Seminari - Dipartimento Computer Science Seminari - Dipartimento Computer Science validi dal 18.01.2022 al 18.01.2023. Cofibrant objects in representation theory - new results and applications. Relatore: Rudradip Biswas; Provenienza: Tata Institute of Fundamental Research; Data inizio: 2022-01-18; Ora inizio: 15.30; Note orario: live on zoom; Referente interno: Lleonard Rubio Y Degrassi. Tue, 18 Jan 2022 15:30:00 +0100 Wide subcategories from cosilting torsion pairs Relatore: Francesco Sentieri; Provenienza: University of Verona; Data inizio: 2022-01-18; Ora inizio: 17.00; Note orario: Aula C, CV1; Referente interno: Lleonard Rubio Y Degrassi. Tue, 18 Jan 2022 17:00:00 +0100 Young Researcher Seminars, Math, Applications and Models Relatore: Matteo Garbelli // Sara Galasso; Provenienza: Università di Trento/Università di Verona // Università degli Studi di Padova; Data inizio: 2022-01-19; Ora inizio: 15.30; Riassunto: First speaker : Matteo Garbelli (Universitagrave; di Trento/Universitagrave; di Verona) Title: Deep Learning and Mean Field Optimal Control from a Stochastic Optimal Control perspective Abstract: In this talk, we illustrate an effective proposal for the mathematical formulation of Deep Learning (DL) based approaches within the contexts of Stochastic Optimal Control (SOC) and Mean-Field Control (MFC). Following a dynamical system perspective, we conduct an in-depth analysis of the Supervised Learning (SL) procedures characterizing Neural Network (NN) models and we show how to translate a SL problem into an optimal (stochastic) MFC one. We also derive two methods to solve this latter: the first is obtained considering the Hamiltonndash;Jacobindash;Bellman (HJB) approach in the Wasserstein space of measures, while the second is based on the MF-Pontryagin maximum principle, providing necessary, weaker, condition the solution must satisfy. Second speaker : Sara Galasso (Universitagrave; degli Studi di Padova) Title: Synchronization in unforced mechanical systems with dissipation Abstract: Every mechanical system has intrinsically some sources of dissipation, with the consequence that the mechanical energy decreases along motions, at a certain rate in time. In fact, physical processes are typically affected by several such sources, each of which might possibly interest only some parts of the system. Mathematically, a first approach -- which allows the problem to be studied in the context of conservative systems -- is not to include in the model the dissipation. This is physically reasonable if the damping is negligible and if one is not interested in the dynamics for asymptotically long times. An alternative -- particularly important in the applications -- is to include in the model forcing terms that restore the energy lost. In between, the reality of dissipative unforced mechanical systems is variegated and challenging. In general, in the study of dissipative systems, questions regarding the asymptotic behaviour become relevant. For example: What can be said about the long-term dynamics when the damping is only partial, at least at first approximation? What about the mid-long-term dynamics? In this talk, we will try to better address these issues, and we shall see, in particular, the implications on the emergence of patterns and collective behaviours -- such as synchronization --, which actually motivated my research as a PhD student. Specifically, we will discussmodels of coupled pendula, both finite- and infinite-dimensional, revisiting some aspects of the well-known Huygens#39;s pendulum clocks. Sala riunioni Secondo Piano Ca#39; Vignal 2 Zoom link : Wed, 19 Jan 2022 15:30:00 +0100 Cyclic (Co)Inductive Reasoning Relatore: Liron Cohen; Provenienza: Ben-Gurion University; Data inizio: 2022-01-25; Ora inizio: 16.30; Note orario: Zoom Meeting; Referente interno: Peter Michael Schuster; Riassunto: Non-well-founded (cyclic) proof theory provides an alternative, more robust approach for formalizing implicit(co)inductive reasoning. This approach has been extremely successful in recent years in supporting implicitinductive reasoning, but is not as well-developed in the context of coinductive reasoning. In this talk I will review thegeneral method of non-well-founded proofs, and put forward a concrete natural framework for (co)inductivereasoning, based on (co)closure operators. This offers a concise framework in which inductive and coinductivereasoning are captured as we intuitively understand and use them. Using this framework I will aim to demonstrate theenormous potential of non-well-founded deduction, both in the foundational theoretical exploration of(co)inductive reasoning and in the provision of proof support for (co)inductive reasoning within (semi-)automated proof tools. Link a Zoom Meeting ID: 858 4037 9195 Passcode: 383761. Tue, 25 Jan 2022 16:30:00 +0100 Workshop "Reducing complexity in algebra, logic, combinatorics" Relatore: several speakers; Provenienza: from project REDCOM; Data inizio: 2022-02-02; Ora inizio: 15.30; Note orario: live on zoom; Referente interno: Lleonard Rubio Y Degrassi; Riassunto: 15:00-15:30 Gloria Tabarelli, University of Verona Graphs with large palette index 15:40-16:10 Francesca Fedele, University of Padova Ext-projectives in subcategories of triangulated categories Coffee break 16:40 -17:10 Ingo Blechschmidt, Universitauml;t Augsburg Without loss of generality, any reduced ring is a field For further information see here. Wed, 2 Feb 2022 15:30:00 +0100 Numerical aspects of high-performance and scientific computing (MAT/08 - 2 ECTS) Relatore: Lukas Einkemmer; Provenienza: University of Innsbruck; Data inizio: 2022-03-28; Referente interno: Marco Caliari; Riassunto: From March 28 to April 8 - 2022. Please contact. Prof. Marco Caliari for info and details. The recent change towards massively parallel compute architectures (such as graphic processing units, GPUs, and supercomputers with millions of cores) has major implications for the design of efficient numerical algorithms. In fact, in many situations looking at the sequential performance of an algorithm gives a very misleading picture of its actual performance in real-world applications (e.g. performing computer simulations to optimize aircraft in an industrial setting or understanding the complex dynamics inside fusion reactors). To fully exploit modern high-performance computing systems requires algorithms that parallelize well (i.e. can be distributed into largely independent tasks). Many of the classic algorithms, such as FFT or spline interpolation, however, require a large amount of communication between these tasks. Moreover, due to their increased arithmetic throughput, modern computer systems favor higher-order methods. This requires the design of new numerical algorithms as well as to develop theoretical tools to help us understand which algorithms work well for which type of problems. In this mini-course we will discuss how such numerical algorithms are constructed, consider their accuracy, and discuss the aspects relevant to implementing them efficiently. In particular, we will consider, both from an algorithmic as well as from a high-performance computing viewpoint, what is required to conduct large-scale computer simulations of kinetic plasma dynamics using a dynamical low-rank approach. We will also consider some examples of industrial interest (e.g. fluid flow over an airflow). Mon, 28 Mar 2022 00:00:00 +0200