Related papers: Lecture Notes on Support Preconditioning

We study the principal subspaces of higher level standard $A_2^{(2)}$-modules, extending earlier work in the level one case, by Calinescu, Lepowsky, and Milas. We prove natural presentations of principal subspaces and also of certain…

When deploying deep learning models to a device, it is traditionally assumed that available computational resources (compute, memory, and power) remain static. However, real-world computing systems do not always provide stable resource…

The program of studying general nonlinear Markov processes was put forward in V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by the…

This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models.…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of…

These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.

In these lectures, we give a pedagogical introduction to the superconformal index. This is the writeup of the lectures given at the Winter School "YRISW 2020" and is to appear in a special issue of JPhysA. The lectures are at a basic level…

The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for…

Discussion of "Treelets--An adaptive multi-Scale basis for sparse unordered data" [arXiv:0707.0481]

CONTENTS: Lecce Workshop presentations available online; Borel cardinalities below c_0; Hereditarily non-topologizable groups; A hodgepodge of sets of reals; Random gaps; Covering a bounded set of functions by an increasing chain of…

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

These 1992 lectures notes present a powerful formalism mostly developed in the 1980s by Borderies, Goldreich and Tremaine to address planetary ring dynamical issues. These notes make a special emphasis on ring microphysics, quantified with…

These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on…

Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…

I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…

We propose a new class of multi-layer iterative schemes for solving sparse linear systems in saddle point structure. The new scheme consist of an iterative preconditioner that is based on the (approximate) nullspace method, combined with an…

In machine learning applications, predictive models are trained to serve future queries across the entire data distribution. Real-world data often demands excessively complex models to achieve competitive performance, however, sacrificing…

These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$-Positivity Preserver, and their Generators''. The lecture was given at the University of Konstanz in the winter semester 2025/26.

Recently, pretext-task based methods are proposed one after another in self-supervised video feature learning. Meanwhile, contrastive learning methods also yield good performance. Usually, new methods can beat previous ones as claimed that…