Courses organized by Dipartimento di Matematica e Informatica

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Second Joint Summer School on Nanotechnology

Course outline: 

The Joint Summer School on Nanotechnology presents a variety of selected topics in nanoscience & nanotechnology addressing the fabrication, characterization and modeling of nanostructures and nanodevices. The school aims as well at highlighting the potential applications and the economic impact of nanotechnology in the society of today and tomorrow.

Through a balanced mix of lectures and poster sessions the school will cover:

science and engineering of matter with the goal of emphasizing the relationships between nanostructure and properties at the macroscopic scale (nano materials);
design and fabrication of nanodevices with specific functions using bottom up and top down approaches (nano devices);
design and assembly of materials and devices in complex systems (nano systems).
The approach is multi-disciplinary and lectures are tailored for a broad audience of PhD students and young researchers active in different areas of the large domain of nanotechnology. Top level scientist in different fields (material science, engineering, bio based sciences, physics and chemistry) will tutorially introduce the contents of their lectures and will bring their point of view on the research topics they are currently interested in. Participating students will have a unique opportunity to broaden their views of nanotechnology, to learn new experimental techniques and theoretical methods, to meet top class scientists active in the field and to build and strengthen a personal network of relations with peers.

Hybrid Automata

Course outline: 
  • Hybrid Automata: Syntax and Semantics
  • The reachability problem for Hybrid Automata
  • Undecidability: reductions from a 2-Counter Machine
  • Decidable classes for reachability: timed, rectangular, o-minimal, ...
  • Decision techinques: (Bi)Simulation, Cylindric Algebraic Decomposition, Selection theorems, approximate semantics
  • Applications with examples: Repressilator, Deltha-Notch, Escherichia coli

Logic Programming, Knowledge Representation, and Non Monotonic Reasoning

Course outline: 
  • Introduction
  • Syntax and Semantics of First order Logic
  • Horn and Definite clauses; definite programs (pure Prolog); minimal Herbrand model
  • Minimal model as the least fix point of a monotone operator; complexity (for finite Herbrand universe)
  • General programs and their semantics; stable models; ASP
  • ASP programming (exercises); examples of encoding of CSP in ASP (Coloring, N-queens, Sudoku, ...)
  • Action Description Languages (syntax and semantics) and applications
  • Expressiveness and complexity classes for KR
  • Intelligence and Machines: the intentionality issue (prof. Montanari)

More infos at Logic Programming, Knowledge Representation, and Non Monotonic Reasoning (in italian).

Approximation Algorithms

Course outline: 
  • Existence and difficulty of polynomial approximability.
  • The class APX and APX-hardness.
  • Approximation algorithms for metric TSP.
  • Examples of 2-approximation for Vertex Cover.
  • 1/2-approx for Max-Cut.
  • Randomized approximation algorithms and derandomization.
  • Greedy algorithms and application of rounding for Set Covering.
  • Polynomial Time Approximation Schemes (PTAS) : knapsack and bin packing.
  • Approximation algorithms in bioinformatics.

As a prerequisite, I assume each participant has already followed some courses on algorithms and data structures, and is familiar with basic graph theory concepts and combinatorial optimization problems. Hopefully, he has also some basic knowledge of integer linear programming.

I will provide lecture notes (in Italian) and maybe copies of some relevant papers.