I am very excited I will be giving a minitutorial on Applied Nonlinear Perron–Frobenius Theory at the SIAM conference on Applied Linear Algebra (LA21).
I will present the tutorial together with Antoine Gautier.
We will introduce the concept of multihomogeneous operators and we will present the state-of-the-art version of the nonlinear Perron-Frobenius theorem for nonnegative nonlinear mappings. We will discuss several numerical optimization implications connected to nonlinear and higher-order versions of the Power and the Sinkhorn methods and several open challenges, both from the theoretical and the computational viewpoints. We will also discuss numerous problems in data mining, machine learning and network science which can be cast in terms of nonlinear eigenvalue problems with eigenvector nonlinearities and we will show how the nonlinear Perron-Frobenius theory can help solve them.
I have accepted an invite to serve as associate editor in the Survey & Review section of SIAM Review (SIREV), the flagship section of one of the highest impact applied math journal. Excited and looking forward to starting!
Excited that our paper Ergodicity coefficients for higher-order stochastic processes, joint work with Dario Fasino, has been accepted on the SIAM Journal on Mathematics of Data Science
Last day of the first virtual SIAM Imaging Science conference today. I am presenting a talk at the minisymposium Nonlinear Spectral Analysis with Applications in Imaging and Data Science organized by Leon Bungert (Friedrich-Alexander Universitaet Erlangen-Nuernberg, Germany), Guy Gilboa (Technion Israel Institute of Technology, Israel) and Ido Cohen (Israel Institute of Technology, Israel).
These are title and abstract of my talk:
Nodal Domain Theorem for the p-Laplacian on Graphs and the Related Multiway Cheeger Inequality
We consider the p-Laplacian on discrete graphs, a nonlinear operator that generalizes the standard graph Laplacian (obtained for p=2). We consider a set of variational eigenvalues of this operator and analyze the nodal domain count of the corresponding eigenfunctions. In particular, we show that the famous Courant’s nodal domain theorem for the linear Laplacian carries over almost unchanged to the nonlinear case. Moreover, we use the nodal domains to prove a higher-order Cheeger inequality that relates the k-way graph cut to the k-th variational eigenvalue of the p-Laplacian.
Below you can find my slides, in case you wish to have a look at them
I will preset my first ever Virtual Poster at the first official virtual SIAM Network Science workshop!
Des Higham will present our work on higher-order eigenvector-based network coefficients on July 10, 9am Pacific Time (5pm UK, 6pm EU)
My poster session room will be on nonlinear eigenevector centralities and will be on for 45 min starting at 4pm Pacific Time (midnight UK, 1am EU). Lots of coffee is planned for that day. You may wish to have a look at my poster:
We are organizing a “Marie Skłodowska Curie Action Day” virtual event to illustrate some fundamental aspects of Horizon 2020 MSC fellowships. We will discuss some of the application rules, evaluation criteria, how do we think a successful application should be written and we will share personal experiences as recipients and supervisors of MSC individual fellowships.
This event has been promoted and coordinated by my amazing colleague Elisabetta Baracchini
Michael Schaub, Santiago Segarra and I are organizing a virtual minisymposium on Learning from data on networks within the SIAM Conference on Mathematics of Data Science 2020, happening virtually during the whole month of June. See also the conference’s virtual program.
Our mini will take place on June 30, staring at 10:00 am Eastern time (Boston)
[7am California, 9am Texas, 3pm UK, 4pm EU, 10pm China]
For more details and to register to join the event online (free of charge), please see the minisymposium webpage.
Modern societies increasingly depend on complex networked systems to support our daily routines. Electrical energy is delivered by the power grid; the Internet enables almost instantaneous world-wide interactions; our economies rest upon a complex network of inter-dependencies spanning the globe. Networks are ubiquitous in complex biological, social, engineering, and physical systems. Understanding structures and dynamics defined over such networks has thus become a prevalent challenge across many disciplines. A recurring question which appears in a wide variety of problems is how one can exploit the interplay between the topological structure of the system and available measurements at the nodes (or edges) of the networks. The goal of this minisymposium is to bring together researchers from different mathematical communities – from network science, machine learning, statistics, signal processing and optimization – to discuss and highlight novel approaches to understand and learn from data defined on networks.
Excited to take part today at the Open House event for the Master’s Degree in Data Science at the Department of Mathematics of the University of Padova. I will give a high-level introduction to the problem of link prediction in networks and how to use PageRank eigenvectors to compute a mathematically informed prediction. The live streaming of the event is available on youtube.
The COVID19 pandemic resulted in the mass cancellation of in-person conferences and seminars across the globe. Wonderful initiatives have resulted as a response to this unfortunate situation. For example, many scientific communities worldwide have started “One World” online seminar series and several conference committees are working in order to put forward online versions of traditional meetings.
Here I would like to list the initiatives related to my research interests that I am aware of. If you know of any other online meeting I have missed, please do let me know!
|OWML||One World Seminar Series on the Mathematics of Machine Learning||Wednesdays @ 12 noon ET (UTC-4)||Zoom|
|OWSP||One World Signal Processing Seminar||Fridays||Zoom|
|MADS||Mathematical Methods for Arbitrary Data Sources||Mondays @ 2pm CET (UTC+2)||Zoom|
|E-NLA||Online seminar series on Numerical Linear Algebra||Wednesdays @ 4pm CET (UTC+2)||Zoom|
|MINDS||One World Mathematics of INformation, Data, and Signals Seminar||Thursdays @ 2:30pm EDT (UTC-4)||—|
|OPT||One World Optimization Seminar||Mondays @ 3pm CEST (UTC+2)||Zoom|
|IMAGINE||Imaging & Inverse Problems||Wednesdays @ 4pm CET (UTC+2)||Zoom|
|GAMENET||One World Mathematical Game Theory Seminar||Mondays @ 3pm CEST (UTC+2)||Zoom|
|PROB||One World Probability Seminar||Weekends @ 3-4pm CEST (UTC+2)||Zoom|
Our paper Total variation based community detection using a nonlinear optimization approach, joint work with Andrea Cristofari and Francesco Rinaldi from the University of Padua, has been accepted on the SIAM Journal on Applied Mathematics
I am traveling today to visit and give a talk at the pure, applicable and numerical mathematics seminar at University of Kent, Canterbury (UK). Thanks Bas Lemmens and Marina Iliopoulou for the invitation and for hosting me!
I am in Oxford (UK) today, giving a talk at the Rutherford Appleton Lab and Uni of Oxford’s Numerical Analysis group joint seminar on Computational Mathematics and Applications. Thank you Michael Wathen and Tyrone Rees for the invitation!
Our paper A framework for second order eigenvector centralities and clustering coefficients, joint work with Francesca Arrigo and Des Higham, has been accepted in the Proceedings of the Royal Society Series A
Starting from March 1, I will be visiting the University of Padua to teach the doctoral course Eigenvector methods for learning from data on networks for the PhD program in Computational Mathematics. You can use this link if you wish to enroll for my course. Thanks Michela for the invitation!
I have been invited to give a plenary talk this summer at the Householder Symposium XXI. You can read the abstract of my talk from the book of abstracts. Looking forward for this exciting opportunity!
Konstantin successfully passed today his preliminary PhD exam. Congratulations!
Our paper Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs is being presented today by Pedro Mercado at NeurIPS 2019. You may wish to have a look at the poster:
Excited to be part of the Program Committee of the SIAM Workshop on Network Science!
We invite contributions focused on all aspects of mathematical, algorithmic, data analysis, and computational techniques in network science and its applications. Accepted submissions will be featured in the workshop as a 20-minute talk, 5-minute talk, or poster.
Submission deadline: February 20, 2020
Twitter feed: #SIAMNS20
The 7th edition of the Rome Moscow summer school on Matrix Methods and Applied Linear Algebra is in preparation! This is the 10th anniversary of this exciting series of summer schools. The tentative dates for the school are:
The school is meant for both final years undergraduate and graduate students who are intrigued by Applied Mathematics and Matrix Methods. The summer school takes place over the course of one entire month—in the two beautiful cities of Rome (Italy) and Moscow (Russia)—and thus it allows the students to really work over the topics that are discussed. Also it is a wonderful occasion to meet new people in the field of Applied Linear Algebra. I have been student of several editions of the school and strongly encourage participation. Please, feel free to contact me if you have questions.
I am delighted to hear that our paper Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs – with Pedro Mercado and Matthias Hein – has been accepted on the proceedings of this year’s NeurIPS conference.