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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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