Related papers: Leo and me
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
Computer Science education has been evolving over the years to reflect applied realities. Until about a decade ago, theory of computation, algorithm design and system software dominated the curricula. Most courses were considered core and…
The Wigner's friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between…
The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics,…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
This is the text of my talk at CMU on Feb. 4, 2010 were I gave the second public presentation of the Univalence Axiom (called "equivalence axiom" in the text). The first presentation of the axiom was in a lecture at LMU Munich in November…
Content: Qualitative and ad-hoc descriptions of observations of the "undergraduate" and "graduate" effects. Comparisons between the classical models of both undergraduate and graduate systems separately lead to the conclusion that a…
I recall my interactions with Julian Schwinger, first as a graduate student at Harvard, and then as a postdoc at UCLA, in the period 1968--81, and subsequently. Some aspects of his legacy to physics are discussed.
This volume is our tribute to David A. Freedman, whom we regard as one of the great statisticians of our time. He received his B.Sc. degree from McGill University and his Ph.D. from Princeton, and joined the Department of Statistics of the…
In this very personal workography, I relate my 40-year experiences as a researcher and educator in and around Artificial Intelligence (AI), more specifically Natural Language Processing. I describe how curiosity, and the circumstances of…
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
Boltzmann introduced in the 1870's a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His entropic functional for classical systems was…
In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
This paper presents a brief account of some of the my early research interests. This historical account starts from my laurea thesis on Signal Theory and my master thesis on Computation Theory. It recalls some results in Combinatory Logic…
Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has…
Autonomous agents powered by LLMs and Retrieval-Augmented Generation (RAG) are proficient consumers of digital content but remain unidirectional, a limitation we term epistemic asymmetry. This isolation leads to redundant reasoning and…
Twenty years ago Breiman (2001) called to our attention a significant cultural division in modeling and data analysis between the stochastic data models and the algorithmic models. Out of his deep concern that the statistical community was…
This study is about public-private research collaboration. In particular, we want to measure how the propensity of academics to collaborate with their colleagues from private firms varies over time and whether the typical profile of such…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…