Research
Research
Research
Research
532+ open-access research outputs.
Motivated by the exact weight perfect matching problem and recent parameterized algorithms for finding an $\ell$-th smallest perfect matching, we study structural properties of edge-weight symmetries …
We present a computational study of diffusion synthetic acceleration (DSA) for the monoenergetic, isotropically scattering $S_N$ transport equations, discretised in space by a polytopic discontinuous …
When considering a model selection or, more generally, an aggregation approach for adaptive statistical inference, it is often necessary to compute estimators over a wide range of model complexities i…
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order …
These personal reminiscences of the great Russian mathematician Sergey K. Godunov (1929-2023) arose from a request by his daughter, Ekaterina, to contribute a piece to a book she is writing about her …
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise …
The notion of asymptotic space for an unbounded metric space has been introduced by Micha Gromov in 1980s. It is intended to capture the structure of a metric space at infinity. The most comprehensive…
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, …
We review recent developments in the theory of compact hyper-K\"ahler varieties, from the viewpoint of Lagrangian fibrations, moduli spaces of stable sheaves, and derived categories. These notes origi…
In implicit time marching of the radiative transfer equation (RTE), the resulting linear systems are commonly solved using source iteration with diffusion synthetic acceleration (SI-DSA). Despite its …
In this paper, we introduce a new notion called the \textit{set of missing generators} $\mathcal{M}(g)$ for a generator (or primitive element) $g$ of the cyclic group $\mathbb{Z}_p^*$, where $p$ is an…
We construct an explicit flat one-parameter family of 22-dimensional Artinian $k$-algebras whose special fibre is the spider algebra $k[x,y,z]/(x^8, y^8, z^8, xy, xz, yz)$ and whose generic fibre is t…
Neural networks are increasingly deployed in safety- and mission-critical pipelines, yet many verification and analysis results are produced outside the programming environment that defines and runs t…
This paper makes significant progress towards resolving a conjecture relating strong forcing axioms like $PFA$ and the derived model at a limit of Woodin cardinals $\kappa$. In particular, using a con…
The basic power function $t_n(x)=x^n$ is in some sense a classical limit for large $x$, of the monictised Chebyshev polynomial of the first kind $T_n(x)/2^{n-1}$. A theorem of Ritt says they are the o…
This paper introduces and solves the Generalized Heron-Waist Problem (GHWP), that integrates the classical Heron problem of optimal hub location and the waist problem of minimal-perimeter configuratio…
We show that given an $n$-vertex graph $G$ of diameter 3 we can decide if $G$ is $3$-colourable in time $2^{O(n^{2/3-\varepsilon})}$ for any $\varepsilon < 1/33$. This improves on the previous best al…
In this paper, we introduce the bivariate exponential generating function $F_l(x,y)$ for the number of level-$l$ faces of an exponential sequence of arrangements (ESA), and establish the formula $F_l(…
The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective ma…
We study the question of the least number of random edges that need to be added to a P\'osa-Seymour graph, that is, a graph with minimum degree exceeding $\frac k{k+1}n$, to secure the existence of th…
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