The central focus of chemical kinetics is the determination of the rate at which one or more molecules react to transform into new molecules through the rearrangements of chemical bonds.
Theoretically, chemical kinetics lies at the interface between quantum and classical mechanics, with the explicit formulation of rate laws requiring an extensive use of statistical thermodynamics.
In the last years a priori rate calculations for gas phase reactions have undergone a gradual but dramatic transformation, with current predictions often rivaling the accuracy of the best available experimental data.
In this seminar I will talk about the current status of ab initio chemical kinetics and of the challenges that must still be met in order to transform this branch of physical chemistry from a qualitative to a quantitative predictive science. A few example of research areas were contributions are necessary are the following: 1) the efficient determination of absolute and relative minima as well as first order saddle points on multidimensional potential energy surfaces for which gradient and, if necessary, Hessian information is available; 2) the determination of the number of energy states for a collection of non harmonic quantum oscillators; 3) the determination of a large number of eigenvalues for the quantum Hamiltonian of multidimensional rotors; 4) efficient approaches for the integration of the energy and momentum resolved master equation for chemically reactive systems.
We will present work on the mechanisms used for establishing or restoring epithelial integrity which are motivated by experimental work on development and wound healing in Zebrafish and drosophila and on gap closure in monolayers of MDCK cells or keratinocytes. These works concern mathematical modeling of the dynamics of epithelial tissues pulled by lamellipodal crawling or the contraction of actomyosin cables at the gap boundary. We are particularly interested in the influence of the wound/gap geometry on the closure mechanism.
This seminar is organized within the Research project MFAG 17412 «Mathematical insights of glioblastoma growth: a mechano-biology approach for patientspecific clinical tools» funded by the Italian Association for Cancer Research (AIRC), Project coordinator Prof. Pasquale Ciarletta
We will present work on the mechanisms used for establishing or restoring epithelial integrity which are motivated by experimental work on development and wound healing in Zebrafish and drosophila and on gap closure in monolayers of MDCK cells or keratinocytes. These works concern mathematical modeling of the dynamics of epithelial tissues pulled by lamellipodal crawling or the contraction of actomyosin cables at the gap boundary. We are particularly interested in the influence of the wound/gap geometry on the closure mechanism.
This seminar is organized within the Research project MFAG 17412 «Mathematical insights of glioblastoma growth: a mechano-biology approach for patientspecific clinical tools» funded by the Italian Association for Cancer Research (AIRC), Project coordinator Prof. Pasquale Ciarletta
Network Science is a rapidly growing interdisciplinary area at the intersection of mathematics, computer science, and a multitude of disciplines from the natural and life sciences to the social sciences and even the humanities. Network analysis methods are now widely used in proteomics, in the study of social networks (both human and animal), in finance, in ecology, in bibliometric studies, in archeology, and in a host of other fields. In this talk I will introduce the audience to some of the mathematical and computational problems and methods of complex networks, with an emphasis on the basic notions of centrality and communicability. More specifically, I will describe some of the problems in large-scale numerical linear algebra arising in this area, and how they differ from the corresponding problems encountered in more traditional applications of numerical analysis. The talk will be accessible to students, requiring only a modest background in linear algebra, numerical analysis and graph theory.
Contacts: paola.antonietti@polimi.it, paolo.zunino@polimi.it
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
Compositional data are multivariate observations carrying only relative information, popularly expressed in percentages, proportions, mg/kg, etc. Because of features inherent to compositional data, such as scale invariance and the relative scale, the statistical analysis of raw compositional data often leads to spurious results. Natural principles of compositional data are followed by the Aitchison geometry on a simplex, the sample space of compositional data (Aitchison, 1986; Pawlowsky-Glahn et al., 2015). However, because most standard statistical methods rely on the Euclidean geometry in real space, compositional data need to be converted to this space prior to statistical processing. In the lecture, we will present the log ratio methodology for dealing with compositional data and several types of their coordinate representations, such as orthonormal log-ratio coordinates, pivot coordinates, weighted pivot coordinates (Hron et al., 2017), or symmetric balances (!
Kynvclova et al., 2017). Their usage will be demonstrated on examples.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
Quale è il legame tra le onde elettromagnetiche appartenenti a quella parte dello spettro che chiamiamo visibile e la nostra visione? L’interpretazione che il nostro occhio e il nostro cervello forniscono della realtà circostante è così complessa che è necessario tenere conto di tantissimi fattori per comprendere ad esempio perché vediamo alcuni colori o percepiamo il contrasto in un certo modo. Uno degli esempi più affascinanti è sicuramente quello delle opere pittoriche, dove spesso ci rendiamo conto che l’artista dimostra una comprensione, almeno
implicita, del funzionamento della nostra percezione veramente interessante. Questi aspetti saranno mostrati con alcuni esperimenti dal vivo che vogliono rendere più chiari i concetti espressi.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
The terrestrial atmosphere provides the arena for physical processes on multiple spatial and temporal scales. Numerical methods used to solve the governing hyperbolic models must simulate features of meteorological interest accurately while handling efficiently fast and less significant wavelike phenomena. Tight production constraints in operational numerical weather prediction (NWP) drive the development of scalable dynamical cores to keep up with computing architectures that increasingly rely on massively parallel systems for performance.
While spectral transform and grid-point models have traditionally held sway in operational NWP and climate prediction, finite element methods have been gaining ground in recent years, due to their straightforward accuracy-tuning capabilities and flexibility towards unstructured grid arrangements in a context of deteriorating parallel performance of legacy codes. The seminar will present a mixed finite element-based dynamical core for the solution of the nonhydrostatic compressible equations under gravity. The mimetic spatial discretization reproduces continuous vector identities at the discrete level and ensures desirable properties such as pointwise mass conservation. Placement of the thermodynamic variable in a horizontally discontinuous, vertically continuous function space was recently shown to remove spurious buoyancy modes. Time discretization is handled by an iterative semi-implicit method. The numerical scheme is coded in object-oriented Fortran within a novel co-des!
igned software framework using PSyClone, a Python-based domain-specific compiler. The new paradigm enables a clear separation of the scientific routines from the computational infrastructure, greatly facilitating portability across platforms and performance optimization.
Results on two- and three-dimensional benchmarks of nonhydrostatic dynamics with idealized orography closely match those of existing models. Scaling scores will also be presented that highlight the model's computational performance.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
The brain is an organ with high energy needs. While it represents only 2% of the body
weight it grabs at least 20% of its total energy needs. The consumed energy can come from many
forms such as glutamate, glucose, oxygen and also lactate. Moreover energy is necessary to support
neural activity. But because energy management in healthy and tumoral cells can be difficult to
observe and explain experimentally, we use mathematical modeling to help to describe and
understand cells energy changes. We present here a time-delayed system and two fast-slow systems
describing the local mechanisms of interest. We will also compare simulations with MRS and
litterature data and discuss our results.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
Multidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools.
We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases.
For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, we exploit a suitable parametrization based on the parallel factor (PARAFAC) decomposition which enables to achieve both parameter parsimony and to incorporate sparsity effects. Our contribution is twofold: first, we provide an extension of multivariate econometric models to account for both tensor-variate response and covariates; second, we show the effectiveness of proposed methodology in defining an autoregressive process for time-varying real economic networks.
Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We show the efficiency of the MCMC procedure on simulated datasets, with different size of the response and independent variables, proving computational efficiency even with high-dimensions of the parameter space. Finally, we apply the model for studying the temporal evolution of real economic networks.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
I will present a series of works in collaboration with Henri Berestycki (PSL), dealing with systems of predators interacting with a single prey. The system is linked to the Lotka-Volterra model of interaction with diffusion, but unlike more classic works, we are interested in studying the case where competition between predators is very strong: in this context, the original domain is partitioned in different sub-territories occupied by different predators. The question that we ask is under which conditions the predators segregate in packs and whether there is a benefit to the hostility between the packs. More specifically, we study the stationary states of the system, the stability of the solutions and the bifurcation diagram, and the asymptotic properties of the system when the intensity of the competition becomes infinite.
Michele Benzi is full professor of Numerical Analysis at the Scuola Normale Superiore in Pisa. Until 2018 he was the Samuel Candler Dobbs Professor of Mathematics and Computer Science at Emory University, where he was on the faculty for 18 years, following positions at Los Alamos National Laboratory, CERFACS, and the University of Bologna. He received his PhD in 1993 from North Carolina State University and his Laurea degree from the University of Bologna in 1987. His main research interests are in numerical linear algebra, with a broad range of applications including CFD, Quantum Chemistry, and Network Science. He serves or has served on the editorial board of a number of scientific journals, and is a Fellow of both SIAM and the American Mathematical Society.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica