Related papers: Strong approximation methods in group theory, an L…
This work develops algorithms for non-parametric confidence regions for samples from a univariate distribution whose support is a discrete mesh bounded on the left. We generalize the theory of Learned-Miller to preorders over the sample…
Recent development in large language models (LLMs) has demonstrated impressive domain proficiency on unstructured textual or multi-modal tasks. However, despite with intrinsic world knowledge, their application on structured tabular data…
These are the notes from Asger T\"ornquist's Appalachian Set Theory lectures at Carnegie Mellon University. They form a chapter in the LMS lecture notes series 406.
Reading is a complex process which requires proper understanding of texts in order to create coherent mental representations. However, comprehension problems may arise due to hard-to-understand sections, which can prove troublesome for…
We give an expanded treatment of our lecture series at the 2017 Groups St Andrews conference in Birmingham on local-global conjectures and the block theory of finite reductive groups.
Most universities in the United States encourage their students to explore academic areas before declaring a major and to acquire academic breadth by satisfying a variety of requirements. Each term, students must choose among many thousands…
This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.
The talk contains a short introduction to mesonic Chiral Perturbation Theory (ChPT). In addition four disparate areas where some progress has been made in recent years are discussed. These are the last fit of the order $p^4$…
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.
There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…
Large Language Models (LLMs) have demonstrated proficiency in a wide array of natural language processing tasks. However, its effectiveness over discourse-level event relation extraction (ERE) tasks remains unexplored. In this paper, we…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
Presentation for a talk "Two betting strategies that predict all compressible sequences" given at Seventh International Conference on Computability, Complexity and Randomness (CCR 2012)…
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as…
We propose a deep learning model for identifying structure within experiment narratives in scientific literature. We take a sequence labeling approach to this problem, and label clauses within experiment narratives to identify the different…
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…