Mathematicians have long been interted in rigorously understanding the conductivity properties of disordered materials at the quantum level, in particular after the work of the Nobel Prize winning American physicist Philip W. Anderson (1923-2020)
In 1990, Klein, Lacroix and Speis analyzed a well studied random operator model for an electron moving on a portion of lattice of the form Z × [0, W], W ? N and subject to a random potential, called Anderson model on the strip. They showed, in particular, that such a model boasts spectral localization on all of its energy spectrum, a well defined mathematical property that is a very powerful signature of the electron getting trapped in a region by the potential.
In thie present work, we focus on a more general model of a quantum particle with internal degrees of freedom moving in a quasi 1D random medium (disordered quantum wire), that we call "generalized Wegner Orbital Model".
In particular, we prove spectral and dynamical localization at all energies for such a model suggesting that the disordered materials belonging to the wide class described by this model are all perfect insulators.
In this talk, I will start by introducing basic concepts related to Anderson Localization in general, then move to the specific model considered in this work, and outline our proof of its spectral localization. The proof combines techniques from probability theory, spectral theory of selfadjoint operator and ergodic theory, with an unexpected algebraic twist...
In the talk, we briefly discuss the main epidemiological features of SARS-CoV-2 one year into the pandemic, giving also a short account of the public data available for Italy and of the main limits of lay analyses.
We then discuss an accurate method for short-term forecasting ICU occupancy at local level. Our approach is based on an optimal ensemble of two simple methods: a generalized linear mixed regression model which pools information over different areas, and an area-specific non-stationary integer autoregressive methodology. Optimal weights are estimated using a leave-last-out rationale.
Daily predictions between February 24th and November, 27th 2020 have a median error of 3 beds (third quartile: 8) at regional level, with coverage of 99% prediction intervals that exceeds the nominal one.
Finally we present a different method based on a modified non-linear GLM for each indicator, including the potential effect of exogenous variables, based on appropriate distributional assumptions and a logistic-type growth curve. This allows us to accurately predict important characteristics of the epidemic (e.g., peak time and height).
Based on joint works with Pierfrancesco Alaimo di Loro, Fabio Divino, Giovanna Jona Lasinio, Gianfranco Lovison, Antonello Maruotti, Marco Mingione
Lo scopo di questo seminario è di introdurre alcuni semplici modelli matematici nell'ambito della dinamica delle popolazioni. Dopo aver considerato i primi modelli per una o più popolazioni, dovuti a Verhulst, Lotka e Volterra, ci soffermeremo in particolare su uno dei modelli di base per lo studio della propagazione delle epidemie: il modello SIR di Kermack e McKendrick.
When searching for solutions to Sobolev-supercritical elliptic problems, a major difficulty is the lack of Sobolev embeddings, that entrains a lack of compactness. In this talk, I will discuss how symmetry and monotonicity properties can help to overcome this obstacle. In particular, I will present a recent result concerning the existence of axially symmetric solutions to a semilinear equation, in collaboration with A. Boscaggin, F. Colasuonno and T. Weth.
Hemodynamics modeling has become mature enough to simulate local fluid dynamics changes due to a surgery or device implantation. However taking into account their interactions with the rest of the circulation, or even the downstream vascular bed not accessible by imaging remains challenging. We will present multi-fidelity models and computational methods that have been developed to tackle this issue for patient-specific image-based modeling. We will demonstrate through examples of congenital heart disease and coronary vascular disease how such simulations can be performed by including morphological and functional data. Finally we will discuss the advantage of combining these simulations with supervised machine learning as a tool to predict abdominal aneurysm growth risk and palliate the lack of mechanistic growth equations.
Contatto: paolo.zunino@polimi.it
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
In this talk we present new results framing into the recent theory of Measure Differential Equations introduced by B. Piccoli (Rutgers University-Camden). The state space where these evolution equations are set is the Wasserstein space of probability measures, hence tools of Optimal Transport are essential. The key point here is that the vector field itself maps into the space of probability measures lying on the tangent bundle, in a way compatible with the projection on the state space. We give a stronger definition of solution which indeed “selects” only one of the (not unique) solutions in the sense of Piccoli. In addition to uniqueness, we are also able to prove stability results. To do so, we borrow ideas from the theory of evolution equations driven by dissipative operators on Hilbert spaces, giving a notion of solution in terms of a so called Evolution Variational Inequality.
This is a joint work with G. Savaré (Bocconi University) and G. E. Sodini (TUM-IAS).
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
In this talk we will consider the problem of obtaining a spectral resolution for a densely defined closed normal operator on a Clifford module $\mathcal{H}_n := \mathcal{H} \otimes \mathbb{R}_n$, where $\mathcal{H}$ is a real Hilbert space and $\mathbb{R}_n := \mathbb{R}_{0, n}$ is the Clifford algebra generated by the units $e_1, \ldots, e_n$ with $e_i e_j = -e_j e_i$ for $i \neq j$ and $e_j^2 = -1$ for $j=1,\ldots, n$. We shall see that any densely defined closed normal operator on a Clifford module admits an integral representation which is analogous to the integral representation for a densely defined closed normal operator on a quaternionic Hilbert space (which one may think of as a Clifford module $\mathcal{H}_2$) discovered by Daniel Alpay, Fabrizio Colombo and the speaker in 2014. However, the Clifford module setting sketched above with $n > 2$ presents a number of technical difficulties which are not present in the quaternionic Hilbert space case.
In order to prove this result, one needs to slightly generalise the notion of $S$-spectrum to allow for operators which are not necessarily paravector operators, i.e., operators of the form $T =T_0 + \sum_{j=1}^n T_j e_j$. This observation has implications on a generalisation of the $S$-functional calculus and some related function theory which we shall briefly highlight.
The main thrust of this talk is based on joint work with Fabrizio Colombo. The work on the $S$-functional calculus is joint work with Fabrizio Colombo, Jonathan Gantner and Irene Sabadini. The work on the related function theory is joint work with Fabrizio Colombo, Irene Sabadini and Stefano Pinton.
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
Affronteremo alcuni aspetti della fisica dei campi gravitazionali estremi e dei buchi neri, in connessione anche con le recenti scoperte e con i lavori di Roger Penrose. Faremo poi cenno alla termodinamica dei buchi neri.
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
We deal with nonlinear fourth-order evolution equations describing the dynamics of beams with one or more intermediate piers. We study the role of the geometry of the structure (that is, of the position of the piers), as well as the effect of a nonhomogeneous density, in the (linear) stability of bi-modal solutions. The analysis gives some evidence that both the asymmetry and the nonhomogeneity reinforce the structure
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
In this talk I will speak about bitcoins and cryptocurrencies, how they work and their perspectives. I will consider the possible applications in business and IOT.
Irene Vignon-Clementel is directrice de recherche (prof. equiv.) at Inria, the French National Institute for Research in Digital Science and Technology. She holds a 'habilitation' degree in Applied Mathematics (Sorbonne U., formerly U. Pierre & Marie Curie) and a PhD in Mechanical Engineering (Stanford U.). Her research focuses on modeling and numerical simulations of physiological flows to better understand a number of pathophysiologies and their treatment (surgical planning, medical device design), especially related to blood circulation and breathing. This requires developing models of different complexities, coupling them, that their numerical implementation is robust, and that their parameters are based on medical or experimental data specific to a subject. Applications include congenital and acquired cardiovascular diseases, respiratory diseases and liver pathophysiology, and more recently the interpretation of non-invasive dynamic imaging. Irene VC is member of several conference committees, of the Int. J. Num. Methods Biomed. Eng. editorial board, of the VPHi board, of the scientific advisory committee for the 3DS-FDA ENRICHMENT Project, and was co-chair of the international conference VPH2020. She received the top recipient award of the western states American Heart Association fellowship (2004-2006), the student award at the World Congress of Computational Mechanics by the USACM and the USACM Executive Committee (2006), Inria excellence awards (2012 and 2016), and has been awarded an ERC consolidator grant (2019). She has been working with companies and clinicians as a PI in a number of national and international grants such as a Leducq transatlantic network of excellence, and actively promoting the computational bioengineering and medicine interface through co-supervision of MD-PhDs, joint research projects, conference organization and interface articles with clinicians.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica