Seminari - Dipartimento Computer Science Seminari - Dipartimento Computer Science validi dal 15.10.2019 al 15.10.2020. From the potential to the first Hochschild cohomology group of a cluster tilted algebra Relatore: Ibrahim Assem; Provenienza: Université de Sherbrooke; Data inizio: 2019-10-15; Ora inizio: 10.00; Note orario: Sala Riunioni II piano; Referente interno: Lidia Angeleri; Riassunto: vedi Seminar Representation Theory. Tue, 15 Oct 2019 10:00:00 +0200 Merging Combinatorial Design and Optimization: the Oberwolfach Problem Relatore: Fabio Salassa; Provenienza: Politecnico di Torino; Data inizio: 2019-11-13; Ora inizio: 14.30; Referente interno: Giuseppe Mazzuoccolo; Riassunto: Combinatorial optimization is a subset of mathematical optimization that is related to operations research, algorithm theory, and computational complexity theory. It consists of finding an (optimal) object from a finite set of objects and in many such problems, exhaustive search is not tractable. Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. Combinatorial Design and Combinatorial Optimization, though apparently different research fields, share common problems, such as for example sudokus, covering arrays, tournament design and more in general problems that can be represented on graphs. Aim of the talk is to present intersections and possible contributions to Combinatorial Design given by the application of Combinatoria l Optimization techniques and solution methods. This is accomplished by the presentation of results on the Oberwolfach Problem (OP) where interaction of methods from both domains enabled us to solve large OP instances in limited computational time and at the same time to derive a theoretical result for general classes of instances . p { margin-bottom: 0.25cm; line-height: 115%; }. Wed, 13 Nov 2019 14:30:00 +0100 Ritmi caotici e ritmi euclidei. Relatore: Davide Pigozzi; Provenienza: Università di Verona; Data inizio: 2019-11-13; Ora inizio: 15.30; Note orario: (al termine del seminario di Fabio Salassa); Referente interno: Giuseppe Mazzuoccolo; Riassunto: Punto di partenza egrave; una ricerca condotta da piugrave; Universitagrave; americane nello studio dei ritmi euclidei. Un ritmo euclideo egrave; un ritmo ottenuto mediante lrsquo;algoritmo di Euclide; essi distribuiscono gli impulsi ritmici nel modo piugrave; uniforme possibile in un insieme di pulsazioni regolari nel tempo. Questa famiglia di ritmi si interseca con una famiglia di ritmi, chiamati ritmi Erdouml;s. Secondo una ricerca musicologica, la maggior parte dei ritmi nella World music egrave; di natura Euclidea(Toussaint). I ritmi Erdouml;s hanno una struttura legata alla geometria combinatoria e sono un problema ldquo;dualerdquo; dei noti difference sets studiati in geometria combinatoria nel secondo Novecento. Si definiscono dunque ritmi caotici discreti i ritmi che si identificano con un difference set. Si daranno esempi musicali esistenti di tutte le famiglie di ritmi prese in considerazione e si daragrave; un tentativo di definizione di ritmo ordinato e di ritmo caotico da un punto di vista percettivo. Si puograve; estendere la teoria dei ritmi alla teoria degli spazi discreti di note musicali. Si troveranno cosigrave; forti analogie tra costruzioni ritmiche e ricerca di sottoinsiemi propri di note. Wed, 13 Nov 2019 15:30:00 +0100 Introduction to Clustering Relatore: Prof. Blaz Zupan; Provenienza: University of Ljubljana; Data inizio: 2019-11-29; Ora inizio: 16.00; Note orario: Sala Verde; Riassunto: p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Helvetica Neue'; color: #454545} span.s1 {text-decoration: underline ; color: #e4af0a} Clustering is a crucial procedure in exploratory data analysis. Given some data, clustering, combined with some visualization, is probably where start to fish for any useful data patterns. I will carry out a hands-on workshop where we will dive into some of the most famous clustering approaches. These will include hierarchical clustering, k-means, DBSCAN, and network-based clustering. We will also combine clustering algorithms with dimensionality reduction and embedding approaches, and learn about principal component analysis, multidimensional scaling, and t-SNE. We will learn how to apply these techniques to images that we will profile with deep learning models. During the workshop, we will use Orange, a data mining framework, and participants are welcome to download and install it from to follow along. Contact Person: C. Combi. Fri, 29 Nov 2019 16:00:00 +0100 Mathematical modelling of liquid crystals and industrial applications Relatore: Prof. Apala Majumdar; Provenienza: Strathclyde (UK); Data inizio: 2019-12-15; Note orario: 15/12-21/12/2019; Referente interno: Giandomenico Orlandi; Riassunto: Course title: Mathematical modelling of liquid crystals and industrial applications Lecturer: Prof. Apala Majumdar (Strathclyde, UK) Dates: 15-21/12/2019 OVERVIEW: Materials science and engineering has witnessed unprecedented growth in recent years with the advent of biological materials, colloids, metamaterials, topological materials etc. Soft matter is at the forefront of contemporary materials research. Soft matter is a phrase used for materials that are intermediate between conventional solids and liquids in terms of their physical properties. Soft matter is fairly ubiquitous in our everyday lives and can be found in display devices, pharmaceuticals, agrochemicals, cosmetics, fibres, and are even found in the human body as biological soft matter e.g. the cell cytoskeleton. Collectively, soft matter products contribute over 200 billion GBP to the world economy and relevant industries employ over 900,000 people. Nematic liquid crystals are paradigm examples of soft matter. They are complex liquids with a degree of long-range orientational order i.e. they have certain distinguished directions and consequently, direction-dependent physical, optical, mechanical and rheological properties. Indeed, it is the directional nematic response to external light and electric fields that makes them the working material of choice for the multi-billion dollar liquid crystal display industry. Nematic liquid crystals today have applications far beyond the display industry in the health industry, microfluidics and nano-technologies. The mathematics and theory of nematic liquid crystals is deep and challenging. In fact, Pierre de Gennes was awarded the Nobel Prize for Physics in 1991, partially for his theories for nematic liquid crystals and these theories have a profound role in science and technology too. In this mini-course, we review the mathematical theories theories for nematic liquid crystals and how they can be applied to display devices, as practical case studies. We will review the celebrated Landau-de Gennes and Oseen-Frank theories for nematic liquid crystals, the key concepts of birefringence, response to external fields, anchoring and topological defects. We will then apply these concepts to the Post Aligned Bistable Nematic Device designed by Hewlett Packard, the Zenithally Bistable Nematic Device and the Planar Bistable Nematic Device, with a discussion of the static and time-dependent properties. The course has a two fold purpose. Firstly, the course will serve as an introductory course to the multi-faceted field of nematic liquid crystals and their applications in an interdisciplinary setting. Secondly, the course will describe certain generic concepts for soft matter, the rich underpinning mathematical frameworks and how mathematics can transform materials research into a predictive science. LECTURE PLAN : The course is compressed into 7 lectures of 50 minutes each. The lecture slides will be made publicly available through the university website. Day 1 : Lecture 1 : Introduction to the theory and physics of nematic liquid crystals - history, different phases and introduction to concept of partial order. Lecture 2 : The Oseen Frank theory for nematic liquid crystals - definition of director and the Oseen-Frank free energy. Day 2 : Lecture 3: Birefringence and Dielectric Anisotropy; the classical Freedericksz Transition for Nematic Liquid Crystals. Lecture 4 : The Landau-de Gennes theory for nematic liquid crystals - the Q-tensor order parameter, the free energy and the equilibrium equations. Day 3: Lecture 5 : Case Study I - Mathematical Modelling of the Post Aligned Bistable Nematic Device and Topological Mechanisms for Multistability. Day 4 :Lecture 6: Case Study II - Mathematical Modelling of the Planar Bistable Nematic Device ndash; static equilibria Lecture 7 : Case Study II ndash; Switching Mechanisms for the Planar Bistable Nematic Device REFERENCES: Gennes and J.Prost. The physics of liquid crystals. Oxford University Press. 1995 I.W.Stewart. The static and dynamic continuum theories for nematic liquid crystals. Taylor&Francis, 2004. A.Majumdar, C.J.P.Newton, J.M.Robbins & M.Zyskin. Topology and Bistability in Liquid Crystal Devices. Physical Review E, 75, 2007. G.Canevari, A.Majumdar & A.Spicer. Order reconstruction for nematics on squares and hexagons: a Landau-de Gennes study. SIAM Journal of Applied Mathematics, 77, 2017. Y.Wang, G.Canevari and A.Majumdar. Order reconstruction for nematics on squares with isotropic inclusions: a Landau-de Gennes study. SIAM Journal of Applied Mathematics, 79, 2019. C.Luo, A.Majumdar & R.Erban. Multistability in planar liquid crystal wells. Physical Review E, 85, 2012. contact person: Giandomenico Orlandi. Sun, 15 Dec 2019 00:00:00 +0100 Essentials of reaction-diffusion equations in Mathematical Biology Relatore: Prof. Tommaso Lorenzi; Provenienza: St Andrews (UK); Data inizio: 2020-01-07; Note orario: starting date 07/01; Referente interno: Giandomenico Orlandi; Riassunto: Title: Essentials ofreaction-diffusion equationsin Mathematical Biology Lecturer: Tommaso Lorenzi (St. Andrews) dates: 7/1-10/1/2020 Abstract This course will provide a gentle introduction to reaction-diffusion equations in mathematical biology. The course will be organised into five related parts as follows: 1) Conservation equations 2) Linear reaction-diffusion equations 3) Nonlinear reaction-diffusion equations 4) Systems of nonlinear reaction-diffusion equations 5) Nonlocal reaction-diffusion equations Recommended Books J.D. Murray, Mathematical Biology I: An Introduction, Springer, 3rd ed. 2003 J.D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer, 3rd ed. 2003 B. Perthame, Transport Equations in Biology, Birkh auser, 2007 B. Perthame, Parabolic Equations in Biology -- Growth, Reaction, Movement and Diffusion, Springer, 2015 Contact person: Giandomenico Orlandi. Tue, 7 Jan 2020 00:00:00 +0100