Related papers: Strong approximation methods in group theory, an L…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
Learned sparse retrieval (LSR) is a family of neural retrieval methods that transform queries and documents into sparse weight vectors aligned with a vocabulary. While LSR approaches like Splade work well for short passages, it is unclear…
This is an extended abstract for the conference "Microlocal2011 : Microlocal Methods in Mathematical Physics and Global Analysis Universit\"at T\"ubingen, June 14 - 18, 2011"
These are lecture notes from a course offered at the Bangalore School on Statistical Physics - X, during 17-28 June 2019, [ https://www.icts.res.in/program/bssp2019 ] at International centre of theoretical physics (ICTS), Bangalore. These…
For both human readers and pre-trained language models (PrLMs), lexical diversity may lead to confusion and inaccuracy when understanding the underlying semantic meanings of given sentences. By substituting complex words with simple…
The focus of this article is to define the descriptively approximations in proximal relator spaces. Afterwards, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…
We have extended the multilevel summation (MLS) method, originally developed to evaluate long-range Coulombic interactions in molecular dynamics (MD) simulations [Skeel et al., J. Comput. Chem., 23, 673 (2002)], to handle dispersion…
A talk presented at the April 2016 APS meeting in Salt Lake City: The speaker had the great good fortune to take an undergraduate course in group theory from Sidney Coleman, and (after graduate school away) was hired by Coleman to a…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal…
Time series classification is an important problem in data mining with several applications in different domains. Because time series data are usually high dimensional, dimensionality reduction techniques have been proposed as an efficient…
In recent years, significant progress has been made in the field of robotic reinforcement learning (RL), enabling methods that handle complex image observations, train in the real world, and incorporate auxiliary data, such as…
In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense of Tao) which simultaneously generalize lattices in lcsc…
These are lecture notes for a mini-course given at the St. Petersburg School in Probability and Statistical Physics in June 2012. Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov…
Sequential decision making under uncertainty is central to many Process Systems Engineering (PSE) challenges, where traditional methods often face limitations related to controlling and optimizing complex and stochastic systems.…