Related papers: The work of Hugo Duminil-Copin
Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.
On the occasion of Elliott Lieb being awarded the Gauss Prize 2022, we give a non-technical overview over some of his seminal works in mathematical physics. We emphasize, in particular, his work on Coulomb many-body systems and functional…
The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and…
The main purpose of this paper is to facilitate the communication between the Analytic, Probabilistic and Algorithmic communities. We present a proof of convergence of the Hamiltonian (Hybrid) Monte Carlo algorithm from the point of view of…
In the quest to align deep learning with the sciences to address calls for rigor, safety, and interpretability in machine learning systems, this contribution identifies key missing pieces: the stages of hypothesis formulation and testing,…
The impact of individual scientists is commonly quantified using citation-based measures. The most common such measure is the h-index. A scientist's h-index affects hiring, promotion, and funding decisions, and thus shapes the progress of…
Decision-makers abhor uncertainty, and it is certainly true that the less there is of it the better. However, recognizing that uncertainty is part of the equation, particularly for deciding on environmental policy, is a prerequisite for…
The influence of new techniques on the discovery and characterization of pulsating variables has been enormous. In this paper, I will review the methods and results of a number of research programmes which have dramatically altered our…
Recent years have seen dramatic progress in cosmology and particle astrophysics. So much so that anyone who dares to offer an overview would certainly risk him- or herself for being incomplete and biased at best, and even incorrect due to…
We propose a comprehensive bibliometric study of the profile of Nobel prizewinners in chemistry and physics from 1901 to 2007, based on citation data available over the same period. The data allows us to observe the evolution of the…
The problem of characterization of Gibbs random fields is considered. Various Gibbsianness criteria are obtained using the earlier developed one-point framework which in particular allows to describe random fields by means of either…
A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious…
In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists for over 50 years. A version of this note also serves as an…
Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow…
On July 5th, 2022, Maryna Viazovska was awarded a Fields Medal for her solution of the sphere packing problem in eight dimensions, as well as further contributions to related extremal problems and interpolation problems in Fourier analysis.…
While the ``hierarchy of science'' has been widely analysed, there is no corresponding study of the status of subfields within a given scientific field. We use bibliometric data to show that subfields of mathematics have a different…
In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such…
A toy-model of publications and citations processes is proposed. The model shows that the role of randomness in the processes is essential and cannot be ignored. Some other aspects of scientific publications rating are discussed.
Peer reviewed publications are considered the gold standard in certifying and disseminating ideas that a research community considers valuable. However, we identify two major drawbacks of the current system: (1) the overwhelming demand for…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…