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Title Interactions, automata, and names
Teacher Emilio Tuosto
Syllabus
Abstract:
Motivation/Overview: Automata are fundamental tools for research in computer science, logic, and mathematics. Notably, automata-based models have been introduced to capture aspects of modern concurrent and distributed systems. Also, automata have been used to investigate languages with richer structure than classical formal languages, more precisely, languages over infinite alphabets.Currently, researchers are studying unyfing models of those apparently complementary lines of research.
These lectures will review a few models of automata with names and/or automata over infinite alphabets.  Besides the theoretical aspects the course will also touch on the use of automata-based verification of concurrent systems.

Objectives: After successful completion of the course, participants
will
- undestand the current developments in the theory of automata with names
- acquire notions of nominal computations
- be able to apply automata-based techniques for modelling abstract computations
Materials
Period
Calendar
3 - 14 December ---- 11-13  ---- Sala Seminari Ovest
 
Title Combinatoria Enumerativa e Applicazioni all'Analisi degli Algoritmi
Teacher Simone Rinaldi e Andrea Frosini
Syllabus

Introduction to Enumerative Combinatorics: how to count; bijective methods;
permutations; special numbers; generating functions; methods for
enumeration: inclusion/exclusion principle, Schueztemberger methodololgy,
ECO method; asymptotics.

Introduction to Discrete Tomography. How to model discrete finite objects,
and the concept of projection. The problems of consistency, uniqueness and
reconstruction in DT; main results. Different concepts of projection: recent
results and open problems.

Materials
Period
Calendar
 ‘Combinatoria enumerativa e biiettiva’ (Simone Rinaldi)
- mercoledì 24 ottobre, Dip. di Matematica pian dei mantellini 44, Siena
  Aula Magari h.10-13 e h.15-17
- venerdì 24 ottobre, Dip. di Matematica pian dei mantellini 44, Siena
  Aula Magari h.10-13 e h.16-18
 
 
 
'Algoritmi per la Tomografia Discrete’ (Andrea Frosini)
- lunedì 5 novembre, Centro didattico, viale Morgagni 48, Firenze
 Aula 226, h.10-13 e h.15-18
- mercoledì 7 novembre, Centro didattico, viale Morgagni 48, Firenze
  Aula 226, h.11-13 e h.15-17

Title Logica Matematica
Teacher Montagna
Syllabus

Logica proposizionale. Semantica e calcoli a sequenti, completezza. Forme normali. Risoluzione proposizionale, completezza. Caso Horn. Cenni di teoria della complessità. Horn e 2-CNF-SAT sono in P, CNF-SAT è NP-completo.

Logica del primo ordine. Semantica di Tarski. Calcolo dei sequenti. Completezza. Teorema di Herbrand. Unificazione, risoluzione al primo ordine,  e sua completezza.

Macchine di Turing. Funzioni parziali ricorsive. Il problema dell'arresto. Definibilità degli insiemi r.e. nei numeri naturali. Indecidibilità dell'artmetica e della logica del primo ordine. Il Programma di Hilbert e il suo fallimento (Teoremi di Goedel).

Logiche non classiche (cenni). Logica intuizionista, semantica di Kripke. Logiche fuzzy e applicazioni a: (a) Gioco di Ulam con bugie; (b) probabilità; (c) controllo fuzzy (il tutto solo accennato).

Alcune lezioni saranno tenute dal Prof. Sorbi.

--- inizio previsto: 10 aprile

Materials
Period
Calendar
 
 
Title Fixed Points in Computer Science
Teacher Zoltan Esik, Dept. of Computer Science University of Szeged
Syllabus
Fixed point operations are commonly used to describe the semantics of recursion. Most fixed point operations (metric fixed points, least or greatest fixed points, initial fixed points) in computer science satisfy the same equational properties that define iteration theories.
The equational axioms of iteration theories may be separated into two groups, the Conway identities and the group identities associated with the finite (simple) groups. In addition to equational axiomatizations, we will also cover axiomatizations by universal Horn sentences. A major result is that, in the ordered setting, the fixed point inequation together with the parameter inequation and the fixed point induction rule are complete for the equational theory. Moreover, by adding the operation of one-sided residuation, it is possible to obtain finite equational axiomatizations.
Fixed point operations are central to computer science. They occur in automata and language theory, programming semantics and programming logic, concurrency, computability and complexity, to mention a few areas.
We will  present applications of the theory of fixed points to these fields.
Materials
Period
Calendar
May, 7-19

Title Modelli matematici in Biologia
Teacher Dott. Angelo Di Garbo, ricercatore presso l’Istituto di Biofisica del CNR di Pisa
Syllabus

SCOPO: fornire agli studenti gli strumenti di base per lo studio teorico di sistemi biologici.

Sistemi dinamici discreti e continui. Stati stazionari e stabilita’. Soluzioni periodiche. Teoria delle biforcazioni. Teoria del caos deterministico.

Modelli discreti di popolazioni con singola specie: analisi dell’equilibrio e comportamento caotico.

Modelli continui di popolazioni con singola specie.

Dinamica di popolazioni con piu’ specie interagenti: modello di Lotka-Volterra.

Modelli matematici del sistema immunitario, di malattie infettive e di crescita tumorale.

Modelli neurali: Hodgkin-Huxley, FitzHugh-Nagumo, Integrate & Fire.

Dinamica degli enzimi e modelli in biologia molecolare. Dinamica del calcio cellulare.

Equazione di Fisher. Teoria lineare e nonlineare del DNA. Formazione di patterns. Instabilita’ di Turing. Modelli di crescita tumorale.

Cenni sull’analisi non lineare di segnali biologici: serie temporali, teorema di Takens, determinazione dei parametri di ricostruzione dello spazio delle fasi. Stima di invarianti dinamici.

 

Libri consigliati:
- J.D. Murray, Mathematical Biology, Springer-Verlag (1989);
- Materiale fornito dal docente.

Materials
Period
Calendar
 10-14 e 24-28 settembre
 
Title Web Mining and Social Network Analysis
Teacher Dino Pedreschi - Università di Pisa, Knowledge Discovery and Data Mining Lab
Syllabus
Corso della laurea magistrale - undergraduate course
 
Goals
 
Over the past decade there has been a growing public fascination with the complex "connectedness" of modern society. This connectedness is found in many contexts: in the rapid growth of the Internet and the Web, in the ease with which global communication now takes place, and in the ability of news and information as well as epidemics and financial crises to spread around the world with surprising speed and intensity. These are phenomena that involve networks and the aggregate behavior of groups of people; they are based on the links that connect us and the ways in which each of our decisions can have subtle consequences for the outcomes of everyone else.
 
This course is an introduction to the analysis of complex networks, with a special focus on social networks and the Web - its structure and function, and how it can be exploited to search for information. Drawing on ideas from computing and information science, applied mathematics, economics and sociology, the course describes the emerging field of study that is growing at the interface of all these areas, addressing fundamental questions about how the social, economic, and technological worlds are connected.
 
Syllabus
 
1) Graph theory and social networks
Graphs
Social, information, biological and technological networks Strong and weak ties Networks in their surrounding context
 
2) The World Wide Web
The structure of the Web
Link analysis and Web search
Web mining e sponsored search markets
 
3) Network dynamics
Information cascades
Power laws and rich-get-richer phenomena The small-world phenomenon
Epidemics
 
Textbooks
 
David Easley, Jon Kleinberg: Networks, Crowds, and Markets. http://www.cs.cornell.edu/home/kleinber/networks-book/
 
Reading:
M. E. J. Newman: The structure and function of complex networks, SIAM
Review, Vol. 45, p. 167-256, 2003.
A.-L. Barabasi. Linked. PLUME, Penguin Group, 2002.
Duncan J. Watts. Six Degrees: The Science of a Connected Age. Norton, New York, 2003.
Materials
Period
Calendar
2nd term (starting end of february)

Title Internet: Structure, Statistical Analysis and Dynamic Evolution
Teacher Luciano Lenzini, Dipartimento Ingegneria dell'Informazione, Università di Pisa
Syllabus
Abstract:
Many large natural, social, and technological systems can be successfully described within a unified formalism that combines elements of graph theory and statistical physics. This formalism has been developed in the last few years, and has already become the so-called science of complex networks.
This course provides an introduction to the Internet in terms of it being a complex network.
Two main aspects are addressed: measurement systems and modeling the temporal evolution.
 
The course is thus structured into two parts covering:

Internet as a Graph and Measurement Issues
This part introduces the basic concepts that allow the Internet to be described as a graph, and outlines how to measure topological information. It covers the goals of various kinds of Internet measurements, the challenges in measuring the Internet, the methods and tools that have been developed to carry out such measurements, and the results that have been obtained to date in this field .

Modeling the Internet Dynamic
Most of the networks observed in nature and technology have a scale-free nature, characterized by the presence of power-law distributions. This part reviews this class of scale-free network models (Barabasi-Albert Models) which until a few years ago were used to model the temporal evolution of the Internet.
However, recent Internet measurements have proved that Internet growth can no longer be modeled by the Barabasi-Albert model. This part of the course will conclude by showing how international research is attempting to recover from this model.
 
Bibliography relevant for the course:
- G. Caldarelli, "Scale-Free Networks: Complex Webs in Nature and Technology", Oxford University Press (2007)
- S.N.  Dorogovtsev and J.F.F.  Mendes.  "Evolution of Networks", Oxford University Press (2003)
- R.  Pastor-Satorras and A.  Vespignani, "Evolution and Structure of the Internet", Cambridge University Press (2004)
 
Sala Seminari Ovest: NEW SCHEDULE

Mercoledi 18 aprile, ore 9-11, aula Seminari Est


Giovedi 19 aprile, ore 9-11, aula Seminari Est


Lunedi 23 aprile, ore 9-11, aula Seminari Est


Martedi 24 aprile, ore 9-11, aula Seminari Est


Mercoledi 2 maggio, ore 9-11, aula Seminari Est


Giovedi 3 maggio, ore 9-11, aula Seminari Est


Venerdi 4 maggio, ore 9-11, aula Seminari Ovest

 
Materials
Period
Calendar
 
 
Title STT - Semantica e Teoria dei Tipi
Teacher Ugo Montanari
Syllabus
Corso della laurea magistrale - undergraduate course
 
Finalità del Corso
Verranno presentate alcune proprietà fondamentali dei modelli di calcolo, come la semantica operazionale ed astratta, la struttura dei tipi, l'ordine superiore, la concorrenza, l'interazione. Verranno utilizzate la semantica algebrica e la teoria elementare dei tipi, ma non vi sono prerequisiti eccetto una conoscenza elementare dell'algebra e della logica.
 
Programma del Corso
Il lambda calcolo con tipi semplici
L'isomorfismo di Curry-Howard
Il PCF e il suo modello cpo, con applicazione ai linguaggi di programmazione funzionali Elementi di tipi ricorsivi e polimorfi, con applicazione ai linguaggi di programmazione orientati agli oggetti Le categorie come algebre parziali Categorie monoidali, cartesiane e cartesiane chiuse (CCC) Le CCC come modelli del lambda calcolo con tipi semplici Specifiche algebriche, categorie di modelli e aggiunzioni La semantica operazionale come costruzione universale Le reti di Petri e i loro modelli monoidali (strettamente) simmetrici I sistemi di riscrittura etichettati (LTS) come coalgebre I sistemi LTS composizionali come bialgebre Il Calculus for Communicating Processes (CCS) e il Pi-calcolo di Milner e i loro modelli bialgebrici.
 
Materiali Didattico:
John Mitchell, "Foundations for Programming Languages", MIT Press,
1996. Capitoli:
2.5,4,5,7.2,9,10,11.
Note manoscritte.
 
Orario del Corso: da definire.
Modalita' d'Esame: Da definire.
Materials
Period
Calendar
Orario:
Martedì 11:00-13:00 aula L1 Polo Fibonacci
Mercoledì 11:00-13:00 aula N1 Polo Fibonacci.

Gli interessati inviino  un messaggio a ugo@di.unipi.it.

La prima lezione sarà il martedì 21 c.m. 11:00-13:00 in aula L1 Polo Fibonacci.

Attachment
Title Advanced programming models & paradigms for multicore and distributed architectures
Teacher Marco Danelutto
Syllabus
Vedere immagine allegata.
Materials
Period
Calendar
21.V - 1.VI  2012
 
Title Advanced Topics in Cloud and P2P Computing
Teacher F.Baiardi (FB), L.Ricci(LR), D.Sgandurra(DS)
Syllabus

The course is focused on the methodologies that aim to improve security and safety in the complex virtual networks underlying cloud or p2p computing. In this context, we will present virtualization technology as an enabling technology, policies and mechanisms to solve the challenging security problems posed by cloud computing. The second part of the course introduces the epidemic approach as a tool to improve the safety of p2p systemand it presents both the underlying mathematical models and a set of applications exploitingthis paradigm.

 
Topics 
Cloud Computing: Taxonomy and Enabling Technologies       2 h.    FB  
    
Attacks and Countermeasures
    cloud cartography                                     2 h.    FB
    proof of retrievability                               2 h.    FB
    xss /xsrf                                             2 h.    FB
    introspection, attestation, trusted computing         2 h.    DS
    homomorphic encryption                                2 h.    FB
 
P2P Computing: epidemics Protocols
    Discrete Time Markov Chains: Definition, Convergence, Solving Markov Chains,  2 h. LR
    Random Walks on Graphs: Applications: Web Search, P2P Search, Encounter-times in Mobile Networks 2 h. LR
 Epidemic on Networks: SI and SIR model, Fluid Models, Applications: P2P search, Virus spread, Advertising. 2 h. LR:
 Gossip Algorithms: Random Peer Sampling, Overlay Construction, Security in P2P overlays 2 h. LR.


Examination:     In depth examination of a subject related to the course topics
Materials
Period
Calendar
July 9th-13th, 10 hours
July 16th-20th, 10 hours

The exact timetable will be notified

Title Apprendimento Automatico: Reti Neurali e Metodi Avanzati
Teacher Alessio Micheli
Syllabus
Corso della laurea magistrale - undergraduate course (6CFU)
 
Materials
Period
Calendar
2nd term (starts at the end of february)
 
Title A framework for processes inspired by the functioning of living cells: Natural Computing Approach
Teacher Grzegorz Rozenberg
Syllabus
Materials
Period
Calendar

Sarà tenuto nei giorni 4, 5, e 6 Giugno (forse ci sarà un'estensione anche il 7 Giugno) dalle 10 alle 13 in aula 003

presso il Dipartimento di Scienze Matematiche e Informatiche, Pian dei Mantellini, 44, Siena.