Related papers: Leo and me
Link prediction appears as a central problem of network science, as it calls for unfolding the mechanisms that govern the micro-dynamics of the network. In this work, we are interested in ego-networks, that is the mere information of…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
Born in Sydney, Australia, on April 20, 1939, Chris Heyde shifted his interest from sport to mathematics thanks to inspiration from a schoolteacher. After earning an M.Sc. degree from the University of Sydney and a Ph.D. from the Australian…
Let $U$ be a unitary operator acting on the Hilbert space $\ch$, and $\a:\{1,..., 2k\}\mapsto\{1,..., k\}$ a pair partition. Then the ergodic average $$ \frac{1}{N^{k}}\sum_{n_{1},...,n_{k}=0}^{N-1} U^{n_{\a(1)}}A_{1}U^{n_{\a(2)}}...…
At the end of the 19th century light was regarded as an electromagnetic wave propagating in a material medium called ether. The speed c appearing in Maxwell's wave equations was the speed of light with respect to the ether. Therefore,…
We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelh{\"o}f Hypothesis and the Riemann…
Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and…
Beginning in the 1970s, statistician-cum-logician Per Martin-L\"of wrote a series of papers developing what became Martin-L\"of type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired…
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\it the…
The Friendship Theorem states that if in a party any pair of persons has precisely one common friend, then there is always a person who is everybody's friend and the theorem has been proved by Paul Erd\H{o}s, Alfr\'{e}d R\'{e}nyi, and Vera…
In the fall of 1924, Enrico Fermi visited Paul Ehrenfest at Leyden on a 3-month fellowship from the International Education Board (IEB). Fermi was 23 years old. In his trip report to the IEB, Fermi says he learned a lot about cryogenics and…
The COVID-19 pandemic necessitated social distancing at every level of society, including universities and research institutes, raising essential questions concerning the continuing importance of physical proximity for scientific and…
Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones, 1977). Cohen (1982) described an adaptation with less explicit competition suitable for…
To make decisions we are guided by the evidence we collect, as well as the opinions of friends and neighbors. How do we integrate our private beliefs with information we obtain from our social network? To understand the strategies humans…
Among the impressive contributions of Andrej N. Kolmogorov's to mathematics in the 20th century, his 1954 invariant tori theorem is still little understood from a historical point of view [Dumas 2014]. Vladimir I. Arnold, who entered Moscow…
In the framework of on-line learning, a learning machine might move around a teacher due to the differences in structures or output functions between the teacher and the learning machine. In this paper we analyze the generalization…
We develop information theory for the temporal behavior of memoryful agents moving through complex -- structured, stochastic -- environments. We introduce and explore information processes -- stochastic processes produced by cognitive…
Lecture given Friday 7 April 1995 at the Santa Fe Institute, Santa Fe, New Mexico. The lecture was videotaped; this is an edited transcript.
From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied…
Recent years have seen dramatic progress in the study of joint ergodicity, i.e. a scenario in which a multiple ergodic average converges in norm to the product of integrals of individual functions. This survey, accompanying the talk given…