Research
Research
Research
Research
444+ open-access research outputs.
Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate function…
Let H(k) be the smallest N such that every finite coloring of [N] contains a monochromatic or rainbow k-term arithmetic progression. Erd\H{o}s and Graham asked whether $H(k)^{1/k}/k \to \infty$ (Probl…
We provide an end-to-end workflow to rigorously compute the monodromy of Belyi maps from exact equations over number fields using certified homotopy continuation. We then apply this method at scale to…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databa…
Extremal Graph Theory heavily relies on exploring bounds and inequalities between graph invariants, a task complicated by the rapid combinatorial explosion of graphs. Various tools have been developed…
The House of Graphs is an online database of graphs which can be accessed at https://houseofgraphs.org/. It serves as a central repository for complete lists of graphs for various graph classes. Howev…
We prove that over function fields F_q(t), the Tate-Shafarevich group |Sha| is an invariant of the cyclotomic type of the L-polynomial, so that |Sha|-stratified murmuration densities reduce to type-we…
We construct an infinite family of 6-regular graphs $\{G_n\}_{n\ge 3}$ by taking $n$ copies of the Petersen graph and wiring corresponding vertices according to an $n$-cycle permutation. Each $G_n$ ha…
We investigate the interaction between Birch and Swinnerton-Dyer (BSD) invariants and the murmuration phenomenon for elliptic curves over the rational numbers. Our study, based on a dataset of 3,064,7…
Classical metric spaces often fail to model data-intensive systems where repetition and frequency of values are meaningful. In applications such as transactional databases, sensor logs, and record lin…
Given an elliptic curve $E$ over $\Q$ and a nontrivial element $\sigma$ of its Shafarevich--Tate group $\Sha(E)$, we introduce the \textbf{Visualization category} $\V(E; \sigma)$ of abelian varieties …
We develop an explicit theory of formal modular forms over arbitrary number fields $K$, as functions of modular points. We define modular points for $\Gamma_0({\mathfrak n})$ and $\Gamma_1({\mathfrak …
Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over $\mathbb{Q}$ for which the strong Birch-Swinnerton-Dyer (BSD) conje…
We study a multi-commodity Freeway Network Control (FNC) problem aiming at achieving optimal operation of a transportation network through the use of ramp metering and variable speed limits. Straightf…
We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galer…
This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point set…
The task of maintaining a predefined level of effect in a dynamical plant by applying periodic control actions often arises in e.g. process control and medicine. When the state variables of the plant …
We study the problem of matching correlated VAR time series databases, where a multivariate time series is observed along with a perturbed and permuted version, and the goal is to recover the unknown …
We develop a computational framework for classifying Galois groups of irreducible degree-7 polynomials over~$\mathbb{Q}$, combining explicit resolvent methods with machine learning techniques. A datab…
All Resolutions Inference (ARI) is a post hoc inference method for functional Magnetic Resonance Imaging (fMRI) data analysis that provides valid lower bounds on the proportion of truly active voxels …
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