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X-WR-CALNAME;VALUE=TEXT:Eventi DIAG
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DTSTART:20231029T030000
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UID:calendar.25717.field_data.0@glad.uniroma1.it
DTSTAMP:20260405T091303Z
CREATED:20230607T082449Z
DESCRIPTION:AbstractSpectral properties of graphs are of paramount importan
 ce. While important properties of graphs are reflected in properties of th
 eir spectra\, fundamental connections between spectral and topological pro
 perties of graphs are at the core of some successful approaches in a numbe
 r of problems\, e.g.\, graph partitioning or community detection. At the s
 ame time\, graph spectra are related to key properties of random walks in 
 graphs. These\, in turn\, describe key aspects of some fundamental dynamic
 s on graphs.The goal of this course is introducing students to these topic
 s\, providing an overview of key notions\, some reference applications and
  how spectral properties of graphs can be investigated from different pers
 pectives\, leading to insights into applications of interest both in compu
 ter science and other areas of research.Speakers: Prof. Luca Becchetti (Sa
 pienza University) and Prof. Francesco Pasquale (University Tor Vergata Ro
 me)Course schedule    Monday\, June 12th9am - 11am. Francesco PasqualeIntr
 oduction to Markov chains and random walks. Examples: birth-and-death chai
 ns. Applications: An algorithm for 3-SAT with running time O((4/3)^n \poly
 (n)).11am - 1pm. Francesco PasqualeRandom walks\, stationary distributions
 . Irreducibility and aperiodicity\, lazy chains. Total variation distance\
 , mixing time. Relaxation time and the second eigenvalue. Mixing and relax
 ation.Tuesday\, June 13th10am - 12am noon. Luca BecchettiGraphs and graph 
 matrices. Spectral theorem for symmetric matrices. Variational characteriz
 ation of eigenvalues. Graph matrices.2pm - 4pm. Luca BecchettiBottlenecks 
 and cuts. Finding cuts of minimum conductance. Easy part of Cheeger's ineq
 uality. Sparse cuts and Laplacian's second eigenvecto's profile: Examples.
 Wednesday\, June 14th10am - 12am noon. Francesco PasqualeSampling and coun
 ting\, the Monte Carlo Method. Approximate sampling and approximate counti
 ng. Application: DNF-counting. Introduction to the Markov Chain Monte Carl
 o method.2pm - 4pm. Luca BecchettiHard part of Cheeger's inequality and im
 plications.Thursday\, June 15th10am - 12am noon. Francesco PasqualeTechniq
 ues for bounding mixing time: coupling\, path coupling\, bottleneck ratio.
  Example: Random walk on the hypercube.2pm - 4pm. Luca BecchettiEigenvalue
 s\, bottlenecks and rapid mixing. Mixing time and conductance. Expanders a
 nd expander mixing lemma.Friday\, June 16th10am - 12am noon. Francesco Pas
 qualeThe Markov Chain Monte Carlo method. Application: Approximate countin
 g proper colorings.2pm - 4pm. Luca Becchetti: Spectral Graph TheoryBeyond 
 conductance: graph partitioning and k-way constant. Brief overview of high
 er-order Cheeger's inequalities. Spectral embeddings and Spectral graph cl
 ustering with examples.Zoom link: https://uniroma1.zoom.us/j/98700192862?p
 wd=VlRPQmEyQjJUWXdjTzJyMFVDZEVXdz09 
DTSTART;TZID=Europe/Paris:20230612T090000
DTEND;TZID=Europe/Paris:20230616T160000
LAST-MODIFIED:20230607T082905Z
LOCATION:Room B203@DIAG\, via Ariosto 25\, Rome
SUMMARY:PhD course - Spectral graph theory and random walks: connections an
 d applications - Luca Becchetti (Sapienza University) and Francesco Pasqua
 le (University Tor Vergata Rome)\n\n\n  \n  \n\n    \n\n\nLuca\n\n\nBecche
 tti  \n\n  \n\n    \n\n\n\n\n\nProfessore associato\n\n\npagina personale
 \n\nstanza: \n\nB206\n\ntelefono: \n\n+39 0677274025  \n\n  \n\n    \n\nBi
 ografia: \n\n\n\nPosition:\n\n\n- December 2012 - present: Associate Profe
 ssor at Dipartimento di Ingegneria Gestionale 'Antonio Ruberti'\, Sapienza
  University of Rome.\n\n\n- March 2001 - December 2012: Research associate
  at Dipartimento di Ingegneria Gestionale 'Antonio Ruberti'\, Sapienza Uni
 versity of Rome.\n\n\nEducation:\n\n\n- PhD in computer engineering at Dip
 artimento di Ingegneria Gestionale 'Antonio Ruberti'\, Sapienza University
  of Rome\, 1998\n\n\n- M. Sc. in computer engineering at Dipartimento di I
 ngegneria Gestionale 'Antonio Ruberti'\, Sapienza University of Rome\, 199
 5\n\n\nVitae:\n\n\nA longer version of my curriculum can be found at this 
 link\n\n\n \n\n\nInteressi di ricerca: \n\n\n\nI have a background interes
 t in the design and analysis of algorithms for NP-hard and on-line optimiz
 ation problems\, with emphasis on network efficient design and resource al
 location. More recently\, I studied problems arising in the modelling and 
 analysis of algorithms and techniques for the mining and analysis of large
  scale information networks\, such as Internet and the Web.\n\n\nCurrent r
 esearch directions include  the application of spectral graph theory techn
 iques to fully distributed graph clustering and the algorithmic modelling 
 and analysis of large complex systems. A new further research direction is
  the application of advanced graph mining and spectral analysis techniques
  in the emerging area of Network Medicine.\n\n\nqualifica_rr: \n\nAssociat
 e professors
URL;TYPE=URI:http://glad.uniroma1.it/node/25717
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