Related papers: Notes on Probability Theory
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…
This note is my comment on Glenn Shafer's discussion paper "Testing by betting", together with two online appendices comparing p-values and betting scores.
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
In research policy, effective measures that lead to improvements in the generation of knowledge must be based on reliable methods of research assessment, but for many countries and institutions this is not the case. Publication and citation…
Presentation for a talk "Two betting strategies that predict all compressible sequences" given at Seventh International Conference on Computability, Complexity and Randomness (CCR 2012)…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
These notes closely correspond to a series of lectures given by the first author in Toulouse, on the recent extension of the theory of ODE well-posedness to abstract spaces, jointly obtained by the two authors. In the last part, we describe…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and Dewey (2002) and V\'azquez, Flammini, Maritan and Vespignani…
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
This textbook compiles the lecture notes from security courses taught at Oxford in the 2000s, at Royal Holloway in the 2010s, and currently in Hawaii. The early chapters are suitable for a first course in security. The middle chapters have…
The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…
This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The…
Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the "receiver"). We study the exponent of the error probability of the second type. Previously, an achievable…