Eventi
I will present different nonparametric methods for data distributed over complex spatial domains. First I will consider the problem of density estimation. Specifically I will propose a nonparametric penalized likelihood approach for data distributed over planar domains with complex geometries. The model formulation is based on a regularization with differential operators, and it is made computationally tractable by means of finite elements. In this setting, I will describe a permutation procedure for one and two samples hypothesis testing. Then I will consider hypothesis testing procedures in the case of spatial regression models with differential regularization. In particular, I will propose a test based on sign-flipping. I will present the performances of the proposed methods via simulation studies and application to real data.
Contatto: laura.sangalli@polimi.it
This talk offers an introductory look at how superoscillatory sequences can be utilized to approximate generalized functions. After an introduction to superoscillations, I will briefly discuss how such sequences can be used to approximate tempered distributions, and will then focus on their role in the context of the theory of hyperfunctions. The talk will be based on a series of papers jointly coauthored with F.Colombo, I.Sabadini, and A.Yger.
In the theory of linearly elastic fracture mechanics one-dimensional debonding models, or peeling tests, provide a simplified but still meaningful version of crack growth models based on Griffith's
criterion. They are both described by the wave equation in a time-dependent domain coupled with suitable energy balances and irreversibility conditions.Unlike the general framework, peeling tests allow to deal with a
natural issue of great interest arising in fracture mechanics. It can be stated as follows: although all these models are dynamic by nature, the evolution process is often assumed to be quasistatic (namely the
body is at equilibrium at every time) since inertial effects can be neglected if the speed of external loading is very slow with respect to the one of internal oscillations. Despite this assumption seems to
be reasonable, its mathematical proof is really far from being achieved.In this talk we validate the quasistatic assumption in a particular damped debonding model, showing that dynamic evolutions converge to the quasistatic one as inertia and viscosity go to zero. We also highlight how the presence of viscosity is crucial to get this kind of convergence.
We consider the Laplace operator with the Robin boundary condition with negative coefficient
on bounded domains with cusps. We show that if the cusps is not too strong, then the operator is bounded from below and calculate the leading term in the asymptotic expansion of its negative eigenvalues as the coefficient of the boundary condition tends to infinity. This is a joint work with Konstantin Pankrashkin.
The NMD behavioural models are a crucial driver of the maturity transformation activity and bank's profitability because their goal is to estimate the stable source of funding, the volume that can be used for medium long term lending, and the volume that represents a fixed rate cost. Being the nature of the behavioural models very heterogeneous, and the use within the bank so widespread, this presentation aims at introducing a Framework, composed by six Principles, that allows to set the proper modelling of the clients' behavior jointly with the banks' need. Furthermore, an application of the most advanced modeling that considers the financial wealth allocation at clients level will be shown.
This talk outlines a novel numerical approach for accurate and computationally efficient integrations of PDEs governing all-scale atmospheric dynamics. Such PDEs are not easy to handle, due to a huge disparity of spatial and temporal scales as well as a wide range of propagation speeds of natural phenomena captured by the equations. Moreover, atmospheric dynamics constitutes only a small perturbation about dominant balances that result from the Earth gravity, rotation, composition of its atmosphere and the energy input by the solar radiation. Maintaining this mean equilibrium, while accurately resolving the perturbations, conditions the design of atmospheric models and subjects their numerical procedures to stringent stability, accuracy and efficiency requirements.
The novel Finite-Volume Module of the Integrated Forecasting System (IFS) at ECMWF (hereafter IFS-FVM) solves perturbation forms of the fully compressible Euler/Navier-Stokes equations under gravity and rotation using non-oscillatory forward-in-time semi-implicit time stepping and finite-volume spatial discretisation. The IFS-FVM complements the established semi-implicit semi-Lagrangian pseudo-spectral IFS (IFS-ST) with the all-scale deep-atmosphere formulation cast in a generalised height-based vertical coordinate, fully conservative and monotone advection, flexible horizontal meshing and a predominantly local communication footprint. Yet, both dynamical cores can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates and physics parametrisations, thus facilitating their synergetic relation.
The focus of the talk is on the mathematical/numerical formulation of the IFS-FVM with the emphasis on the design of semi-implicit integrators and the associated elliptic Helmholtz problem. Relevant benchmark results and comparisons with corresponding IFS-ST results attest that IFS-FVM offers highly competitive solution quality and computational performance.
Contact: luca.bonaventura@polimi.it
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.
This talk outlines a novel numerical approach for accurate and computationally efficient integrations of PDEs governing all-scale atmospheric dynamics. Such PDEs are not easy to handle, due to a huge disparity of spatial and temporal scales as well as a wide range of propagation speeds of natural phenomena captured by the equations. Moreover, atmospheric dynamics constitutes only a small perturbation about dominant balances that result from the Earth gravity, rotation, composition of its atmosphere and the energy input by the solar radiation. Maintaining this mean equilibrium, while accurately resolving the perturbations, conditions the design of atmospheric models and subjects their numerical procedures to stringent stability, accuracy and efficiency requirements.
The novel Finite-Volume Module of the Integrated Forecasting System (IFS) at ECMWF (hereafter IFS-FVM) solves perturbation forms of the fully compressible Euler/Navier-Stokes equations under gravity and rotation using non-oscillatory forward-in-time semi-implicit time stepping and finite-volume spatial discretisation. The IFS-FVM complements the established semi-implicit semi-Lagrangian pseudo-spectral IFS (IFS-ST) with the all-scale deep-atmosphere formulation cast in a generalised height-based vertical coordinate, fully conservative and monotone advection, flexible horizontal meshing and a predominantly local communication footprint. Yet, both dynamical cores can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates and physics parametrisations, thus facilitating their synergetic relation.
The focus of the talk is on the mathematical/numerical formulation of the IFS-FVM with the emphasis on the design of semi-implicit integrators and the associated elliptic Helmholtz problem. Relevant benchmark results and comparisons with corresponding IFS-ST results attest that IFS-FVM offers highly competitive solution quality and computational performance.
Contact: luca.bonaventura@polimi.it
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.
The talk will be concerned with problems of optimal debt management. In a basic model, the interest rate as well as the bankruptcy risk are given a priori. In this case the borrower faces a standard problem of optimal control.
In alternative, debt management can be modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio surpasses a given threshold, bankruptcy occurs.
The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of part of their investment.
Existence and properties of optimal feedback strategies for the borrower will be discussed, in a stochastic framework as well as in the limit deterministic setting.
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.
In one space dimension, it is well known that hyperbolic conservation
laws have unique entropy-admissible solutions, depending continuously on
the initial data. Moreover, these solutions can be obtained as limits of
vanishing viscosity approximations.
For many years it was expected that similar results would hold in
several space dimensions. However, fundamental work by De Lellis,
Szekelyhidi, and other authors, has shown that multidimensional
hyperbolic Cauchy problems usually have infinitely many weak solutions.
Moreover, all known entropy criteria fail to select a single admissible one.
In the first part of this talk I shall outline this approach based on a
Baire category argument, yielding the existence of infinitely many weak
solutions.
I then wish to discuss an alternative research program,
aimed at constructing multiple solutions to some specific Cauchy
problems. Starting with some numerical simulations, here the eventual
goal is to achieve rigorous, computer-aided proofs of the existence of
two distinct self-similar solutions with the same initial data.
While solutions obtained via Baire category have turbulent nature, these
self-similar solutions are smooth, with the exception of one or two
points of singularity. They are thus much easier to visualize and
understand.
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.
In one space dimension, it is well known that hyperbolic conservation
laws have unique entropy-admissible solutions, depending continuously on
the initial data. Moreover, these solutions can be obtained as limits of
vanishing viscosity approximations.
For many years it was expected that similar results would hold in
several space dimensions. However, fundamental work by De Lellis,
Szekelyhidi, and other authors, has shown that multidimensional
hyperbolic Cauchy problems usually have infinitely many weak solutions.
Moreover, all known entropy criteria fail to select a single admissible one.
In the first part of this talk I shall outline this approach based on a
Baire category argument, yielding the existence of infinitely many weak
solutions.
I then wish to discuss an alternative research program,
aimed at constructing multiple solutions to some specific Cauchy
problems. Starting with some numerical simulations, here the eventual
goal is to achieve rigorous, computer-aided proofs of the existence of
two distinct self-similar solutions with the same initial data.
While solutions obtained via Baire category have turbulent nature, these
self-similar solutions are smooth, with the exception of one or two
points of singularity. They are thus much easier to visualize and
understand.
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica