Related papers: Dream of a Christmas lecture
Recent measures of nonclassical correlations are motivated by different notions of classicality and operational means. Quantum discord has received a great deal of attention in studies involving quantum computation, metrology, dynamics,…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
This was an expository lecture for the graduate student colloquium at the University of Arizona on the topic of numbers.
Causality and causal inference have emerged as core research areas at the interface of modern statistics and domains including biomedical sciences, social sciences, computer science, and beyond. The field's inherently interdisciplinary…
This is the English version of my inaugural lecture at Coll\`ege de France in 2021, available at https://www.youtube.com/watch?v=bxktplKMhKU. I reflect on the difficulty of multi-disciplinary research, which often hinges of unexpected…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
This is an extended version of my Nobel Lecture, delivered on December $8^{th}$ 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this…
While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of…
We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of nonclassical advantages in computation. Completeness results from computational complexity theory lead to the identification of very…
Semi-supervised learning has emerged as an appealing strategy to train deep models with limited supervision. Most prior literature under this learning paradigm resorts to dual-based architectures, typically composed of a teacher-student…
This talk traces the history of RHIC over the last two decades, reviewing the scientific motivations underlying its design, and the challenges and opportunities the machine presents.
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of…
This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.
In this paper we intend to connect two different strands of research concerning the origin of what I shall loosely call "formal" ideas: firstly, the relation between logic and rhetoric - the theme of the 2006 Cambridge conference to which…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
In this paper, we present the Difference- Based Causality Learner (DBCL), an algorithm for learning a class of discrete-time dynamic models that represents all causation across time by means of difference equations driving change in a…
Separation of competing speech is a key challenge in signal processing and a feat routinely performed by the human auditory brain. A long standing benchmark of the spectrogram approach to source separation is known as the ideal binary mask.…