Related papers: A Conversation with Ulf Grenander
These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
Suppose that there is a family of $n$ random points $X_v$ for $v \in V$, independently and uniformly distributed in the square $\left[-\sqrt{n}/2,\sqrt{n}/2\right]^2$ of area $n$. We do not see these points, but learn about them in one of…
The binary Euclidean algorithm is a modification of the classical Euclidean algorithm for computation of greatest common divisors which avoids ordinary integer division in favour of division by powers of two only. The expectation of the…
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…
The success of deep learning has revolutionized many fields of research including areas of computer vision, text and speech processing. Enormous research efforts have led to numerous methods that are capable of efficiently analyzing data,…
Spatiotemporal prediction plays a critical role in numerous real-world applications such as urban planning, transportation optimization, disaster response, and pandemic control. In recent years, researchers have made significant progress by…
For any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. Yet, its full distribution often carries extremely interesting information and can be invoked to put any…
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the…
Processes such as disease propagation and information diffusion often spread over some latent network structure which must be learned from observation. Given a set of unlabeled training examples representing occurrences of an event type of…
Recent work has focused attention on statistical inference for the population distribution of the number of sexual partners based on survey data. The characteristics of these distributions are of interest as components of mathematical…
A random algebraic graph is defined by a group $G$ with a uniform distribution over it and a connection $\sigma:G\longrightarrow[0,1]$ with expectation $p,$ satisfying $\sigma(g)=\sigma(g^{-1}).$ The random graph…
Accurately predicting cellular responses to genetic perturbations is essential for understanding disease mechanisms and designing effective therapies. Yet exhaustively exploring the space of possible perturbations (e.g., multi-gene…
1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: [email protected] 2. Typed by Wenjiao Yan, School of Mathematical Sciences,…
The seminal papers of Pickands [1,2] paved the way for a systematic study of high exceedance probabilities of both stationary and non-stationary Gaussian processes. Yet, in the vector-valued setting, due to the lack of key tools including…
This is a review devoted to some results of Algebraic Programming (Computer Algebra) used in treating several problems of general relativity, based mainly on already published articles. The article contains the talk given by the author at…
These are a set of lecture notes for a mini-course I gave at The University of Warwick from October 30th to November 1st, 2024. Recordings of the lectures are available on Oleg Zaboronski's webpage at…