Eventi
Plateau problem consists in finding a surface of minimal area among the ones spanning a given curve. It is among the oldest problem in the calculus of variations and its study lead to wonderful development in mathematics.
Federer and Fleming integral currents provide a suitably weak solution to the Plateau problem in arbitrary Riemannian manifolds, in any dimension and
co-dimension. Once this week solution has been found a natural question consists in understanding whether it is classical one. i.e. a smooth minimal surface. This is the topic of the regularity theory, which naturally splits into interior regularity and boundary regularity.
After the monumental work of Almgren, revised by De Lellis and Spadaro, interior regularity is by now well understood. Boundary regularity is instead less clear and some new phenomena appear.
Aim of the talk is to give an overview of the problem and to present some boundary regularity results we have obtained in the last years.
Plateau problem consists in finding a surface of minimal area among the ones spanning a given curve. It is among the oldest problem in the calculus of variations and its study lead to wonderful development in mathematics.
Federer and Fleming integral currents provide a suitably weak solution to the Plateau problem in arbitrary Riemannian manifolds, in any dimension and
co-dimension. Once this week solution has been found a natural question consists in understanding whether it is classical one. i.e. a smooth minimal surface. This is the topic of the regularity theory, which naturally splits into interior regularity and boundary regularity.
After the monumental work of Almgren, revised by De Lellis and Spadaro, interior regularity is by now well understood. Boundary regularity is instead less clear and some new phenomena appear.
Aim of the talk is to give an overview of the problem and to present some boundary regularity results we have obtained in the last years.
I will review some recent results on quantum-mechanical many-body problem and formulate some open problems.
The importance of electrolyte concentrations for the cardiac function is well established. Electrolyte variations can lead to arrhythmias onset, due to their important role in the action potential (AP) genesis and in maintaining cell homeostasis. However, most of the human AP computer models available in the literature were developed with constant electrolyte concentrations, and fail to simulate physiological changes induced by electrolyte variations. This is especially true for Ca2+, even in the most widely used models in cardiac electrophysiology.
The new human ventricular model (BPS2020, [1]), based on O’Hara-Rudy (ORd, [2]) model, aims to correct simulate changes due to electrolytes and answer the question: "which are the quantitative contributions of the mechanisms involved in the relationship between extracellular calcium concentration [Ca2+]o and the AP?"[3], using human-based modeling and simulations since they could provide useful support to investigate this phenomenon.
From earlier studies, it is well known that the L-type Ca2+ current (ICaL) is the ionic current mainly affected by [Ca2+]o changes. In particular, calcium-dependent inactivation (CDI) seems to play the most significant role. For this reason, the main changes needed with respect to ORd are: (i) increased sensitivity of ICaL current inactivation to [Ca2+]o; (ii) a single compartment description of the sarcoplasmic reticulum; iii) the replacement of Ca2+ release.
BPS2020 can simulate the physiological APD-[Ca2+]o relationship, while also retaining the well-reproduced properties of ORd (APD rate dependence at [K+]o=4mM, restitution, accommodation, and current block effects). We also used BPS2020 to generate an experimentally-calibrated population of models to investigate: (i) the occurrence of repolarization abnormalities in response to hERG current block; (ii) the rate adaptation variability; (iii) the occurrence of alternans and delayed after-depolarizations at fast pacing. Our results indicate that we successfully developed an improved version of ORd, which can be used to investigate electrophysiological changes and pro-arrhythmic abnormalities induced by electrolyte variations and current block at multiple rates and at population level.
[1] Bartolucci C, Passini E, Hyttinen J, Paci M, Roth BJ. Simulation of the Effects of Extracellular Calcium Changes Leads to a Novel Computational Model of Human Ventricular Action Potential With a Revised Calcium Handling 2020;11:1-20. doi:10.3389/fphys.2020.00314.
[2] O’Hara T, Virág L, Varró A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential: Model formulation and experimental validation. PLoS Comput Biol 2011;7.
[3] Bartolucci C, Paci M, Severi S. Investigation of the Extracellular Calcium Effects on Action Potential using the Most Recent Human Ventricular Cell Models. 2020 Comput Cardiol Conf 2020;47:7-10. doi:10.22489/cinc.2020.296.
Contatto: francesco.regazzoni@polimi.it
Current technology for decelerating a spacecraft from the high speed of atmospheric entry to the final stages of landing on Mars is based on parachute systems and dates back to NASA’s Viking Program. To enable future exploration missions featuring sophisticated robots and safely land heavier spacecraft on Mars, it must be advanced to a new level of performance at supersonic speeds. For this purpose, larger than before high-speed parachutes and inflatable drag devices are needed. Recently, it has become clear that the design, development, and maturing of such devices for future use at Mars cannot be performed by relying only on flight tests. It requires guidance from predictive simulations based on a high-fidelity, multi-disciplinary computational model for parachute inflation dynamics (PID) and drag prediction. The development of such a model is a formidable challenge. It must be able to predict various instabilities of a parachute such as flutter and pulsation, and assess the influence on its performance of several factors including material and geometric porosities, and the influence of temperature and strain rate on the stress field experienced in the supersonic regime. This lecture will discuss an ongoing effort at Stanford University, in collaboration with NASA and the Jet Propulsion Laboratory, for the development of such a computational model and some associated computational innovations. These include: a computationally tractable, data-driven framework for nonlinear, dynamic, multiscale modeling of membrane woven fabrics; a discrete-event-free, spurious-oscillation-free, and total variation diminishing embedded (immersed) boundary method for highly nonlinear fluid-structure interaction problems; a homogenization approach with subgrid scale modeling for treating porous wall boundary conditions; an energy-conserving, second-order accurate approach for enforcing transmission conditions at the interface between fluid and structural representations of disparate spatial dimensions; and a fast, massively parallel, load-balanced, adaptive mesh refinement methodology for tracking wall boundaries, boundary layers, and flow features such as shocks and wakes in an embedding domain. The lecture will report on some validation results for the simulation of the supersonic inflation dynamics of the parachute that landed Curiosity Rover on August 6, 2012. It will also highlight outstanding mathematical and numerical challenges associated with the simulation of PID from an initial condition where the parachute geometry is at bag strip, and with time-step restrictions induced by rapidly evolving fluid/structure interfaces.
Work in collaboration with Phil Avery, Jonathan Ho, Daniel Huang, Sebastian Grimberg.
Contact: Alfio Quarteroni, alfio.quarteroni@polimi.it
Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures, Chairman of the Department of Aeronautics and Astronautics, and Director of the Stanford-KACST Center of Excellence for Aeronautics and Astronautics at Stanford University. His research interests are in computational engineering sciences for the design and analysis of complex systems in aerospace, mechanical, and naval engineering. He is a Member of the National Academy of Engineering, a Member of the Royal Academy of Engineering (UK), a Member of the Lebanese Academy of Sciences, a Doctor Honoris Causa from Ecole Centrale de Nantes, a Doctor Honoris Causa from Ecole Normale Supérieure Paris-Saclay, a designated ISI Highly Cited Author, and a Fellow of AIAA, ASME, IACM, SIAM, USACM, and WIF. He has trained more than 90 PhD and post-doctoral students. For his research on aeroelasticity, aeroacoustic scattering, CFD, dynamic data-driven systems, fluid-structure interaction, high performance computing, and model reduction, he has received many professional and academic distinctions including: the Ashley Award for Aeroelasticity and the Structures, Structural Dynamics and Materials Award from AIAA; the Lifetime Achievement Award and the Spirit of St Louis Medal from ASME; the Gordon Bell Prize and the Sidney Fernbach Award from IEEE; the Gauss-Newton Medal from IACM; the Grand Prize from the Japan Society for Computational Engineering Science; and the John von Neumann Medal from USACM. He was knighted in France in the Order of Academic Palms, appointed on the Scientific Advisory Board of the US Air Force, and selected by the US Navy recruiters as a Primary Key-Influencer and flown by the Blue Angels.
Un paradosso può essere caratterizzato come un argomento che, muovendo da premesse apparentemente inattaccabili e impiegando solo passaggi apparentemente validi, porta ad una conclusione inaccettabile. I paradossi si sono rivelati una fonte inestimabile di progresso per la conoscenza scientifica, soprattutto in logica e nei fondamenti della matematica. In questo seminario, presenterò un approccio unificato a due tipi fondamentali di paradosso: i paradossi semantici e i paradossi della vaghezza (“paradossi soritici”). Svilupperò un modello formale della nozione di paradosso, e lo applicherò per mostrare che i paradossi semantici e quelli soritici rivelano una struttura simile. Concluderò con alcune prospettive per ulteriori applicazioni del modello.
Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures, Chairman of the Department of Aeronautics and Astronautics, and Director of the Stanford-KACST Center of Excellence for Aeronautics and Astronautics at Stanford University. His research interests are in computational engineering sciences for the design and analysis of complex systems in aerospace, mechanical, and naval engineering. He is a Member of the National Academy of Engineering, a Member of the Royal Academy of Engineering (UK), a Member of the Lebanese Academy of Sciences, a Doctor Honoris Causa from Ecole Centrale de Nantes, a Doctor Honoris Causa from Ecole Normale Supérieure Paris-Saclay, a designated ISI Highly Cited Author, and a Fellow of AIAA, ASME, IACM, SIAM, USACM, and WIF. He has trained more than 90 PhD and post-doctoral students. For his research on aeroelasticity, aeroacoustic scattering, CFD, dynamic data-driven systems, fluid-structure interaction, high performance computing, and model reduction, he has received many professional and academic distinctions including: the Ashley Award for Aeroelasticity and the Structures, Structural Dynamics and Materials Award from AIAA; the Lifetime Achievement Award and the Spirit of St Louis Medal from ASME; the Gordon Bell Prize and the Sidney Fernbach Award from IEEE; the Gauss-Newton Medal from IACM; the Grand Prize from the Japan Society for Computational Engineering Science; and the John von Neumann Medal from USACM. He was knighted in France in the Order of Academic Palms, appointed on the Scientific Advisory Board of the US Air Force, and selected by the US Navy recruiters as a Primary Key-Influencer and flown by the Blue Angels.
The financial technology revolution is a reality, as the financial world is gradually transforming into a digital domain of high-volume information and high-speed data transformation and processing. The more this transformation takes place, the more consumer and investor behaviour shifts towards a pro-technology attitude of financial services offered by market participants, financial institutions and financial technology companies. This new norm is confirming that information technology is driving innovation for financial technology. In this framework, the value of big data, artificial intelligence and machine learning techniques becomes apparent. The aim of this chapter is multi-fold. Firstly, a multidimensional descriptive analysis is shown to familiarise the reader with the extent of penetration of the above in the financial technology road-map. A short non-technical overview of the methods is then presented. Next, the impact of data analytics and relevant techniques on the evolution of financial technology is explained and discussed along with their applications’ landscape. The chapter also presents a glimpse of the shifting paradigm these techniques bring forward for several fintech related professions, while artificial intelligence and machine learning techniques are tied with the future challenges of AI ethics, regulation technology and the smart data utilisation.
Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures, Chairman of the Department of Aeronautics and Astronautics, and Director of the Stanford-KACST Center of Excellence for Aeronautics and Astronautics at Stanford University. His research interests are in computational engineering sciences for the design and analysis of complex systems in aerospace, mechanical, and naval engineering. He is a Member of the National Academy of Engineering, a Member of the Royal Academy of Engineering (UK), a Member of the Lebanese Academy of Sciences, a Doctor Honoris Causa from Ecole Centrale de Nantes, a Doctor Honoris Causa from Ecole Normale Supérieure Paris-Saclay, a designated ISI Highly Cited Author, and a Fellow of AIAA, ASME, IACM, SIAM, USACM, and WIF. He has trained more than 90 PhD and post-doctoral students. For his research on aeroelasticity, aeroacoustic scattering, CFD, dynamic data-driven systems, fluid-structure interaction, high performance computing, and model reduction, he has received many professional and academic distinctions including: the Ashley Award for Aeroelasticity and the Structures, Structural Dynamics and Materials Award from AIAA; the Lifetime Achievement Award and the Spirit of St Louis Medal from ASME; the Gordon Bell Prize and the Sidney Fernbach Award from IEEE; the Gauss-Newton Medal from IACM; the Grand Prize from the Japan Society for Computational Engineering Science; and the John von Neumann Medal from USACM. He was knighted in France in the Order of Academic Palms, appointed on the Scientific Advisory Board of the US Air Force, and selected by the US Navy recruiters as a Primary Key-Influencer and flown by the Blue Angels.
Numero riunione:121 183 7342 Password: M6Fm8ZnPFk3
There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects. But how much understanding can one really gain about an infinite group by examining its finite images? Sometimes little, sometimes a lot. In this colloquium talk, I will sketch the rich history of this problem and describe how input from geometry and low-dimensional topology, mingling with algebra and arithmetic, have transformed the subject in recent years. I shall also describe some open problems.
Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures, Chairman of the Department of Aeronautics and Astronautics, and Director of the Stanford-KACST Center of Excellence for Aeronautics and Astronautics at Stanford University. His research interests are in computational engineering sciences for the design and analysis of complex systems in aerospace, mechanical, and naval engineering. He is a Member of the National Academy of Engineering, a Member of the Royal Academy of Engineering (UK), a Member of the Lebanese Academy of Sciences, a Doctor Honoris Causa from Ecole Centrale de Nantes, a Doctor Honoris Causa from Ecole Normale Supérieure Paris-Saclay, a designated ISI Highly Cited Author, and a Fellow of AIAA, ASME, IACM, SIAM, USACM, and WIF. He has trained more than 90 PhD and post-doctoral students. For his research on aeroelasticity, aeroacoustic scattering, CFD, dynamic data-driven systems, fluid-structure interaction, high performance computing, and model reduction, he has received many professional and academic distinctions including: the Ashley Award for Aeroelasticity and the Structures, Structural Dynamics and Materials Award from AIAA; the Lifetime Achievement Award and the Spirit of St Louis Medal from ASME; the Gordon Bell Prize and the Sidney Fernbach Award from IEEE; the Gauss-Newton Medal from IACM; the Grand Prize from the Japan Society for Computational Engineering Science; and the John von Neumann Medal from USACM. He was knighted in France in the Order of Academic Palms, appointed on the Scientific Advisory Board of the US Air Force, and selected by the US Navy recruiters as a Primary Key-Influencer and flown by the Blue Angels.
Neurodegeneration will undoubtedly become a major challenge in medicine and public health caused by demographic changes worldwide. More than 45 million people are living with dementia today and this number is expected to triple by 2050. Recent studies have reinforced the hypothesis that the prion paradigm, the templated growth and spreading of misfolded proteins, could help explain the progression of a variety of neurodegenerative disorders. However, our current understanding of prion-like growth and spreading is rather empirical. Here we show that a physics-based reaction-diffusion model can explain the growth and spreading of misfolded protein in a variety of neurodegenerative disorders. We combine the classical Fisher-Kolmogorov equation for population dynamics with anisotropic diffusion and simulate misfolding across representative sections of the human brain and across the brain as a whole. Our model correctly predicts amyloid-beta deposits and tau inclusions in Alzheimer's disease, alpha-synuclein inclusions in Parkinson's disease, and TDP-43 inclusions in amyotrophic lateral sclerosis. To reduce the computational complexity, we represent the brain through a connectivity-weighted Laplacian graph created from 418 brains of the Human Connectome Project. Our brain network model correctly predicts the key characteristic features of whole brain models at a fraction of their computational cost. Our results suggest that misfolded proteins in various neurodegenerative disorders grow and spread according to a universal law that follows the basic physical principles of nonlinear reaction and anisotropic diffusion. Our simulations can have important clinical implications, ranging from estimating the socioeconomic burden of neurodegeneration to designing clinical trials and pharmacological intervention.
Contatto: alfio.quarteroni@polimi.it
Ellen Kuhl is the Robert Bosch Chair of Mechanical Engineering at Stanford University. She is a Professor of Mechanical Engineering and, by courtesy, Bioengineering. She received her PhD from the University of Stuttgart in 2000 and her Habilitation from the University of Kaiserslautern in 2004. Her area of expertise is Living Matter Physics, the design of theoretical and computational models to simulate and predict the behavior of living structures. Ellen has published more than 200 peer-reviewed journal articles and edited two books; she is an active reviewer for more than 20 journals at the interface of engineering and medicine and an editorial board member of seven international journals in her field. Ellen is the current Chair of the US National Committee on Biomechanics and a Member-Elect of the World Council of Biomechanics. She is a Fellow of the American Society of Mechanical Engineers and of the American Institute for Mechanical and Biological Engineering. She received the National Science Foundation Career Award in 2010, was selected as Midwest Mechanics Seminar Speaker in 2014, and received the Humboldt Research Award in 2016. Ellen is an All American triathlete on the Wattie Ink. Elite Team, a multiple Boston, Chicago, and New York marathon runner, and a Kona Ironman World Championship finisher.
There are two crucial operators in the theory of Dunkl harmonic analysis. The first is the Dunkl transform, which generalizes the Fourier transform. The second is the intertwining operator, which maps ordinary partial derivatives to Dunkl operators. Although some abstract statements are known about the intertwining operator, the explicit formula for classes of reflection groups is generally not known. In recent work Yuan Xu proposed a formula in the case of dihedral groups and a restricted class of functions. We extend his formula to all functions and give a general strategy on how to obtain similar formulas for other reflections groups. This is based on joint work with Pan Lian, available under arXiv:2002.09065 and to appear in J. Funct. Anal.
Ellen Kuhl is the Robert Bosch Chair of Mechanical Engineering at Stanford University. She is a Professor of Mechanical Engineering and, by courtesy, Bioengineering. She received her PhD from the University of Stuttgart in 2000 and her Habilitation from the University of Kaiserslautern in 2004. Her area of expertise is Living Matter Physics, the design of theoretical and computational models to simulate and predict the behavior of living structures. Ellen has published more than 200 peer-reviewed journal articles and edited two books; she is an active reviewer for more than 20 journals at the interface of engineering and medicine and an editorial board member of seven international journals in her field. Ellen is the current Chair of the US National Committee on Biomechanics and a Member-Elect of the World Council of Biomechanics. She is a Fellow of the American Society of Mechanical Engineers and of the American Institute for Mechanical and Biological Engineering. She received the National Science Foundation Career Award in 2010, was selected as Midwest Mechanics Seminar Speaker in 2014, and received the Humboldt Research Award in 2016. Ellen is an All American triathlete on the Wattie Ink. Elite Team, a multiple Boston, Chicago, and New York marathon runner, and a Kona Ironman World Championship finisher.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica