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Prossimi seminari del Dipartimento di Matematica
tra circa 5 ore
Venerdì
17 maggio
Francesco Russo
nel ciclo di seminari: STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ (POSSIBLE SINGULAR) COEFFICIENTS
Seminario di probabilità
ore
11:00
presso - Aula Da Stabilire -
Lunedì
20 maggio
Nikolaos Pallikarakis
Seminario di analisi numerica
ore
10:00
presso Seminario II
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 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 sym-
metric potentials and the inverse transmission eigenvalue problem for spherically sym-
metric 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 source problem, to identify the number, posi-
tions, and strengths of hidden line sources inside a dielectric cylinder. Using classification
Neural Networks, we show that we can predict the unknown number of sources with high
accuracy. We complete this talk with a discussion on an ongoing work for the inverse
source problem to recover the positions and strengths of the sources. 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.
1. N. Pallikarakis and A. Ntargaras, Application of machine learning regression models
to inverse eigenvalue problems, Computers & Mathematics with Applications, 154
(2024).
2. N. Pallikarakis, A. Kalogeropoulos and N. L. Tsitsas, Predicting the number of line
sources inside a cylinder using classification neural networks, (2024), (to appear
in: 2024 IEEE Int. Symp. Antennas Propag. and ITNC-USNC-URSI Radio Sci.
Meet.).
3. N. Pallikarakis, A. Kalogeropoulos and N. L. Tsitsas, Exploring the inverse line-
source scattering problem in dielectric cylinders with deep neural networks, (2024),
(submitted - under review).
Lunedì
20 maggio
Francesco Russo
nel ciclo di seminari: STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ (POSSIBLE SINGULAR) COEFFICIENTS
Seminario di probabilità
ore
11:00
presso - Aula Da Stabilire -
Martedì
21 maggio
Federico Caucci
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore
11:00
presso Aula Vitali
Tba
Martedì
21 maggio
Ermanno Lanconelli
nel ciclo di seminari: MATEMATICI NELLA STORIA
Seminario di analisi matematica, storia della matematica
ore
16:00
presso Aula Pincherle
seminario on line •
'' Nel primo decennio del 1900 si verificò un' improvvisa catalizzazione di idee e metodi che si erano lentamente accumulati nel corso del XIX secolo. Fra i catalizzatori di questo rapido processo vi furono i risultati e le idee presenti nella tesi di dottorato di Lebesgue del 1902''(J. Dieudonné).
L'opera di Lebesgue e le ampie generalizzazioni ad essa seguite hanno modificato i concetti di misura e di integrale così profondamente da rendere la teoria dell'integrazione una esclusiva creazione del ventesimo secolo, nonostante la sua idea originaria risalga ad Archimede.
L'Analisi Matematica negli spazi funzionali infinito dimensionali, nata quasi contemporaneamente all'integrale di Lebesgue, deve a quest'ultimo i suoi più proficui sviluppi. Fra questi la definitiva dimostrazione del ''Principio di Dirichlet'', dato per scontato - a torto - da Riemann, e inserito da Hilbert nell'elenco dei problemi da lui posti al Congresso internazionale di Matematica del 1900.
Mercoledì
22 maggio
Lars Halvard Halle
nell'ambito della serie: TOPICS IN MATHEMATICS 2023/2024
Seminario di algebra e geometria
ore
11:00
presso Aula Cremona
In this talk, I will give a leisurely and subjective introduction to Arithmetic Geometry, focusing on explicit examples and some selected questions. I aim to illustrate how basic questions in Number Theory can naturally lead to rich and interesting topics in Algebra and Geometry. If time permits, I will also indicate how my own research and interests fits into this picture.
Mercoledì
22 maggio
Antonello Pesce
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore
11:00
presso Aula Arzelà
TBA
Mercoledì
22 maggio
Fabrizio Lillo
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di finanza matematica
ore
12:00
Mercoledì
22 maggio
Francesco Russo
nel ciclo di seminari: STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ (POSSIBLE SINGULAR) COEFFICIENTS
Seminario di probabilità
ore
15:00
presso - Aula Da Stabilire -
Venerdì
24 maggio
Francesco Russo
nel ciclo di seminari: STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ (POSSIBLE SINGULAR) COEFFICIENTS
Seminario di probabilità
ore
11:00
presso - Aula Da Stabilire -
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
Luca Motto Ros
nell'ambito della serie: LOGIC, CATEGORIES, AND APPLICATIONS SEMINAR
Seminario interdisciplinare
ore
14:00
presso Seminario I
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
Umberto Guarnotta
Seminario di analisi matematica
ore
17:00
presso Aula Arzelà
seminario on line •
collegamento al meeting
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
Cristian Micheletti
Seminario di algebra e geometria, interdisciplinare
ore
09:30
presso Aula Arzelà
Giovedì
30 maggio
Marco Squassina
nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI
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.
Lunedì
03 giugno
Ulugbek Kamilov
nel ciclo di seminari: OPTIMIZATION BASED MACHINE LEARNING FOR COMPUTATIONAL IMAGING
Seminario di analisi numerica
ore
08:00
presso plesso Belmeloro
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.
Lunedì
03 giugno
Chandler, Edward
nel ciclo di seminari: OPTIMIZATION BASED MACHINE LEARNING FOR COMPUTATIONAL IMAGING LAB
Seminario di analisi numerica
ore
08:00
presso plesso Belmeloro
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;
Martedì
04 giugno
Lorenzo Rosasco
Seminario di analisi numerica
ore
08:00
presso plesso Belmeloro
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.
Mercoledì
05 giugno
Bruno Franchi
nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI
Seminario di analisi matematica
ore
16:00
presso - Aula Da Stabilire -
seminario on line •
Mercoledì
05 giugno
Antonella Guidazzoli
Seminario di analisi numerica
ore
16:30
presso plesso Belmeloro, Via Andreatta 8
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
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.
Giovedì
06 giugno
Giulia Pinto
Seminario di analisi numerica
ore
16:30
presso plesso Belmeloro, Via Andreatta 8, Bologna
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
Angelo Carraggi
Seminario di analisi numerica
ore
16:30
presso plesso Belmeloro, via Andreatta 8, Bologna
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.
Domenica
09 giugno
Michaël Unser
nel ciclo di seminari: FUNCTIONAL OPTIMIZATION METHODS FOR MACHINE LEARNING
Seminario di analisi numerica
ore
08:00
presso plesso Belmeloro
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.
Lunedì
10 giugno
Giuseppe Vicidomini
Seminario di analisi numerica
ore
16:30
presso plesso Belmeloro, Via Andreatta 8, Bologna
Lunedì
10 giugno
Giuseppe Vicidomini
Seminario di analisi numerica
ore
16:30
presso Aula E, plesso Belmeloro, Via Andreatta 8, Bologna
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
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore
12:00
presso Aula Arzelà
TBA
Giovedì
20 giugno
Simone Ciani
nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI
Seminario di analisi matematica
ore
16:00
presso - Aula Da Stabilire -
24/06/2024
28/06/2024
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.
Giovedì
27 giugno
Alessia Kogoj
nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI
Seminario di analisi matematica
ore
16:00
presso - Aula Da Stabilire -
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.
15/07/2024
19/07/2024
19/07/2024
Conference
da lunedì 15 luglio 2024
a venerdì 19 luglio 2024
Conferenza in onore di Dick Canary