27 Febbraio, 2019 11:00

MOX Seminar

Dynamic prediction in Survival analysis: an application to patients with high-grade extremity soft tissue sarcoma

Marta Fiocco, Mathematical Institute Leiden University, The Netherlands

Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

abstract

There is increasing interest in personalized prediction of disease progression. Prediction models are statistical models based on patient and disease
characteristics which are used to inform treatment decisions, to provide personalized risk estimates for a patient. Many available prediction models are limited to predictions from a specific baseline time like diagnosis or shortly before treatment is initiated. It is at this time that the most important decisions on primary treatment are made. It is well known that available prognostic models are important tools for physicians to guide treatment decisions at diagnosis. However, once primary treatment has been initiated, the prognosis of the patient will change over the course of time, as a result of the effect of treatment, like treatment toxicity, clinical events such as disease recurrence that may have occurred, or simply, because of the fact that the patient is still alive. This implies that prediction models need to be updated by using new information about a specific patient that has become available since baseline. Prediction models that incorporate this dynamic aspect are called dynamic prediction models. In the first part of the talk the methodology for dynamic prediction will be discussed. The dynamic aspect of dynamic prediction use information on events and/or measurements up to the present, in order to update the prediction. It will be shown how dynamic predictions may be obtained using the concept of landmarking. In the second part of the talk a dynamic prediction model of survival for patients with high-grade extremity soft tissue sarcoma, will be presented. The model provides updated 5-year survival probabilities from different prediction time points during follow-up. Baseline covariates as well as time-dependent covariates, such as status of local recurrence and distant metastases, are included in the model. This dynamic prediction model which updates survival probabilities over time can be used to make better individualized treatment decisions based on a dynamic assessment of a patient's prognosis.
- van Praag VM , Rueten-Budde A, PERSARC group, van de Sande MA, Fiocco M. A prediction model for treatment decisions in high-grade extremity soft-tissue sarcomas. European Journal of cancer 2017, Volume 83, Pages 313{323
- Rueten-Budde A, van Praag VM , PERSARC group, van de Sande MA, Fiocco M. Dynamic Prediction of Overall Survival for Patients with High-Grade Extremity Soft Tissue Sarcoma. Surgical Oncology Volume 27, Issue 4, December 2018, Pages 695-701.
- Hans van Houwelingen & Hein Putter (2011). Dynamic Prediction in Clinical Survival Analysis. Chapman & Hall. - H. C. van Houwelingen (2007). Dynamic Prediction by Landmarking in Event History Analysis. Scand. J. Stat. 34: 70{85.

Contact: francesca.ieva@polimi.it

27 Febbraio, 2019 15:15

Sezione di Analisi

Rigorous bounds on the heat flux in turbulent convection

Camilla Nobili, Universität Hamburg

Aula seminari 3° piano

abstract

abstract

We are interested in thermal convection as described by the Rayleigh-B ?enard convection model. In this model the Navier-Stokes equations for the (divergence-free) velocity u with no-slip bound- ary conditions is coupled to an advection-diffusion equation for the temperature T with inhomo- geneous Dirichlet boundary conditions. The problem of understanding the (average) upward- heat-transport properties is of great interest for the applications and challenging for the rigorous analysis. We show how the PDE theory (in particular, regularity analysis) can contribute to the understanding of the scaling regimes for the heat transport. After reviewing the theory of Constantin& Doering ’99 we will present some recent results and discuss new challenges.

21 Febbraio, 2019 09:30

MOX Seminar

Morphology and Physiology of the tricuspid and pulmonary valves and right/left ventricular inter-relationships

Antonio Corno, East Midlands Congenital Heart Center, UK.

Aula Seminari III Piano del Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

abstract

The anatomy of the normal tricuspid and pulmonary valve will be explained and illustrated in all the specific elements, in order to provide the background required to then understand the mechanism of their opening and closing. The latter will be explained, with the changes over time of the pressures in the right atrium, right ventricle and pulmonary artery. The anatomical and physiological inter-relationships between right and left ventricle will be finally explained, showing why any change in the volume and/or pressure overload of one ventricle immediately reflects in the functioning of the other ventricle

contact: christian.vergara@polimi.it

19 Febbraio, 2019 10:30

MOX Seminar

Physiology of the heart

Antonio Corno, East Midlands Congenital Heart Center, UK

Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

abstract

The physiology of the heart will be explained, with the changes over time of the pressures in the left atrium, left ventricle and aorta, and the mechanisms of opening and closure of mitral and aortic valve.

Contact: christian.vergara@polimi.it

18 Febbraio, 2019 14:00

MOX Seminar

Morphology of the normal and pathological mitral and aortic valves

Antonio Corno, East Midlands Congenital Heart Center, UK.

Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

abstract

The anatomy of the normal mitral valve and aortic valve will be explained and illustrated in all the specific elements, in order to provide the background required to then understand the mechanism of their opening and closing. The various types of anatomically and functionally bicuspid aortic valve will be then illustrated, with the reasons why the presence of bicuspid aortic valve is frequently associated with malfunctioning of the valve itself and also with diseases of the ascending aorta. Finally, the different mechanism involved in the congenital stenosis and/or regurgitation of the aortic valve will be explained, with the associated consequences on the left ventricular morphology and function.

contact: christian.vergara@polimi.it

14 Febbraio, 2019 14:00

MOX Colloquia

Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics

Javier Bonet, University of Greenwich

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

The presentation will review recent advances in the area of designing and using polyconvex energy potentials to describe the behaviour of solids in the large strain regime in the presence of several physical phenomena such as thermal or electro-mechanical effects. The need for convexity will be justified from the viewpoint of ensuring the existence of real wave speeds in the material at any state of deformation. The convexity of energy potentials with respect to an extended set of variables describing deformation and other multi-physics effects enables the definition of conjugate stresses, thermal and electro-mechanical variables and the formulation of complementary energy functions via the application of the Legendre transforms. In the static case, this leads to the development of a variety of Hu-Washizu or Hellinger-Reissner mixed variation principles that permit the discretisation of different fields with specifically chosen order of accuracy. For instance, in the case of nearly and fully incompressible materials, discretisations that either meet the LBB condition or are appropriately stabilised can be constructed. In the dynamic case, first order conservation laws can be derived for each of the extended set of variables in the energy function. Moreover, convexity enables the definition of a convex entropy-like functional of the primary conserved variables, leading to a symmetrisation of the conservation laws in terms of conjugate stress-like variables and a robust implementation of a Petrov-Galerkin discretisation process. This can be done in a variety of ways, for instance in the case of thermoelasticity two approaches will be discussed, namely, using the Hamiltonian as “entropy-like” convex function or, alternatively, using the so-called “ballistic free energy” as convex entropy extension. Several examples demonstrating the theoretical developments will be provided.


contact: luca.formaggia@polimi.it

Professor Javier Bonet is the Deputy Vice-Chancellor, Research & Enterprise, at the University of Greenwich. He leads all aspects of Greenwich's research and enterprise activities, building on its existing success, as well as contributing to the strategic leadership of the institution. Previously Director of the Welsh government's Sêr Cymru National Research Network in Advanced Engineering and Materials, Javier Bonet was also Professor of Computational Engineering and Head of the College of Engineering at Swansea University. With a background in civil engineering, he graduated from the Polytechnic University of Catalonia in Barcelona, Spain, before coming to the UK to study for a PhD in computational mechanics at Swansea University. Since then he has established a strong reputation as a researcher in areas such as large strain solid mechanics, smooth particle hydrodynamics, error estimation and more recently the use of conservation laws in solid dynamics. He has published over 100 academic papers and co- authored a book on Nonlinear Continuum Mechanics for Finite Element Analysis, widely used as a graduate textbook across the world.

7 Febbraio, 2019 16:00

Seminario Matematico e Fisico di Milano

Spectral synthesis for systems of exponentials and reproducing kernels

Anton Baranov, Saint Petersburg State University

Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50, Milano

abstract

abstract

Let $x_n$ be a complete and minimal system of vectors in a Hilbert space $H$. We say that this system is hereditarily complete or admits spectral synthesis if any vector in $H$ can be approximated by linear combinations of partial sums of the Fourier series with respect to $x_n$. It was a long-standing problem whether any complete and minimal system of exponentials in $L^2(-a,a)$ admits spectral synthesis. Several years ago we gave a negative answer to this question. At the same time we showed that any such system admits the synthesis up to a one- dimensional defect. In the talk we will also discuss related problems for systems of reproducing kernels in Hilbert spaces of entire functions (such as Paley-Wiener, de Branges, Fock).

Professor Javier Bonet is the Deputy Vice-Chancellor, Research & Enterprise, at the University of Greenwich. He leads all aspects of Greenwich's research and enterprise activities, building on its existing success, as well as contributing to the strategic leadership of the institution. Previously Director of the Welsh government's Sêr Cymru National Research Network in Advanced Engineering and Materials, Javier Bonet was also Professor of Computational Engineering and Head of the College of Engineering at Swansea University. With a background in civil engineering, he graduated from the Polytechnic University of Catalonia in Barcelona, Spain, before coming to the UK to study for a PhD in computational mechanics at Swansea University. Since then he has established a strong reputation as a researcher in areas such as large strain solid mechanics, smooth particle hydrodynamics, error estimation and more recently the use of conservation laws in solid dynamics. He has published over 100 academic papers and co- authored a book on Nonlinear Continuum Mechanics for Finite Element Analysis, widely used as a graduate textbook across the world.

31 Gennaio, 2019 14:00

MOX Colloquia

Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University - Spain

Sala Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

The theory of poroelasticity models the interaction between the deformation and the fluid flow in a fluid-saturated porous medium. Poroelastic models are widely used nowadays in the modeling of many applications in different fields, ranging from geomechanics and petroleum engineer, to biomechanics. The poroelastic equations are often solved in a two-field formulation, where the unknowns are the displacement and the pressure, or in a three-field formulation where the velocity of the fluid is included as a primary variable as well. The numerical solution of these models is usually based on finite element methods. In this talk, we will study some stabilized finite element discretizations for both formulations of the poroelastic problem. Moreover, an important aspect in the numerical simulation of these problems is the efficient solution of the large systems of algebraic equations obtained after discretization. The resulting systems are of saddle point type and we will address their efficient solution by designing suitable geometric multigrid methods.

Contact: luca.formaggia@polimi.it

Francisco José Gaspar Lorenz is an associate professor of the Department of Applied Mathematics at the University of Zaragoza, Spain. He received in 2016 a Marie Curie Individual Fellowship, funded from the Horizon 2020 programme. His interests include iterative solution methods, multigrid methods and flow in deformable porous media problems

23 Gennaio, 2019 14:00

MOX Colloquia

Dealing with unreliable computing platforms at extreme scale

Luc Giraud, INRIA (Inria Bordeaux - Sud-Ouest)

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

The advent of extreme scale computing platforms will require the use of parallel resources at an unprecedented scale. On the technological side, the continuous shrinking of transistor geometry and the increasing complexity of these devices affect dramatically their sensitivity to natural radiation leading to a high rate of hardware faults, and thus diminish their reliability. Handling fully these faults at the computer system level may have a prohibitive computational and energetic cost. High performance computing applications that aim at exploiting all these resources will thus need to be resilient. In this talk, we will first give an overview of the current trends towards exascale. We will discuss the new challenges to face in terms of platform reliability and associated variety of possible faults. We will then discuss some of the solutions that have been proposed to tackle these errors before discussing in more details some contributions in sparse numerical linear algebra. First, in the context of computing node crashes, we will discuss possible remedies in the framework of linear system or eigenproblem solutions, that are the inner most numerical kernels in many scientific and engineering applications and also ones of the most time consuming parts. Second, we will discuss a somehow more challenging problem related to silent transient soft-errors produced by natural radiation and consisting in a bit-flip in a memory cell producing unexpected results at the application level. In that context we will consider the conjugate gradient (CG) method that is the most widely used iterative scheme for the solution of large sparse systems of linear equations when the matrix is symmetric positive definite. We will investigate through extensive numerical experiments the sensitivity of of CG to bit-flips and further discuss possible numerical criteria to detect the occurrence of such faults.
The above mentioned research activities have been conducted in collaboration with many colleagues including E. Agullo (Inria), S. Cools (University of Antwerpen), E. Fatih-Yetkin (Kadir Has University), P. Salas (CERFACS), W. Vanroose (University of Antwerpen) and M. Zounon (NAG).

contact: luca.bonaventura@polimi.it

Luc Giraud got his PhD from the Institut National Polytechnique de Toulouse in 1991, he then joint CERFACS as a post-doc, then senior researcher and deputy project leader. In 2005, he left for a full professor position in applied mathematics in the engineer School ENSEEIHT. He joint Inria in 2009 where he leads the Inria project team HiePACS that works on the design of scalable numerical techniques for emerging parallel computers. His main research interests are in numerical linear algebra with applications in various engineering domains.
He currently serves on the editorial board of SIAM SISC and SIMAX.

17 Gennaio, 2019 11:30 in punto

Sezione di Probabilità Quantistica

QUANTUM INCOMPATIBILITY WITNESSES

Alessandro Toigo, Politecnico di Milano

Aula Consiglio VII piano

abstract

abstract

We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement set-up after Alice has announced him the chosen ensemble (pre-measurement scenario), or he is forced to perform the measurement before of Alice’s announcement (post-measurement scenario). In the latter case, he can only post-process his measurement outcome when Alice’s extra information becomes available. We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task within the pre-measurement scenario. This is done by showing that only incompatible measurements allow for an efficient use of pre-measurement information in order to improve Bob’s probability of guessing the correct state. The gap between the guessing probabilities with pre- and post-measurement information is thus a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme.

Luc Giraud got his PhD from the Institut National Polytechnique de Toulouse in 1991, he then joint CERFACS as a post-doc, then senior researcher and deputy project leader. In 2005, he left for a full professor position in applied mathematics in the engineer School ENSEEIHT. He joint Inria in 2009 where he leads the Inria project team HiePACS that works on the design of scalable numerical techniques for emerging parallel computers. His main research interests are in numerical linear algebra with applications in various engineering domains.
He currently serves on the editorial board of SIAM SISC and SIMAX.