LTCC - London Taught Course Centre (Queen Mary Courses)
Topic outline
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MAXIMUM ENTROPY MODELS OF COMPLEX NETWORKS: SLIDES AND HANDWRITTEN NOTES
Lesson 1: Introduction to complex networks and maximum entropy principle
Lesson 2: Maximum Entropy principle Microcanonical and canonical network ensembles, Handwritten notes
Lesson 3: Random graphs and canonical ensembles with expected degree sequence,correlated and uncorrelated networks, Handwritten notes
Lesson 5: Two star and Strauss model. Spatial networks ensembles and latent variables, Block models and inference, Handwritten notes
MAXIMUM ENTROPY MODELS OF COMPLEX NETWORKS: LIVE LECTURES (RECORDING AVAILABLE BY FOLLOWING THE LECTURE LINK)
Mondays 14 February -14 March 3:50pm-5:50pm
The course will take place online in the Blackboard Collaborate see link (Guest Link sent by private email) -
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These are the official lecture notes on which the course is based.
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This (optional) problem sheet provides some practice on some of the topics discussed in the lectures.
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The assessment problems are due for the 8th March 2021.
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MTP24, 15/01/24, Lecture 1 slides
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LECTURE 1: Basics of Measure Theory
Sample problems: 4, 6, 7, 10, 13, 14
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Lecture 1: solutions to selected problems
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Lecture 1 Recording, 9/11/2020
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MTP24, 22/01/2024, Lecture 2 slides
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LECTURE 2: Random variables, independence, integration and conditioning (printed LN)Sample problems: 1, 4, 5, 7
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Handwritten notes on Conditional Concepts
(Zoom Lecture 18/11/22)
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MTP24 - Lecture 3 slides, 29/01/24: Conditional concepts and martingales.
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Lecture 2: solutions to problems
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Lecture 2 Recording 16/11/2020
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Lecture 3: solutions to selected problems
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Lecture 3 Recording, 23/11/2020
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MTP24-Lecture 4 slides
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Lecture 4: The Brownian motion (printed LN)
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Handwritten notes accompanying Lecture 4, 29/11/2021
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Lecture 4 recording, 30/11/2020, 10:30-12:30
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Lecture 5: Weak convergence of measures and the invariance principle (printed LN)
sample problems: 2,3,4,6
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Handwritten LN, accompanying Lecture 5, 6/12/2021
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Lecture 5, Recording 7/12/2020
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2019/20 Exam "Measure-Theoretic Probability"
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2019/20 Exam "Measure-Theoretic Probability" (Solutions)
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LTCC: MTP exam 2021-22
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Lecture 1-Topology of sublevel sets, operation of attaching cells, Morse functions,
Morse Lemma, existence of Morse functions, crossing a Morse critical value. Main
theorem of Morse theory. Morse inequalities. Examples: spheres, complex projective
spaces, etc.
Lecture 2- Smale’s solution of Generalised Poincare Conjecture.
H-cobordism theorem. Ideas and techniques of the proof.
Lecture 3- Planar linkages and their configuration spaces. Formula for their Betti
numbers. Walker’s Conjecture.
Lecture 4- Spaces of polygons in high dimensions, classification of these spaces in
combinatorial terms.
Lecture 5- Robot motion planning and topology. Schwarz genus of a fibration. Lusternik-
Schnirelmann theory. Topological complexity.
- Recommended reading:
1. J. Milnor, Morse theory. 1963
2. J. Milnor, Lectures on the h-cobordism theorem. 1965.
3. M. Farber, Invitation to topological robotics, EMS, 2008.
- Additional Optional reading:
M. Farber and V. Fromm, The topology of spaces of polygons. Trans. Amer. Math. Soc.
365 (2013), no. 6, 3097–3114.
- Prerequisites:
Basic homology theory of cell complexes, basic knowledge smooth manifolds.
Lecturer Details:
Lecturer: Professor Michael Farber
Lecturer home institution: Queen Mary University of London
Lecturer e-mail: M.Farber@qmul.ac.uk
Lecturer telephone number: 07906345551