WSAM I, 18-24 янв, 2006, Маскат, Оман

WINTER SCHOOL IN APPLIED MATHEMATICS 
Winter School in Applied Mathematics
Muscat, Sultanate of Oman, 21 January — 6 February 2006

 

Organising Committee of the School
Muscat, Sultanate of OmanShati Al-Qrum, Way 2830

House 2260, Villa TGT

TGT Oil and Gas Services, LLC

Tel: 00968 24696407, 95395882

Fax: 00968 24696409

info@tgtoil.com

www.tgtoil.com

 

Plenary speakers:

1) A. Karuzin (Kazan State University)
2) V. Arkhipov (Kazan State University)

Speakers:

1) N. Neprimerov (Kazan State University)
2) A. Kuznetsova (Kazan State University)
3) A. Aslanyan (TGT)
4) D. Ivanov (TGT)

Scientific programme:

1. Discrete geometry

  •  Discrete calculus
  •  Discrete geometry
  •  Interpolation methods
  •  Mathematical statistics
  •  Data Mining

  •  Non-linear regressions
  •  Neural network analysis


2.  Miscellaneous

 

Lecture programme:

Andrey Karuzin

Part 1:

1. Setting up a minimisation problem. Classification of minimisation methods.
2. One-dimensional minimisation problem. Powell’s quadratic interpolation.
3. Matrix decomposition methods (LU, LDLt, QR, latent root).
4. Gradient descent method. Quasi-Newton methods: Modified Cholesky factorisation method.
5. Setting up a problem of minimising functions that are represented as a sum of squares. The Gauss-Newton method, selection of a search direction for a non-square Jacobian.
6. The Levenberg-Marquardt and dogleg methods based on the concept of confidence region.

Part 2:

7. The problems of Delaunay triangulation and Voronoi categorisation. Limitation of Voronoi cells.
8. Problems solved by Delaunay triangulation (point set clustering and convex hull construction, cluster boundaries, area calculation, etc.).

Part 3:

9. Unsolved optimisation problems and different-length parts of individual problems:
1) Inverse Laplace transformation problem
2) Random number generator
3) Calculations with arbitrary accuracy using long numbers
4) Drawing isolines and their identification
5) Miscellaneous

Part 4:

1. Basic principles behind any discrete space
2. Yakupov’s discrete space (brief review and detailed description)
3. A discrete quasi-regular model of fluid as a research programme (Yakupov’s report)
4. Basic concepts of loop quantum gravity as an alternative discrete theory (based on Lee Smolin’s paper published in the Science World Journal)

Vladimir Arkhipov
Statistical physics methods:
1. Zwanzig-Mori’s kinetic equations for time correlation functions. Memory function approximation methods based on short description principles. Spectrum of the relaxation process’ Non-Markovian parameter.
2. Information theoretic approach in the study of dynamic disorder in complex systems. Informational dynamic entropy. Formation and destruction of time correlations.
3. Some aspects of using mathematical concepts of statistical physics in the humanitarian area.

Alla Kuznetsova
Pressure relaxation in a closed porous reservoir.

Dmitry Ivanov
1. Introduction to data mining
2. Methods of network function construction

Arthur Aslanyan
1. Introduction to neural network modelling

Guided tours:

Fort Nakhal, an ostrich and crocodile farm, thermal springs (1 day)
Turtle Beach, Wadi Shab gorge, Sink Hole (2 days)
Sultan’s Palace, traditional Arab market, Golden Gate

Schedule:

21 January — Saturday
09:00 Opening ceremony
09:30 A lecture by Prof. N. Neprimerov
10:50 Buffet lunch
22 January — Sunday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Optimisation methods
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
23 January — Monday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Optimisation methods
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
24 January — Tuesday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Optimisation methods
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
25 January — Wednesday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Optimisation methods
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
26 January — Thursday
Trips to Fort Nakhal, an ostrich and crocodile farm and thermal springs
27 January — Friday
A tour of the city of Muscat
28 January — Saturday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Discrete geometry
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
29 January — Sunday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Discrete geometry
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
30 January — Monday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Yakupov’s discrete space-time
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
31 January — Tuesday
09:00 — 10:20 V. Arkhipov: Statistical physics methods
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Yakupov’s discrete space-time
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
1 February — Wednesday
09:00 — 10:20 A. Kuznetsova: Pressure relaxation in a closed porous reservoir
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Yakupov’s discrete space-time
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions
2 & 3 February — Thursday & Friday
Trips to the Turtle Beach, Wadi Shab gorge and Sink Hole
4 February — Saturday
09:00 — 10:20 D. Ivanov: Methods of network function construction
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Karuzin: Yakupov’s discrete space-time
12:00 — 14.00 Lunch
14:00 — 15:20 Discussions
5 February — Sunday
09:00 — 10:20 D. Ivanov: Introduction to data mining
10:20 — 10:40 Coffee break
10:40 — 12:00 A. Aslanyan: Introduction to neural network modelling
12:00 — 14:00 Lunch
14:00 — 15:20 Discussions

6 February — Monday
Closing ceremony & banquet

Янв 18-24, 2006; Оман, Маскат