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Reminder: Seminar today (Stefano Cipolla)
by Fabio Durastante 18 Jun '21

18 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… <https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base…> Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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Colloquium on 16/06 at 5pm (Volker Mehrmann)
by Paola Boito 16 Jun '21

16 Jun '21

Dear all, An online colloquium of the Department of Mathematics at UniPi is planned on June 16 at 17:00. You are all welcome! The speaker is Volker Mehrmann (TU Berlin). Title: Energy based modeling, simulation, and control. Mathematical theory and algorithms for the solution of real world problems. Abstract: Energy based modeling via port-Hamiltonian systems is a relatively new paradigm in all areas of science and engineering. These systems have wonderful mathematical properties, concerning their analytic, geometric and algebraic properties, but also with respect to their use in numerical algorithms for space-time discretization, model reduction and control. We will introduce the model class and their mathematical properties and we illustrate their usefulness with several real world applications. Google Meet link: https://meet.google.com/qii-tcks-rrr

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Seminar on 18/06 (Stefano Cipolla)
by Leonardo Robol 14 Jun '21

14 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Math Colloquium - Lars Ruthotto - June 17 at 17:00
by Francesco Tudisco 14 Jun '21

14 Jun '21

Dear all, the next GSSI Math Colloquium will be held on *Thursday June 17 at 5pm* (please note **the time is *5pm* instead of the usual 3pm**). The speaker is Lars Ruthotto, with a lecture connecting numerical methods for differential equations and deep learning architectures. More details below. Lars Ruthotto is Associate Professor of Mathematics and Computer Science at Emory University (Atlanta, USA). To attend the talk please use to the following Zoom link: https://us02web.zoom.us/j/85179454721?pwd=TjA0V2M3L3lVTk1NNEdVcGpQcXlTdz09 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: Numerical Methods for Deep Learning motivated by Partial Differential Equations Abstract: Understanding the world through data and computation has always formed the core of scientific discovery. Amid many different approaches, two common paradigms have emerged. On the one hand, primarily data-driven approaches—such as deep neural networks—have proven extremely successful in recent years. Their success is based mainly on their ability to approximate complicated functions with generic models when trained using vast amounts of data and enormous computational resources. But despite many recent triumphs, deep neural networks are difficult to analyze and thus remain mysterious. Most importantly, they lack the robustness, explainability, interpretability, efficiency, and fairness needed for high-stakes decision-making. On the other hand, increasingly realistic model-based approaches—typically derived from first principles and formulated as partial differential equations (PDEs)—are now available for various tasks. One can often calibrate these models—which enable detailed theoretical studies, analysis, and interpretation—with relatively few measurements, thus facilitating their accurate predictions of phenomena. In this talk, I will highlight recent advances and ongoing work to understand and improve deep learning by using techniques from partial differential equations. I will demonstrate how PDE techniques can yield better insight into deep learning algorithms, more robust networks, and more efficient numerical algorithms. I will also expose some of the remaining computational and numerical challenges in this area. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/51fd86c2-9ac2-482f-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 04/06 (Margherita Porcelli)
by Leonardo Robol 04 Jun '21

04 Jun '21

Speaker: Margherita Porcelli Affiliation: Università di Bologna Time: Friday, 04/06/2021, 16:00 Title: Relaxed Interior point methods for low-rank semidefinite programming problems In this talk we will discuss a relaxed variant of interior point methods for semidefinite programming problems (SPDs). We focus on problems in which the primal variable is expected to be low-rank at optimality. Such situations are common in relaxations of combinatorial optimization problems, for example in maximum cut problems as well as in matrix completion problems. We exploit the structure of the sought solution and relax the rigid structure of IPMs for SDP. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. In this talk we will focus on second-order approaches and discuss the difficulties arising in the linear algebra phase. A prototype implementation is shown as well as computational results on matrix completion problems. In particular, we will consider mildly-ill conditioned and noisy random problems as well as problems arising in diverse applications as the matrix to be recovered represents city-to- city distances, a grayscale image, game parameters in a basketball tournament. This is joint work with S. Bellavia (Unifi) and J. Gondzio (Univ. Edinburgh) https://www.dm.unipi.it/webnew/it/seminari/relaxed-interior-point-methods-l… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 14/05 (Alfredo Buttari)
by Leonardo Robol 14 May '21

14 May '21

Speaker: Alfredo Buttari Affiliation: CNRS, IRIT, Toulouse Time: Friday, 14/05/2021, 16:00 Title: Reducing the complexity of linear systems solvers through the block low-rank format Direct linear system solvers are commonly regarded as robust methods for computing the solution of linear systems of equations. Nonetheless, their complexity makes the handling of very large size problems difficult or unfeasible due to excessive execution time or memory consumption. In this talk we discuss the use of low-rank approximation techniques that allow for reducing this complexity at the price of a loss in precision which can be reliably controlled. To take advantage of these low-rank approximations, we have designed a format called block low-rank (BLR) whose objective is to achieve a favorable compromise between complexity and efficiency of operations thanks to its regular structure. We will present the basic BLR format as well as more advanced variants and the associated algorithms; we will analyze their theoretical properties and discuss the issues related to their efficient implementation on parallel computers. We will specifically focus on the use of BLR for the solution of sparse linear systems. The ombination of this format with sparse direct methods, such as the multifrontal one, leads to efficient parallel solvers with scalable complexity. These can either be used as standalone direct solvers or in combination with other techniques such as iterative or multigrid methods. We will present experimental results on real-life problems obtained by integrating the BLR format within the MUMPS parallel sparse direct solver. https://www.dm.unipi.it/webnew/it/seminari/reducing-complexity-linear-syste… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 07/05 (Stefano Pozza)
by Leonardo Robol 07 May '21

07 May '21

Speaker: Stefano Pozza Affiliation: Charles University, Prague Time: Friday, 07/05/2021, 16:00 Title: The Short-term Rational Lanczos Method and Applications Rational Krylov subspaces have become a reference tool in dimension reduction procedures for several application problems. When data matrices are symmetric, a short-term recurrence can be used to generate an associated orthonormal basis. In the past this procedure was abandoned because it requires twice the number of linear system solves per iteration than with the classical long-term method. We propose an implementation that allows one to obtain key rational subspace matrices without explicitly storing the whole orthonormal basis, with a moderate computational overhead associated with sparse system solves. Several applications are discussed to illustrate the advantages of the proposed procedure. https://www.dm.unipi.it/webnew/it/seminari/short-term-rational-lanczos-meth… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 23/04 (Philipp Birken)
by Leonardo Robol 23 Apr '21

23 Apr '21

Speaker: Philipp Birken Affiliation: Lund University Time: Friday, 23/04/2021, 16:00 Title: Conservative iterative solvers in computational fluid dynamics The governing equations in computational fluid dynamics such as the Navier-Stokes- or Euler equations are conservation laws. Finite volume methods are designed to respect this and the theorem of Lax-Wendroff underscores the importance of it. It roughly states that for a nonlinear (!) scalar conservation law in 1D , if the numerical method with explicit Euler time integration is consistent and (locally) conservative, then in case of convergence, the numerical method converges to a weak solution. When using implicit time integration, the widespread believe in the community is that conservation is lost. This is however, not necessarily due to the time integration, but due to the use of iterative solvers. We first present a catalogue of iterative solvers that preserve the weaker property of global conservation to identify candidates of solvers that preserve local conservation as used in the Lax-Wendroff theorem. We then proceed to prove an extension of the Lax-Wendroff theorem for the situation that we perform a fixed number of steps of a so called pseudo time iteration per time step. It turns out that in this case, the numerical method converges to a weak solution of the conservation law with a modified propagation speed. This can be exploited to improve performance of the iterative method. https://www.dm.unipi.it/webnew/it/seminari/conservative-iterative-solvers-c… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 09/04 (Jie Meng)
by Leonardo Robol 09 Apr '21

09 Apr '21

Speaker: Jie Meng Affiliation: Università di Pisa Time: Friday, 09/04/2021, 16:00 Title: Geometric means of quasi-Toeplitz matrices We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matrices A = (a_{i,j}) i,j=1,2,... of the form A = T(a) + E, where E represents a compact operator, and T(a) is a semi-infinite Toeplitz matrix associated with the function a, with Fourier series \sum_{l} a_l e^{ilt} , in the sense that (T(a))_{i,j} = a_{j-i}. If a is real valued and essentially bounded, then these matrices represent bounded self-adjoint operators on l^2. We consider the case where a is a continuous function, where quasi-Toeplitz matrices coincide with a classical Toeplitz algebra, and the case where a is in the Wiener algebra, that is, has absolutely convergent Fourier series. We prove that if a_1, ... , a_p are continuous and positive functions, or are in the Wiener algebra with some further conditions, then means of geometric type, such as the ALM, the NBMP and the Karcher mean of quasi-Toeplitz positive definite matrices associated with a_1, ..., a_p , are quasi-Toeplitz matrices associated with the geometric mean (a_1 ... a_p)^{1/p}, which differ only by the compact correction. We show by numerical tests that these operator means can be practically approximated. https://www.dm.unipi.it/webnew/it/seminari/geometric-means-quasi-toeplitz-m… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Ivan Markovsky - March 30 at 18:00
by Francesco Tudisco 29 Mar '21

29 Mar '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will take place tomorrow *March 30 at 18:00 (CET)*. The speaker is Ivan Markovsky from Vrije Universiteit Brussel (Belgium) who will give a talk on Data-driven dynamic interpolation and approximation. Abstract and more info below. The seminar will be given via Zoom. To attend the seminar please use the following link: https://us02web.zoom.us/j/85393475759?pwd=ckNDOGNGY0d0bTBZVXBmd1FibXJVUT09 <https://us02web.zoom.us/j/85393475759?pwd=ckNDOGNGY0d0bTBZVXBmd1FibXJVUT09> 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 Tomorrow! Francesco and Nicola ------------------------------------------------- Data-driven dynamic interpolation and approximation The behavioral system theory give theoretical foundation for nonparameteric representations of linear time-invariant systems based on Hankel matrices constructed from data. These data-driven representations led in turn to new system identification, signal processing, and control methods. In particular, data-driven simulation and linear quadratic tracking control problems were solved using the new approach [1,2]. This talk shows how the approach can be used further on for solving data-driven interpolation and approximation problems (missing data estimation) and how it can be generalized to some classes of nonlinear systems. The theory leads to algorithms that are both general (can deal simultaneously with missing, exact, and noisy data of multivariable systems) and simple (require existing numerical linear algebra methods only). This opens a practical computational way of doing system theory and signal processing directly from data without identification of a transfer function or a state space representation and doing model-based design. References: [1] I. Markovsky and P. Rapisarda. “Data-driven simulation and control”. Int. J. Control 81.12 (2008), pp. 1946--1959. [2] I. Markovsky. A missing data approach to data-driven filtering and control. IEEE Trans. Automat. Contr., 62:1972--1978, April 2017. [3] I. Markovsky and F. Dörfler. Data-driven dynamic interpolation and approximation. Technical report, Vrije Universiteit Brussel, 2021. Available from http://homepages.vub.ac.be/~imarkovs/publications/ddint.pdf — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/51aafd85-e7f6-58a0-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 19/03 (Alice Cortinovis)
by Leonardo Robol 19 Mar '21

19 Mar '21

Speaker: Alice Cortinovis Affiliation: EPFL Time: Friday, 19/03/2021, 16:00 Title: Randomized trace estimates for indefinite matrices with an application to determinants Randomized trace estimation is a popular technique to approximate the trace of a large-scale matrix A by computing the average of quadratic forms x^T * A * x for many samples of a random vector X. We show new tail bounds for randomized trace estimates in the case of Rademacher and Gaussian random vectors, which significantly improve existing results for indefinite matrices. Then we focus on the approximation of the determinant of a symmetric positive definite matrix B, which can be done via the relation log(det(B)) = trace(log(B)), where the matrix log(B) is usually indefinite. We analyze the convergence of the Lanczos method to approximate quadratic forms x^T * log(B) * x by exploiting its connection to Gauss quadrature. Finally, we combine our tail bounds on randomized trace estimates with the analysis of the Lanczos method to improve and extend an existing result on log determinant approximation to not only cover Rademacher but also Gaussian random vectors. https://www.dm.unipi.it/webnew/it/seminari/randomized-trace-estimates-indef… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Eugene Tyrtyshnikov - Today at 18:00
by Francesco Tudisco 09 Mar '21

09 Mar '21

Good morning everyone, This is just a gentle reminder about *today's seminar by Eugene Tyrtyshnikov* (MSU and INM-RAS). The seminar will take place *at 18:00* via the Zoom meeting: https://us02web.zoom.us/j/84101660726?pwd=TDhrWlFKdnhQVnBTZFdMWmw3Q3J4QT09 Hope to see you all there! Francesco and Nicola ---------------- Tikhonov's solution to a class of linear systems equivalent within perturbations A standard approach to incorrect problems suggests that a problem of interest is reformulated with the knowledge of some additional a-priori information. This can be done by several well-known regularization techniques. Many practical problems are successfully solved on this way. What does not still look as completely satisfactory is that the new reset problem seems to appear rather implicitly in the very process of its solution. In 1980, A. N. Tikhonov proposed a reformulation [1] that arises explicitly before the discussion of the solution methods. He suggested a notion of normal solution to a family of linear algebraic systems described by a given individual system and its vicinity comprising perturbed systems, under the assumption that there are compatible systems in the class notwithstanding the compatibility property of the given individual system. Tikhovov proved that the normal solution exists and is unique. However, a natural question about the correctness of the reset problem was not answered. In this talk we address a question of correctness of the reformulated incorrect problems that seems to have been missed in all previous considerations. The main result is the proof of correctness for Tikhonov's normal solution. Possible generalizations and difficulties will be also discussed. [1] A. N. Tikhonov, Approximate systems of linear algebraic equations, USSR Computational Mathematics and Mathematical Physics, vol. 20, issue 6 (1980) — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2fe6fc1f-c30c-9ee8-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Eugene Tyrtyshnikov - March 9 at 18:00
by Francesco Tudisco 08 Mar '21

08 Mar '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. *The seminar schedule is changed and will now run on Tuesdays @ 18:00 (CET)* most of the times. This week's seminar is on *March 09 at 18:00 (CET).* The speaker is Eugene Tyrtyshnikov from Moscow University and INM-RAS (Russia). The talk will be focused on the Tikhonov solution to a class of linear system problems. Please find abstract and title below. The seminar will be given via Zoom. To attend the seminar please use the following link: https://us02web.zoom.us/j/84101660726?pwd=TDhrWlFKdnhQVnBTZFdMWmw3Q3J4QT09 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 Tuesday! Francesco and Nicola ------ Tikhonov's solution to a class of linear systems equivalent within perturbations A standard approach to incorrect problems suggests that a problem of interest is reformulated with the knowledge of some additional a-priori information. This can be done by several well-known regularization techniques. Many practical problems are successfully solved on this way. What does not still look as completely satisfactory is that the new reset problem seems to appear rather implicitly in the very process of its solution. In 1980, A. N. Tikhonov proposed a reformulation [1] that arises explicitly before the discussion of the solution methods. He suggested a notion of normal solution to a family of linear algebraic systems described by a given individual system and its vicinity comprising perturbed systems, under the assumption that there are compatible systems in the class notwithstanding the compatibility property of the given individual system. Tikhovov proved that the normal solution exists and is unique. However, a natural question about the correctness of the reset problem was not answered. In this talk we address a question of correctness of the reformulated incorrect problems that seems to have been missed in all previous considerations. The main result is the proof of correctness for Tikhonov's normal solution. Possible generalizations and difficulties will be also discussed. [1] A. N. Tikhonov, Approximate systems of linear algebraic equations, USSR Computational Mathematics and Mathematical Physics, vol. 20, issue 6 (1980) — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FWkAyR1tebRPom…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 05/03 (Davide Bianchi)
by Leonardo Robol 05 Mar '21

05 Mar '21

Speaker: Davide Bianchi Affiliation: University of Insubria Time: Friday, 05/03/2021, 16:00 Title: Compatibility, embedding and regularization of non-local random walks on graphs Several variants of the graph Laplacian have been introduced to model non-local diffusion pro- cesses, which allow a random walker to “jump” to non-neighborhood nodes, most notably the path graph Laplacians and the fractional graph Laplacian, see [2, 3]. From a rigorous point of view, this new dynamics is made possible by having replaced the original graph G with a weighted complete graph G 0 on the same node-set, that depends on G and wherein the presence of new edges allows a direct passage between nodes that were not neighbors in G. A natural question arises: are the dynamics on the “old” walks along the edges of G compatible with the new dynamics? Indeed, it would be desirable to introduce long-range jumps but preserving at the same time the original dynamics if we move along the edges of G. In other words, for any time-interval where does not take place any long-range jump, a random walk on G 0 should be indistinguishable from the original random walk on G. One can easily figure this by a simple but clarifying example: let us suppose that our random walker is surfing the Net (the original graph G), and just for the sake of simplicity let us suppose that the Net is undirected. The walker then can move towards linked web-pages with a probability that can be both uniforms on the number of total links or dependent on some other parameters. Suppose now that we allow the walker to jump from one web-page to non-linked web-pages by just typing an URL address in the navigation bar so that he can virtually reach directly any possible web-pages on the Net (the induced graph G 0 ). If in any moment, for any reason, the walker is forced again to surf the Net by just following the links, then we should see him moving exactly as he used to do, namely, the probability he moves to the next linked web-page has to be the same as before. Unfortunately, in general, the induced complete graph G 0 , defined accordingly to the proposal in the literature, breaks that compatibility and the new models cease to be expressions of the original model G. In this talk, we will present some of the main results obtained in [1]. We will first introduce a rigorous definition of compatibility and embedding, which stem from a probabilistic and purely an- alytical point of view, respectively. Secondly, we will propose a regularization method to guarantee such compatibility and preserving at the same time all the nice properties granted by G 0 . Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Michael Schaub - Today at 18:00
by Francesco Tudisco 17 Feb '21

17 Feb '21

Good morning everyone, This is just a gentle reminder about *today's seminar* on "Learning from signals on graphs with unobserved edges" by Michael Schaub (RWTH Aachen University). Abstract below. Please note that the seminar talk has been pushed back by one hour and *will take place at 18:00*. The Zoom link for the talk is: https://us02web.zoom.us/j/87171939595 Hope to see you all there! Francesco and Nicola ---------------------------------------------- Speaker: Michael Schaub, RWTH Aachen University https://michaelschaub.github.io/ Title: Learning from signals on graphs with unobserved edges Abstract: In many applications we are confronted with the following system identification scenario: we observe a dynamical process that describes the state of a system at particular times. Based on these observations we want to infer the (dynamical) interactions between the entities we observe. In the context of a distributed system, this typically corresponds to a "network identification" task: find the (weighted) edges of the graph of interconnections. However, often the number of samples we can obtain from such a process are far too few to identify the edges of the network exactly. Can we still reliably infer some aspects of the underlying system? Motivated by this question we consider the following identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes. More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic blockmodel (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy. We further discuss some possible variations and extensions of this problem setup. This talk is part of NOMADS — Numerical ODEs, Matrix Analysis and Data Science — seminar at GSSI: https://num-gssi.github.io/seminar/ — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/c82561f8-8a98-5698-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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NumPi seminars - Doodle
by Leonardo Robol 15 Feb '21

15 Feb '21

Dear all, as usual, we will soon start with the NumPi seminars for the second semester. As in the first semester, they will be online. In order to minimize the overlap with teaching activities and other commitments, we have prepared a Doodle where (if you wish to attend the seminars) you can choose your preferred time slot(s). Please note that the Doodle is for this week, but it is intended for a "generic week" of this semester. The first seminar will likely be at the beginning of March. Doodle link: https://doodle.com/poll/a4fpmfwat7q62rnu P.S.: In case you wish to propose some speakers (or yourself as a speaker), feel free to drop us an e-mail. Best wishes, -- Fabio Durastante and Leonardo Robol.

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[NOMADS] Seminar - Michael Schaub - Feb 17 at 17:00
by Francesco Tudisco 15 Feb '21

15 Feb '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be on Wednesday February 17 at 17:00 (CET) by Michael Schaub from RWTH Aachen University (Germany). The talk will be focused on a method for learning the structure of a network given few observations of a diffusive process on the unknown graph. Title and abstract are below. To attend the semimar please use the following link: https://us02web.zoom.us/j/87171939595 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit. Francesco and Nicola -------- Title: Learning from signals on graphs with unobserved edges In many applications we are confronted with the following system identification scenario: we observe a dynamical process that describes the state of a system at particular times. Based on these observations we want to infer the (dynamical) interactions between the entities we observe. In the context of a distributed system, this typically corresponds to a "network identification" task: find the (weighted) edges of the graph of interconnections. However, often the number of samples we can obtain from such a process are far too few to identify the edges of the network exactly. Can we still reliably infer some aspects of the underlying system? Motivated by this question we consider the following identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes. More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic blockmodel (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy. We further discuss some possible variations and extensions of this problem setup. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2f2274b3-9a34-5b45-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Lothar Reichel - Today at 17:00
by Francesco Tudisco 04 Feb '21

04 Feb '21

Good morning everyone, This is just a gentle reminder about today's seminar "Large-scale regression with non-convex loss and penalty" by Lothar Reichel (Kent State University, USA). Abstract below. The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/89724684523 Please feel free to distribute this announcement as you see fit. Hope to see you there! Francesco and Nicola ---------- Title: Large-scale regression with non-convex loss and penalty Description: We do non-convex optimization with application to image restoration and regression problems for which a sparse solution is desired. ---------- — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/02613376-994d-c51e-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Lothar Reichel - Feb 4 at 17:00
by Francesco Tudisco 01 Feb '21

01 Feb '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given on *Thursday* (not Wednesday as usual) *February 4 at 17:00 (CET)* by *Lothar Reichel* from Kent State University (USA). --- Title: Large-scale regression with non-convex loss and penalty Description: We do non-convex optimization with application to image restoration and regression problems for which a sparse solution is desired. --- To attend the seminar please use the following link: https://us02web.zoom.us/j/89724684523 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 Thursday! Francesco and Nicola — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2f5d2866-9537-1186-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Summer School plus Conference on “Mathematics for Nonstationary Signals,and applications in Geophysics and other fields” - L'Aquila (Italy) and online, July 2021
by Federico Poloni 30 Jan '21

30 Jan '21

Inoltro questo annuncio per i potenziali interessati non iscritti al GNCS. Buon week-end, -federico -------- Forwarded Message -------- Subject: Summer School plus Conference on “Mathematics for Nonstationary Signals,and applications in Geophysics and other fields” - L'Aquila (Italy) and online, July 2021 Date: Sat, 30 Jan 2021 10:29:15 +0100 From: Ruggiero Valeria <valeria.ruggiero(a)unife.it> To: gncs-aderenti(a)altamatematica.it Dear Colleagues, we kindly inform you that a Summer School plus Conference on “Mathematics for Nonstationary Signals and applications in Geophysics and other fields”, will take place at the Università degli Studi dell'Aquila, L'Aquila, Italy, and online on July 19-24, 2021. The event will be hybrid, providing the opportunity to everyone to join either in-person or virtually. During the Summer School young researchers and PhD students will have a chance to learn and deepen their knowledge on Mathematics of Signal Processing, in particular on new data analysis tools/techniques for non-stationary time series and their theoretical foundation. The summer school will take place during the first 4 days and it will consist of three courses of 8 hours each. Confirmed Lecturers: Patrick Flandrin - ENS Lyon Yang Wang - HKSTU Hau-tieng Wu - Duke University At the end of the school there will be a 2 days and half Conference and Poster Session during which the speakers will show both the applications of these techniques to real life data and present the current frontiers of the theoretical research. Some slots for contributed talks and posters are still available. Contributed talks will be 30 minutes long (25+5 for questions). Submission deadline is April 30, 2021. Applications for prospective students of the Summer School, as well as speakers of the conference and poster session are now open. Financial support is available for a limited number of participants. For more information and to apply please visit www.cicone.com/NoSAG21.html <http://www.cicone.com/NoSAG21.html> Best regards, The local organizing committee Antonio Cicone - DISIM - Università degli Studi dell'Aquila - L'Aquila Giulia D'Angelo - INAF - Istituto di Astrofisica e Planetologia Spaziali - Roma Enza Pellegrino - DIIIE - Università degli Studi dell'Aquila - L'Aquila Mirko Piersanti - INFN - Universita di Roma "Tor Vergata" - Roma Angela Stallone - INGV - Istituto Nazionale di Geofisica e Vulcanologia - Roma

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Math Colloquium - Anders Hansen - Jan 28
by Francesco Tudisco 28 Jan '21

28 Jan '21

Dear all, * *the next GSSI Math Colloquium will be held on *Thursday January 28 *at***3pm* (Italian time). The speaker is Anders Hansen, <http://www.damtp.cam.ac.uk/research/afha/anders/> with a lecture connecting computational mathematics with deep learning and AI. More details below. Anders Hansen is Associate Professor at University of Cambridge, where he leads the Applied Functional and Harmonic Analysis group, and Full Professor of Mathematics at the University of Oslo. To attend the talk please use to the following *Zoom link*: https://us02web.zoom.us/j/84038062394 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: On the foundations of computational mathematics, Smale's 18th problem and the potential limits of AI Abstract: There is a profound optimism on the impact of deep learning (DL) and AI in the sciences with Geoffrey Hinton concluding that 'They should stop training radiologists now'. However, DL has an Achilles heel: it is universally unstable so that small changes in the initial data can lead to large errors in the final result. This has been documented in a wide variety of applications. Paradoxically, the existence of stable neural networks for these applications is guaranteed by the celebrated Universal Approximation Theorem, however, the stable neural networks are never computed by the current training approaches. We will address this problem and the potential limitations of AI from a foundations point of view. Indeed, the current situation in AI is comparable to the situation in mathematics in the early 20th century, when David Hilbert’s optimism (typically reflected in his 10th problem) suggested no limitations to what mathematics could prove and no restrictions on what computers could compute. Hilbert’s optimism was turned upside down by Goedel and Turing, who established limitations on what mathematics can prove and which problems computers can solve (however, without limiting the impact of mathematics and computer science). We predict a similar outcome for modern AI and DL, where the limitations of AI (the main topic of Smale’s 18th problem) will be established through the foundations of computational mathematics. We sketch the beginning of such a program by demonstrating how there exist neural networks approximating classical mappings in scientific computing, however, no algorithm (even randomised) can compute such a network to even 1-digit accuracy (with probability better than 1/2). We will also show how instability is inherit in the methodology of DL demonstrating that there is no easy remedy, given the current methodology. Finally, we will demonstrate basic examples in inverse problems where there exists (untrained) neural networks that can easily compute a solution to the problem, however, the current DL techniques will need 10^80 data points in the training set to get even 1% success rate. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/b3099d6a-bcef-2052-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Postdoc Position, Krylov Methods, Charles Univ, Czech Rep
by Federico Poloni 25 Jan '21

25 Jan '21

Buongiorno, inoltro questo annuncio, che può essere di interesse per qualche iscritto alla lista. **Postdoc Position, Krylov Methods, Charles Univ, Czech Rep** A postdoc position is 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 appointment period is one year, with the possibility of extension. The postdoc will start before the end of 2021. The start date is negotiable. We are looking for candidates with a strong background in numerical linear algebra. In particular, we seek applicants with expertise in matrix function approximation and Krylov subspace methods. The applicant must hold a Ph.D. degree by the start date. Application deadline: March 15, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions <https://www.starlanczos.cz/open-positions> -- --federico poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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NEPA Seminar (D. Bini)
by Leonardo Robol 15 Jan '21

15 Jan '21

Dear all, on January 19, 3 pm, Dario Bini will give a talk on "Solving Structured Matrix Equations Encountered in the Analysis of Stochastic Processes". The talk is part of the NEPA seminar series, and many more talks will take place in the next weeks. Participation is free, but a registration is required to obtain the Zoom link [1]. [1] https://sites.google.com/unisa.it/nepaseminars Best wishes, -- Leonardo.

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[NOMADS] Seminar - Gianluca Ceruti - Today at 17:00
by Francesco Tudisco 13 Jan '21

13 Jan '21

Good morning everyone, This is just a gentle reminder about today's seminar "Numerical integrators for dynamical low-rank approximation" by Gianluca Ceruti (Uni Tuebingen). Abstract below. The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/82131676880 Hope to see you there! Francesco and Nicola ----------- Gianluca Ceruti <https://na.uni-tuebingen.de/~ceruti/> - University of Tuebingen Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as curse of dimensionality. The amount of data to be stored and treated, grows exponentially, and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. To conclude, via a novel compact formulation of the Tucker integrator, we will further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/46a4a726-fee9-9f0b-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Gianluca Ceruti - Jan 13 at 17:00
by Francesco Tudisco 11 Jan '21

11 Jan '21

Dear all, We hope you all had joyful holidays and wish you all a great start for the new year! We are ready to start with this year's NOMADS seminar at GSSI and would like to invite you to this week's talk. The seminar will be given on Wednesday January 13 at 17:00 (CET) by Gianluca Ceruti from University of Tuebingen. Title, abstract and zoom link are below. 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! Francesco and Nicola ================================ Speaker: Gianluca Ceruti, University of Tuebingen https://na.uni-tuebingen.de/~ceruti/ Zoom link: https://us02web.zoom.us/j/82131676880 Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as curse of dimensionality. The amount of data to be stored and treated, grows exponentially, and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. To conclude, via a novel compact formulation of the Tucker integrator, we will further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FW%3DqD1z%3D9V…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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