Liouville.

• Tuesday, March 14 and April 11, 2023, 10:00 AM:
  The security of online activities – Dr. Silviu-Laurențiu Vasile (ISMMA)
  

Abstract: In our daily activities we constantly interact with series of on-line services which may suppose also a different set of vulnerabilities from the perspective of shared information’s. Common things such as email, wireless network, authentication, authorization can hide a list of technical notions that I will point out in this presentation. I will describe some technical aspects that can be useful in identifying spam messages, checking security of a connection or a malicious site. In the end, I will recommend some measures that may be useful to limit exposure on the Internet.

• Tuesday, March 7, 2023, 10:00 AM:
  Asymptotic behaviour of a one-dimensional avalanche model through a particular stochastic process – Dr. Oana-Valeria Lupașcu-Stamate (ISMMA)
  

Abstract: We develop the study of a binary coagulation-fragmentation equation which describes the avalanches phenomena. We construct first an adapted stochastic process and obtain its behaviour to the equilibrium. Our model is based on self-organized critical (SOC) systems and in particular on a simple sand pile model. Furthermore, we define a stochastic differential equation for this process and propose a numerical method in order to approximate the solution. The key point of our work is a new interpretation of the avalanches phenomena by handling stochastic differential equations with jumps and the analysis of the in-variant behaviour of the stochastic process. The results are obtained jointly with Mădălina Deaconu (Nancy).

• Tuesday, December 20, 2022, 11:00 AM:
  Problema de control H_∞ pentru sisteme parabolice liniare – Dr. Gabriela Marinoschi (ISMMA)
  

Abstract: Se prezintă cadrul general al problemei de stabilizare H_∞ cu control feedback în spații infinit dimensionale pentru probleme parabolice. Se rezolvă o problema de control H_∞ pentru o ecuație parabolică liniară singulară.

• Tuesday, November 15, 2022, 11:00 AM:
  A modified SIR model for Covid-19 spread prediction using neural networks – Drd. Marian Petrica
  

Abstract: We propose an analysis in three stages of Covid19 spread prediction. The first stage is based on the classical SIR model which we do using a neural network. This provides a first set of daily parameters. In the second stage we propose a refinement of the SIR model in which we separate the deceased into a distinct category. By using the first estimate and a grid search, we give a daily estimation of the parameters. The third stage is used to define a notion of turning points (local extremes) for the parameters. We call a regime the time between these points. We outline a general way based on time varying parameters of SIRD to make predictions.

• Thursday, November 3, 2022, 11:00 AM:
  Ecuații eliptice cu coeficienți variabile aleatoare – Prof. Victor Nistor (Institut Élie Cartan de Lorraine, Metz, Franța)
  

Abstract: In prezentarea mea, voi considera o ecuatie eliptica de forma ∑_i;j ∂_i(a_ij∂_ju) = f (si generalizari ale ei). In practica, coeficientii a_ij adesea reprezinta proprietati ale materialelor constitutive. Aceste proprietati nu sunt intotdeauna cunoscute cu exactitate. Din aceasta cauza este important ca acesti coeficienti a_ij sa fie considerati ca variabile aleatoare. Rezultatul principal este ca daca acesti coeficienti urmeaza o lege log-normala, atunci norma solutiei u intr-un spatiu Sobolev H^k este in toate spatiile L^p, p<∞, ca variabila aleatoare.
Colaborare cu M. Kohr, S. Labrunie si H. Mohsen.

• Seminarul va avea loc on-site, în sala “Octav Onicescu”, etaj 4, sala nr. 4331.
  

• Tuesday, October 25, 2022, 10:00 AM:
  O scurta introducere în machine learning – Drd. Vlad Raul Constantinescu
  

Abstract: O sa începem prin a defini problema de învățare automată. Vom prezenta ce metode numerice se folosesc pentru antrenarea algoritmilor de machine learning și ce rezultate de convergență există în literatură. Și în final vom explica ce este o rețea neuronală și care sunt problemele deschise în zona de deep learning.

• Seminarul va avea loc on-site, în sala “Octav Onicescu”, etaj 4, sala nr. 4331.
  

• Thursday, March 24, 2022, 10:00 AM:
  The Schrodinger equation on quantum metric graphs – Dr. Andreea Grecu
  

Abstract: We discuss dispersive properties and Hardy uncertainty principle for the linear Schrodinger equation on quantum metric graphs, together with some well-posedness results for the nonlinear equation, in the deterministic case and with random and white noise dispersion.

• Tuesday, June 29, 2021:
  Mathematica presentation at Institute of Mathematical Statistics and Applied Mathematics – Jon Mcloone (Wolfram)
  

Description: Find out how you can leverage our ready-to-use data, powerful statistical analysis tools and state-of-the-art symbolic and numerical computation to elevate your workflow. The presentation will focus on Mathematica latest features, numeric and symbolic computation, solving ODE, PDE, optimisation, statistics. A Q&A session will also take place with Jon Mcloone, who is a certified Instructor and the Director of Technical Services, Communication and Strategy at Wolfram.

• Monday, May 10, 2021:
  On the stochastic orders of two multivariate distributions families – Drd. Luigi Catană
  

Abstract: We present the results obtained on the stochastic orders for two families of multivariate distributions: the uniform distribution on a convex set and a type of Pareto distribution proposed by Mardia.

• Tuesday, April 13, 2021:
  Time-domain moment matching for nonlinear dynamical systems of ODEs – Something to compute… – Dr. Tudor Ionescu (ISMMA)

Abstract: For nonlinear systems, high dimension and complexity are two major issues in dealing with models suitable for (nonlinear) analysis, simulation and control. Even if the high dimension is reduced, complexity may increase as opposed to linear systems where these notions are identical. Therefore, suitable model reduction is called for. This has been studied recently in the time-domain moment matching framework, where suitable notions of moment have been introduced and families of parameterized reduced order models have been developed. The degrees of freedom are used to enforce/preserve properties or topology, increase accuracy, etc. Same ideas apply to the case of infinite-dimensional systems such as, e.g., time-delayed systems, PDE-based models, etc. where families of finite-dimensional systems can be achieved based on moment matching (download paper).

• Thursday, March 4, 2021:
  Asupra unei ecuaţii neliniare de evoluţie într-un spaţiu abstract de stări în sensul lui Davies – Dr. Cecil Pompiliu Grunfeld (ISMMA)

Rezumat: Rezultate recente privind existenţa şi unicitatea soluţiilor globale în timp ale problemei Cauchy pentru o ecuaţie neliniara de evoluţie, formulată într-un spaţiu abstract de stări în sensul lui Davies (spaţiu Banach ordonat real, cu norma aditivă pe conul pozitiv) sunt prezentate în contextul aplicării la modele neliniare de evoluţie, specifice mecanicii cuantice.

• Tuesday, July 9, 2019:
  Phase-field modeling of prostate cancer growth and treatments – Guillermo Lorenzo (Computational Mechanics & Advanced Materials Group, Department of Civil Engineering and Architecture, University of Pavia, Italy)

Abstract: Prostate cancer is a major health problem among aging men worldwide. Nowadays, most cases are detected and treated at an early stage, when the tumor is still localized within the prostate. However, the limited individualization of the clinical management of this disease has led to significant overtreatment, which may cause adverse side-effects and reduce the patient’s quality of life. Moreover, current diagnostic methods may underestimate tumor aggressiveness, which may hence survive the prescribed treatment and compromise the patient’s life expectancy. Mathematical oncology is a new trend that can contribute to overcome these issues. This approach relies on the use of mathematical models and computer simulations to predict clinical outcomes and design optimal treatments on a patient-specific basis. In this context, I will present mathematical models to describe the evolution of organ-confined prostatic tumors based on key mechanisms and I will show relevant simulations both in experimental setups and organ-scale, patient-specific scenarios. As the development of this disease can be interpreted as an evolving interface problem between healthy and tumoral tissue, these models are based on the phase-field method to account for the coupled dynamics of both tissues. Isogeometric analysis permits to accurately and efficiently address the nonlinearity of the models, the complex anatomy of the prostate, and the intricate tumoral morphologies. The mathematical models and isogeometric methods presented herein provide a patient-specific computational framework to forecast prostate cancer evolution at organ scale, investigate the mechanisms of prostatic tumor growth, and explore optimal treatment strategies.

• Tuesday, July 9, 2019:
  Optimal control for a prostate tumor growth model – Gabriela Marinoschi (ISMMA)

Abstract: We present a phase-field type model consisting of three equations, one accounting for the healthy to tumoral cell transition described by an order parameter, coupled with the equation for the variation of the nutrient. The third equation expresses the evolution of the prostate-specific antigen (PSA) influenced by the order parameter and nutrient concentration. The purpose is to control this system via the nutrient source and a treatment scheme such that to meet some objectives, especially the decrease of the tumor.

• Tuesday, February 19, 2019:
  BEM-CGM algorithms for inverse boundary value problems in 2D steady-state anisotropic heat conduction – Liviu Marin (University of Bucharest and ISMMA)

Abstract: We investigate the numerical reconstruction of the missing thermal boundary conditions on an inaccessible part of the boundary in the case of steady-state heat conduction in anisotropic solids from the knowledge of over-prescribed noisy data on the remaining accessible boundary. This inverse boundary value problem is approached by employing a variational formulation which transforms it into an equivalent control problem. Four such approaches are presented and both a parameter-dependent and a parameter independent gradient based algorithms are obtained in each case. The numerical implementation is realized for the 2D case by employing the boundary element method (BEM) and assuming that the available boundary data are either exact or noisy. For perturbed Cauchy data the numerical solution is stabilized/regularised by stopping the iterative procedure according to Morozov’s discrepancy principle.

• Thursday, March 29, 2018:
  Rolul inegalitatilor de tip Hardy în teoria spatiilor de functii – Petru Mironescu (University Claude Bernard Lyon, France)

Abstract: În prima parte, voi ilustra rolul fundamental al inegalităților lui Hardy în teoria spațiilor de funcții prin două exemple de bază: calculul funcțional în spațiile Sobolev și teoria spațiilor Sobolev cu ponderi. În partea a doua, voi prezenta aplicații ale acestor teorii la studiul funcțiilor Sobolev unimodulare.

• Thursday, October 19, 2017:
  An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology – Cecilia Cavaterra (University of Milan, Italy)

Abstract: We considered an inverse boundary value problem for the monodomain equation, which describes the evolution of the electric potential in the heart tissue. The goal is the determination of a small inhomogeneity inside the domain occupied by the heart from observations of the potential on the boundary. Such a problem is related to the detection of myocardial ischemic regions, characterized by severely reduced blood perfusion and consequent lack of electric conductivity. Both theoretical analysis and numerical reconstruction techniques are developed.