Prossimi seminari del Dipartimento di Matematica

Giovedì
23 maggio
We introduce a novel procedure for computing an SVD-type approximation of a tall matrix A. Specifically, we propose a randomization-based algorithm that improves the standard Randomized Singular Value Decomposition (RSVD). Most significantly, our approach, the Row-aware RSVD (R-RSVD), explicitly constructs information from the row space of A. This leads to better approximations to Range(A) while maintaining the same computational cost. The efficacy of the R-RSVD is supported by both robust theoretical results and extensive numerical experiments. Furthermore, we present an alternative algorithm inspired by the R-RSVD, capable of achieving comparable accuracy despite utilizing only a subsample of the rows of A, resulting in a significantly reduced computational cost. This method, that we name the Subsample Row-aware RSVD (Rsub-RSVD), is supported by a weaker error bound compared to the ones we derived for the R-RSVD, but still meaningful as it ensures that the error remains under control. Additionally, numerous experiments demonstrate that the Rsub-RSVD trend is akin to the one attained by the R-RSVD when the subsampling parameter is on the order of n, for a m×n A, with m >> n. Finally, we consider the application of our schemes in two very diverse settings which share the need for the computation of singular vectors as an intermediate step: the computation of CUR decompositions by the discrete empirical interpolation method (DEIM) and the construction of reduced-order models in the Loewner framework, a data-driven technique for model reduction of dynamical systems.
Sabato
25 maggio
Giacomo Bormetti, Università degli Studi di Pavia
Seminario interdisciplinare
ore 15:00
presso Aula Tonelli
seminario on line •
Sabato
25 maggio
Francesca Morselli, Università degli Studi di Genova
Seminario interdisciplinare
ore 16:20
presso Aula Tonelli
seminario on line •
Lunedì
27 maggio
Introduction to pure jump processes: definitions of (marked) point processes, random measures, and associated counting process.
We show that the natural operation of connected sum for graphs can be used to prove at once most of the universality results from the literature concerning graph homomorphism. In doing so, we significantly improve many existing theorems and solve some natural open problems. Despite its simplicity, our technique unexpectedly leads to applications in quite diverse areas of mathematics, such as category theory, combinatorics, classical descriptive set theory, generalized descriptive set theory, model theory, and theoretical computer science. (Joint work with S. Scamperti)
Martedì
28 maggio
The aim of the talk is to analyze an evolutionary Φ- Laplacian problem, with singular and convective reactions: u_t -A u= f+g .The differential operator A considered is an elliptic operator, driven by a Young function Φ, while the reaction terms are Carathéodory functions obeying suitable growth conditions. The problem possesses three features of interest: • the operator A can be non-homogeneous, and with unbalanced growth; • the reaction term f is singular (i.e., it behaves like u^{−γ} with γ ∈ (0, 1)) and f(x, ·) can be non-monotone); • the reaction term g is convective (i.e., it depends on ∇u). We will first introduce the functional setting of the problem, by recalling the most relevant function spaces involved and their basic properties. Secondly, the main issues concerning both singular and convective terms are highlighted, together with the sub-solution and freezing techniques. Finally, we will briefly sketch the proof of our existence result, based on a priori estimates and a semi-discretization (in time) procedure. The seminar will have an introductory fashion, under the trend proposed by the cycle ASK (Analysis Student Kernel), for young analysis researchers, at the University of Bologna (https://sites.google.com/view/askbologna/home?authuser=1).
Mercoledì
29 maggio
Agnese Barbensi
Seminario di algebra e geometria, interdisciplinare
ore 09:30
presso Aula Arzelà
The last few decades have seen important advances in understanding the consequences of topological constraints in many biological systems. A famous example is the case of knotted proteins, where the presence of entanglement is thought to influence their folding behaviour and mechanisms. More recently, topological data analysis has been providing an effective computational window, aimed at characterising a variety of natural phenomena in terms of their topological features. In this talk, we present techniques and results in computational and applied topology, interpreted broadly, with a focus on applications to biopolymers.
Mercoledì
29 maggio
Cristian Micheletti
Seminario di algebra e geometria, interdisciplinare
ore 11:00
presso Aula Arzelà
I will report on a series of studies where we used molecular dynamics simulations and various models to study how the properties of DNA and RNAs are affected by the presence of knots and other forms of structural entanglement[1]. I will first consider model DNA plasmids that are both knotted and supercoiled, and discuss how the simultaneous presence of knots and supercoiling creates long-lived multi-strand interlockings that might may be relevant for the simplifying action of topoisomerases. I next consider how entangled nucleic acids behave when driven through narrow pores[2-4], a setting that models translocation through the lumen of enzymes, and discuss the biological implication for a certain class of viral RNAs[4]. Bibliography [1] L. Coronel, A. Suma and C. Micheletti, "Dynamics of supercoiled DNA with complex knots", Nucleic Acids Res. (2018) 46 , 7533 [2] A. Suma, V. Carnevale and C. Micheletti, Nonequilibrium thermodynamics of DNA nanopore unzipping, Phys. Rev. Lett., (2023), 130 048101 [3] A. Suma, A. Rosa and C. Micheletti, Pore translocation of knotted polymer chains: how friction depends on knot complexity, ACS Macro Letters, (2015), 4 , 1420-1424 [4] A. Suma, L. Coronel, G. Bussi and C. Micheletti, "Directional translocation resistance of Zika xrRNA” Nature Communications (2020), 11 , art no. 3749
Mercoledì
29 maggio
Mohamed Elhamdadi
Seminario di algebra e geometria, interdisciplinare
ore 12:00
presso Aula Arzelà
Protein are linear molecular chains that often fold to function. We will introduce some algebraic structures, called bondles, modeled on projections of proteins. We will discuss colorings of these projections by bondles and construct the coloring invariant which is used to distinguish proteins. We will also discuss an enhancement of this invariant based on introducing some weights at the bonds thus giving the enhanced invariant as a state sum invariant.
Giovedì
30 maggio
The Poisson point process and Watanabe theorem. Introduction to stochastic integrals with respect to finite variation processes.
Giovedì
30 maggio
Marco Squassina
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
seminario on line • collegamento al meeting
We present some new results about the concavity (up to a transformation) of positive solutions for some classes of quasi-linear elliptic problems, including nonautonomous cases.
Ciclo: Optimization based machine learning for computational imaging Abstract: In many scientific and medical settings, we cannot directly observe images of interest, such as a person’s internal organs, the microscopic structure of materials or cells, or distant stars and galaxies. Rather, we use MRI scanners, microscopes, and telescopes to collect indirect data that require sophisticated algorithms to form an image. Historically, these methods have relied on mathematical models of simple image structures to improve the quality and resolution of the resulting images. More recent efforts harness vast collections of images to train computers to learn more complex models of image structure, yielding more accurate and higher-resolution images than ever. These new methods lead to a renaissance in computational imaging and new insights into designing neural networks and other machine learning models in a principled manner, jointly leveraging both training data and physical models of how imaging data is collected. In this course, we will cover some exciting new directions in this emerging area, such as (a) plug-and-play methods; (b) variational networks and deep unrolling; (c) deep equilibrium models; (d) learning regularization functionals; (e) scalable and mini-batch OPML; (f) diffusion models; (g) self-supervised OPML approaches; (h) robustness and domain adaptation.
Abstract: In many scientific and medical settings, we cannot directly observe images of interest, such as a person’s internal organs, the microscopic structure of materials or cells, or distant stars and galaxies. Rather, we use MRI scanners, microscopes, and telescopes to collect indirect data that require sophisticated algorithms to form an image. Historically, these methods have relied on mathematical models of simple image structures to improve the quality and resolution of the resulting images. More recent efforts harness vast collections of images to train computers to learn more complex models of image structure, yielding more accurate and higher-resolution images than ever. These new methods lead to a renaissance in computational imaging and new insights into designing neural networks and other machine learning models in a principled manner, jointly leveraging both training data and physical models of how imaging data is collected. In this course, we will cover some exciting new directions in this emerging area, such as (a) plug-and-play methods; (b) variational networks and deep unrolling;
Stochastic integral with respect to finite variation processes: integration by parts formula and Itô’s formula.
L'insegnamento fornisce le nozioni necessarie per la comprensione e l'utilizzo dei principali algoritmi di apprendimento. Verranno introdotte le definizioni fondamentali relative ai problemi di apprendimento supervisionato e non supervisionato. Poi verranno presentati alcuni approcci per l'apprendimento statistico supervisionato, come metodi locali e regularization networks, sia nel caso lineare che nonlineare. Verranno altresì introdotte le reti neurali. Il corso conterrà anche un'introduzione a problemi di apprendimento non supervisionato, come clustering a dimensionality reduction. Gli argomenti trattati dal punto di vista teorico, saranno affrontati anche da un punto di vista numerico durante le lezioni in laboratorio.
Martedì
04 giugno
Andrea Di Lorenzo
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 11:00
presso - Aula Da Stabilire -
Blow-ups are fundamental tools in algebraic geometry, and there are several results (e.g the famous Castelnuovo's theorem) that can be used to determine when a variety is obtained as a blow-up of a smooth variety along a smooth center. Weighted blow-ups play a similar role for stacks. In this talk I will present a criterion for finding out if a smooth DM stack is a weighted blow-up. I will apply this result for showing that certain alternative compactifications of moduli of marked elliptic curves are obtained via weighted blow-ups (and blow-downs). This in turn will prove to be useful in order to compute certain invariants, like Chow rings or Brauer groups. First part of this talk is a joint work with Arena, Inchiostro, Mathur, Obinna and Pernice; the second part of this talk is a joint work with L. Battistella.
Introduction to stochastic differential equations driven by pure jump processes: the predictable sigma-algebra and a well-posedness result.
Mercoledì
05 giugno
Mercoledì
05 giugno
This talk will present some case studies on using artificial intelligence (AI) to preserve , study and valorize cultural heritage digital assets. At the heart of the approach is recognizing the need for a human AI frameworks in which data scientists and domain experts collaborate synergistically. Moreover promoting interdisciplinary partnerships is essential touphold ethical principles and serve the public good.
06/06/2024
07/06/2024
Conference
da giovedì 06 giugno 2024 a venerdì 07 giugno 2024
The initative aims at gathering and bringing together young researchers at early stages of their careers in the field of nonlocal/nonlinear elliptic equations and calculus of variations. Ten talks will take place on two different days to leave plenty of room for discussion and interaction among speakers and participants.
Over the years since 1970, Magnetic Resonance Imaging (MRI) has developed into as one of the preferred choices for many radiological exams today. It relies primarily on its ability to detect water, which constitutes a significant portion of most tissues (around 70-90%). Changes in the water content and properties within tissues due to diseases or injuries can be substantial, rendering MRI highly effective in diagnosis due to its sensitivity. ESAOTE specializes in designing MRI systems with low-field technology (0.25 T to 0.4 T), offering several advantages including improved patient comfort, cost reduction, less demanding installation requirements, and lower energy consumption. However, the trade-off for using low-field MRI is a decrease in signal strength, often requiring longer scan times to achieve high-quality diagnostic images. Hence, there is a need for techniques to accelerate image acquisition. Specifically, ESAOTE has developed the Speed-Up technique, inspired to compressed-sensing techniques. Recent advances in collaboration with the Amsterdam University Medical Center aim to improve the reconstruction algorithm using artificial intelligence (AI), while maintaining the diagnostic accuracy of traditional, longer scans. This was achieved by optimizing the k-space undersampling scheme and reconstructions, using the Cascades of Independently Recurrent Inference Machines (CIRIM). Promising image quality was observed up to an acceleration factor of at least 2.5.
Venerdì
07 giugno
Linear stochastic differential equations: the Doléans-Dade exponential. The martingale property of the stochastic integral.
Venerdì
07 giugno
Anomaly detection is a primary need for industrial/manufacturing applications and Datalogic business, but many challenges persist. The collection and annotation of data is expensive and most of the time unpractical as the deployed systems are usually not remotely accessible. The image resolution and the frame rate require computing-intensive algorithms that often do not fit the real-time constraint on embedded devices. In this study, we propose a novel solution that, inspired by recent advancements in this field obtained by normalizing-flow and patch-based feature distribution, combines unsupervised learning with efficient processing to deploy an optimized solution to reach a high classification accuracy while working with few training samples.
Venerdì
07 giugno
Cecilia Rossi
Seminario di storia della matematica
ore 19:00
presso - Aula Da Stabilire -
La storia di Sophie Germain, una delle più brillanti menti matematiche di sempre, vissuta a Parigi tra la fine del Settecento e l’inizio dell’Ottocento, è emblematica del rapporto tra donne e scienza e solleva questioni attuali ancora oggi. Con il suo originale lavoro di ricerca e i suoi importanti contributi scientifici, Sophie Germain si è opposta alla convinzione comune del suo tempo che le donne non fossero capaci di un lavoro scientifico indipendente, cambiando per sempre il concetto di studiosa donna e guadagnandosi il titolo di matematica rivoluzionaria. Nota per gli studi sulle superfici elastiche applicati alla Tour Eiffel, ma soprattutto per i risultati significativi raggiunti nel campo della teoria dei numeri, Sophie Germain si è dovuta in più occasioni fingere uomo per riuscire a coltivare la sua passione per questa disciplina. Dedita interamente alla scienza dall’età di 13 anni, ha dialogato alla pari con i più grandi matematici della sua epoca, ricevendo il plauso, tra gli altri, di Carl Friedrich Gauss, grazie al quale l’Università di Gottinga nel 1830 le riconobbe una laurea honoris causa. Nonostante ciò, i suoi meriti e la sua identità di scienziata sono stati a lungo negati dalla comunità scientifica.
Domenica
09 giugno
Abstract: In this mini-course, we show how various forms of supervised learning can be recast as optimization problems over suitable function spaces, subject to regularity constraints. Our family of regularization functionals has two components: (1) a regularization operator, which can be composed with an optional projection mechanism (Radon transform), and (2) a (semi-)norm, which may be Hilbertian (RKHS) or sparsity-promoting (total variation). By invoking an abstract representer theorem, we obtain an explicit parametrization of the extremal points of the solution set. The latter translates into a concrete neuronal architecture and training procedure. We demonstrate the use of this variational formalism on a variety of examples, including several variants of spline-based regression. We also draw connections with classical kernel-based techniques and modern ReLU neural networks. Finally, we show how our framework is applicable to the learning of non-linearities in deep and not-so-deep networks.
Confocal laser-scanning microscopy (CLSM) has long been celebrated in life-science research for its unique blend of spatial and temporal resolution, coupled with its versatile applications. However, recent advancements in detector technology have sparked a transformative shift in CLSM, triggered by the introduction of novel single-photon array detectors. These detectors, poised to supplant single-element detectors (also known as bucket detectors), offer access to previously discarded sample information, reshaping the trajectory of CLSM. In traditional CLSM, images are generated by raster scanning a focused laser beam across the sample, with single-element detectors registering a single-intensity value at each sample position. In contrast, single-photon array detectors capture true temporal images at each scanning position, transitioning CLSM into image scanning microscopy (ISM). Image scanning microscopy transcends traditional CLSM by generating not merely a two-dimensional dataset but a five-dimensional one, incorporating four spatial dimensions and a temporal dimension. This enables the reconstruction of highly informative and super-resolved images of the sample. This seminar will delve into the foundational principles of ISM, starting with the formulation of the forward model underlying the technique. Subsequently, a maximum likelihood approach, considering Poissonian noise, will be presented for reconstructing super-resolved images from the four-dimensional spatial dataset. An extension of this framework will incorporate the temporal dimension, enabling the reconstruction of fluorescence lifetime images that integrate structural and functional sample information. Furthermore, the seminar will explore leveraging the ISM dataset and deep learning techniques to accurately estimate the point-spread function of the optical system. This has the potential to significantly enhance the quality of reconstructed super-resolved images. By elucidating these advancements and future prospects, this seminar aims to inspire researchers to harness the full potential of ISM in pushing the boundaries of biomedical imaging.
Mercoledì
19 giugno
Katia Colaneri
TBA
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore 12:00
presso Aula Arzelà
TBA
Giovedì
20 giugno
Simone Ciani
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
24/06/2024
28/06/2024
Conference
da lunedì 24 giugno 2024 a venerdì 28 giugno 2024
Noncommutativity is a broad term that occurs in many areas of mathematics. Recently, there have been major developments around noncommutative phenomena related to all fundamental aspects of mathematics. The aim of the conference is to bring together experts in these diverse areas to share new ideas, discuss major recent advances and propose possible future directions.
Martedì
25 giugno
Patrick Guidotti
Seminario di analisi matematica
ore 11:00
presso - Aula Da Stabilire -
Giovedì
27 giugno
By using a Pizzetti's 1909 idea for the classical Laplacian, we introduced a notion of asymptotic average solutions. This notion enables the pointwise solvability of every Poisson equation Lu(x)=−f(x) with continuous data f, where L belongs to a class of hypoelliptic linear partial differential operators whose classical solutions can be characterized in terms of mean value formulae.
Mercoledì
10 luglio
Christopher Eur
TBA
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 14:30
presso - Aula Da Stabilire -
15/07/2024
19/07/2024
Conference
da lunedì 15 luglio 2024 a venerdì 19 luglio 2024
Conferenza in onore di Dick Canary