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Seminar on 17/11 (Francesco Tudisco)
by Leonardo Robol 17 Nov '20

17 Nov '20

Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjacency matrix, for example by considering a triangle involving nodes i, j and k. In other contexts, higher-order information appears explicitly, for example, in a coauthorship network, a document with three authors forms a natural triangle. After reviewing the original LS algorithm I will present our proposed variation of it, which takes directly advantage of higher-order information. A key point of the proposed method is that we replace the standard Laplacian matrix with a nonlinear Laplacian-inspired map which is defined in terms of a order-three tensor. Just like standard LS, we can show convergence of the new nonlinear diffusion process to the gloabal minimum of a constrained semi-supervised loss function that enforces local and global consistency with the input labels. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the proposed model outperforms classical label spreading, hypergraph clustering methods, and graph neural networks. I will also point out some open problems related to both the modeling part and the computational one. https://www.dm.unipi.it/webnew/it/seminari/tensor-method-semi-supervised-le…

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NOMADS seminar @GSSI - Nov 18 and Nov 20
by Francesco Tudisco 16 Nov '20

16 Nov '20

Dear all, We are happy to invite you all to the next NOMADS (Numerical ODEs, Matrix Analysis and Data Science) seminar at GSSI. This week we will have two talks, as per the following schedule: 1) Christian Lubich, University of Tuebingen, Germany Wednesday November 18, 17h00 (CET) 2) Patricia Diaz De Alba, Gran Sasso Science Institute, Italy Friday November 20, 17h15 (CET) All seminars take place via Zoom. See below for additional information (e.g. title, abstract and zoom link). Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday and Friday! Francesco Tudisco and Nicola Guglielmi --------------------------------------------------------------------- November 18, 2020 (Wednesday) at 17h00 (Italian time) Christian Lubich <https://na.uni-tuebingen.de/~lubich/> *Dynamical low-rank approximation* This talk reviews differential equations and their numerical solution on manifolds of low-rank matrices or of tensors with a rank structure such as tensor trains or general tree tensor networks. These low-rank differential equations serve to approximate, in a data-compressed format, large time-dependent matrices and tensors or multivariate functions that are either given explicitly via their increments or are unknown solutions to high-dimensional evolutionary differential equations, with multi-particle time-dependent Schrödinger equations and kinetic equations such as Vlasov equations as noteworthy examples of applications. Recently developed numerical time integrators are based on splitting the projection onto the tangent space of the low-rank manifold at the current approximation. In contrast to all standard integrators, these projector-splitting methods are robust to the unavoidable presence of small singular values in the low-rank approximation. This robustness relies on exploiting geometric properties of the manifold of low-rank matrices or tensors: in each substep of the projector-splitting algorithm, the approximation moves along a flat subspace of the low-rank manifold. In this way, high curvature due to small singular values does no harm. This talk is based on work done intermittently over the last decade with Othmar Koch, Bart Vandereycken, Ivan Oseledets, Emil Kieri, Hanna Walach and Gianluca Ceruti. Zoom link <https://us02web.zoom.us/j/83782294125> Add event to Google calendar <https://calendar.google.com/event?action=TEMPLATE&tmeid=MW83YTByZm1ia2E0MGp…> ------------------------------------------------------------------- ------------------------------------------------------------------- November 20, 2020 (Friday) at 17h30 (Italian time) Patricia Diaz De Alba <http://bugs.unica.it/~patricia/> *Numerical treatment for inverse electromagnetic problems* Electromagnetic induction surveys are among the most popular techniques for non-destructive investigation of soil properties, in order to detect the presence of both ground inhomogeneities and particular substances. Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Based on a non-linear forward model used to describe the interaction between an electromagnetic field and the soil, the aim is to reconstruct the distribution of either the electrical conductivity or the magnetic permeability with respect to depth. To this end, the inversion of both the real (in-phase) and the imaginary (quadrature) components of the signal are studied by a regularized damped Gauss-Newton method. The regularization part of the algorithm is based on a low-rank approximation of the Jacobian of the non-linear model. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. An algorithm for a regularization method that promotes the sparsity of the reconstructed electrical conductivity or magnetic permeability distribution is available. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The whole inversion algorithm has been enclosed in a MATLAB package, called FDEMtools, allowing the user to experiment with synthetic and experimental data sets, and different regularization strategies, in order to compare them and draw conclusions. The numerical effectiveness of the inversion procedure is demonstrated on synthetic and real datasets by using FDEMtools package. Zoom link <https://us02web.zoom.us/j/85165138386> Add event to Google calendar <https://calendar.google.com/event?action=TEMPLATE&tmeid=N2gxdW1xOGhjOTZsa2J…> -------------------------------------------------------------------- — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io

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Canceled event: Seminar on 17/11 (Francesco Tudisco) @ Tue Nov 17, 2020 11:00 - 12:00 (CET) (numpi@di.unipi.it)
by enrico.facca＠gmail.com 13 Nov '20

13 Nov '20

This event has been canceled. Title: [Numpi] Seminar on 17/11 (Francesco Tudisco) Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjac... When: Tue Nov 17, 2020 11:00 – 12:00 Central European Time - Rome Joining info: Join with Google Meet https://meet.google.com/wtx-fpah-paw Calendar: numpi(a)di.unipi.it Who: * enrico.facca(a)gmail.com - organizer * numpi(a)di.unipi.it * f.durastante(a)na.iac.cnr.it * viviani(a)chalmers.se * leonardo.robol(a)unipi.it Invitation from Google Calendar: https://calendar.google.com/calendar/ You are receiving this courtesy email at the account numpi(a)di.unipi.it because you are an attendee of this event. To stop receiving future updates for this event, decline this event. Alternatively you can sign up for a Google account at https://calendar.google.com/calendar/ and control your notification settings for your entire calendar. Forwarding this invitation could allow any recipient to send a response to the organizer and be added to the guest list, or invite others regardless of their own invitation status, or to modify your RSVP. Learn more at https://support.google.com/calendar/answer/37135#forwarding

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Invitation: Seminar on 17/11 (Francesco Tudisco) @ Tue Nov 17, 2020 11:00 - 12:00 (CET) (numpi@di.unipi.it)
by enrico.facca＠gmail.com 13 Nov '20

13 Nov '20

You have been invited to the following event. Title: [Numpi] Seminar on 17/11 (Francesco Tudisco) Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjac... When: Tue Nov 17, 2020 11:00 – 12:00 Central European Time - Rome Joining info: Join with Google Meet https://meet.google.com/wtx-fpah-paw Calendar: numpi(a)di.unipi.it Who: * enrico.facca(a)gmail.com - organizer * numpi(a)di.unipi.it * f.durastante(a)na.iac.cnr.it * viviani(a)chalmers.se * leonardo.robol(a)unipi.it Event details: https://calendar.google.com/calendar/event?action=VIEW&eid=M3Bmcm1maDdobmlk… Invitation from Google Calendar: https://calendar.google.com/calendar/ You are receiving this courtesy email at the account numpi(a)di.unipi.it because you are an attendee of this event. To stop receiving future updates for this event, decline this event. Alternatively you can sign up for a Google account at https://calendar.google.com/calendar/ and control your notification settings for your entire calendar. Forwarding this invitation could allow any recipient to send a response to the organizer and be added to the guest list, or invite others regardless of their own invitation status, or to modify your RSVP. Learn more at https://support.google.com/calendar/answer/37135#forwarding

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Reminder: Seminar on 03/11 (Angelo Casulli)
by Leonardo Robol 03 Nov '20

03 Nov '20

Dear all, this is just a reminder of today's seminar. Best, -- Leonardo. Speaker: Angelo Casulli Affiliation: SNS Time: Tuesday, 03/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Rank-structured QR for Chebyshev rootfinding The computation of the roots of polynomials expressed in the Chebyshev basis has a lot of applications, for instance, it is useful in the computation of real roots of smooth functions. We present an algorithm for the rootfinding of Chebyshev polynomials based on an improvement of the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer. Algorithms , 47.3 (2008): pp. 253-273]. We introduce an aggressive early deflation strategy, and we show that the rank-structure allows to parallelize the algorithm avoiding data dependencies which would be present in the unstructured QR. The method exploits the particular structure of the colleague linearization to achieve quadratic complexity and linear storage requirements. The (unbalanced) QR iteration used for Chebyshev rootfinding does not guarantee backward stability on the polynomial coefficients, unless the vector of coefficients satisfy ||p|| ~ 1, an hypothesis which is almost never verified for polynomials approximating smooth functions. Even though the presented method is mathematically equivalent to the latter algorithm, we show that exploiting the rank structure allows to guarantee a small backward error on the polynomial, up to an explicitly computable amplification factor ɣ(p), which depends on the polynomial under consideration. We show that this parameter is almost always of moderate size, making the method accurate on several numerical tests, in contrast with what happens in the unstructured unbalanced QR. We also discuss the connection between the size of this amplification factor and the existence of a good balancing. This provides some insight on why the accuracy of our method is often very close to the balanced QR iteration. https://www.dm.unipi.it/webnew/it/seminari/rank-structured-qr-chebyshev-roo…

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Seminar on 03/11 (Angelo Casulli)
by Leonardo Robol 28 Oct '20

28 Oct '20

Speaker: Angelo Casulli Affiliation: SNS Time: Tuesday, 03/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Rank-structured QR for Chebyshev rootfinding The computation of the roots of polynomials expressed in the Chebyshev basis has a lot of applications, for instance, it is useful in the computation of real roots of smooth functions. We present an algorithm for the rootfinding of Chebyshev polynomials based on an improvement of the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer. Algorithms , 47.3 (2008): pp. 253-273]. We introduce an aggressive early deflation strategy, and we show that the rank-structure allows to parallelize the algorithm avoiding data dependencies which would be present in the unstructured QR. The method exploits the particular structure of the colleague linearization to achieve quadratic complexity and linear storage requirements. The (unbalanced) QR iteration used for Chebyshev rootfinding does not guarantee backward stability on the polynomial coefficients, unless the vector of coefficients satisfy ||p|| ~ 1, an hypothesis which is almost never verified for polynomials approximating smooth functions. Even though the presented method is mathematically equivalent to the latter algorithm, we show that exploiting the rank structure allows to guarantee a small backward error on the polynomial, up to an explicitly computable amplification factor ɣ(p), which depends on the polynomial under consideration. We show that this parameter is almost always of moderate size, making the method accurate on several numerical tests, in contrast with what happens in the unstructured unbalanced QR. We also discuss the connection between the size of this amplification factor and the existence of a good balancing. This provides some insight on why the accuracy of our method is often very close to the balanced QR iteration. https://www.dm.unipi.it/webnew/it/seminari/rank-structured-qr-chebyshev-roo…

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Reminder: Seminar on 20/10 (Simon Telen)
by Leonardo Robol 19 Oct '20

19 Oct '20

Dear all, this is just a reminder of tomorrow's seminar by Simon Telen. Best, -- Leonardo. Speaker: Simon Telen Affiliation: MPI Leipzig Time: Tuesday, 20/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Solving Polynomial Systems via Truncated Normal Forms Systems of polynomial equations arise from many problems in applied mathematics. Solving such systems is considered a challenging computational problem. An important class of numerical solving methods converts the problem into a system of coupled eigenvalue problems. In order to perform this conversion one has to choose a representation for an algebra naturally associated to the equations. Standard choices (coming from Gröbner bases, border bases, resultants ...) may show some very bad, numerical behaviour, even for generic systems. Truncated normal form methods generalise all the aforementioned approaches and are designed to avoid these numerical issues. I will introduce the theory and give many examples. This is joint work with Bernard Mourrain and Marc Van Barel. https://www.dm.unipi.it/webnew/it/seminari/solving-polynomial-systems-trunc…

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Seminar on 20/10 (Simon Telen)
by Leonardo Robol 13 Oct '20

13 Oct '20

Speaker: Simon Telen Affiliation: MPI Leipzig Time: Tuesday, 20/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Solving Polynomial Systems via Truncated Normal Forms Systems of polynomial equations arise from many problems in applied mathematics. Solving such systems is considered a challenging computational problem. An important class of numerical solving methods converts the problem into a system of coupled eigenvalue problems. In order to perform this conversion one has to choose a representation for an algebra naturally associated to the equations. Standard choices (coming from Gröbner bases, border bases, resultants ...) may show some very bad, numerical behaviour, even for generic systems. Truncated normal form methods generalise all the aforementioned approaches and are designed to avoid these numerical issues. I will introduce the theory and give many examples. This is joint work with Bernard Mourrain and Marc Van Barel. https://www.dm.unipi.it/webnew/it/seminari/solving-polynomial-systems-trunc…

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Seminar on 06/10 (Milo Viviani)
by Leonardo Robol 06 Oct '20

06 Oct '20

Dear all, below you find the first announcement for the NumPI seminars. The seminar will be next week on Tuesday, and will be online using the conference platform available at the math department. You find the link below (which will stay the same for all conferences, assuming it works well). When entering the conference you will be asked if you want to only listen or to join with microphone; I suggest you choose the latter: you will be muted anyway after joining, but will be able to ask questions at the end if you wish. Best wishes, -- Leonardo. Speaker: Milo Viviani Affiliation: Scuola Normale Superiore, Pisa Time: Tuesday, 06/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Symplectic methods for isospectral flows and 2D ideal hydrodynamics The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. Several classical PDEs can indeed be set in this framework, and in particular the 2D hydrodynamical Euler equations. In this talk, I will present some results I have obtained during my PhD studies. In particular, I will show how to derive a new class of numerical schemes for Hamiltonian and non-Hamiltonian isospectral flows, in order to solve the 2D hydrodynamical Euler equations. The use of a conservative scheme has revealed new insights in the 2D ideal hydrodynamics, showing clear connections between geometric mechanics, statistical mechanics and integrability theory. https://www.dm.unipi.it/webnew/it/seminari/symplectic-methods-isospectral-f…

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2 PhD positions at Charles University, Prague
by Paola BOITO 28 Sep '20

28 Sep '20

Cari tutti, su richiesta di Stefano Pozza inoltro volentieri questo annuncio per 2 posizioni di PhD e una come postdoc a Praga. Un caro saluto, Paola *************************************** *2 Ph.D. Positions*, Krylov methods and ODE approximation. Two Ph.D. positions are available within the framework of the Primus Research Programme: "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The four years of Ph.D. studies will be done under the supervision of Dr. Stefano Pozza (PI of the project) in the Department of Numerical Mathematics. The department offers an international environment at one of the top universities in the Czech Republic, and the oldest university in Central Europe. The students will also have the opportunity to work with external collaborators from France, Italy, and the UK. The applicants must hold a Master's degree by the start date of Spring 2021 (to be announced) and should have a strong interest in numerical linear algebra and numerical analysis. Knowledge of Matlab or other programming languages is necessary. Applicants will have to prove their English language level by passing an exam (it is possible to waive the examination under some conditions, see https://www.mff.cuni.cz/en/admissions/admission-procedure-in-phd-programmes…) Application deadline: *November 9, 2020.* More information and application instructions: https://www.starlanczos.cz/open-positions

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