arXiv subjects

Andrew Newman

Publications and source records attributed to Andrew Newman.

At least 19 recordsLinked to original sources

arXiv2026

Kilometer-Scale AI Downscaling of Atlantic Hurricanes with Generative Ensembles

This study presents an AI-based dynamical downscaling system for Tropical Cyclones (TCs). The system incorporates an AI-based limited-area model that downscales 3-hourly low-resolution boundary forcings into hourly high-resolution fields autoregressively, and a diffusion model that converts the outputs into ensembles of hazard-relevant variables. The system is trained on the regridded CONUS404 data with ERA5 forcings, and is evaluated on 20 TCs in 2020--2024. Verification shows stable downscaling performance across Atlantic hurricane seasons, with energy spectra closely matching the CONUS404 reference. The system is also verified to produce skillful TC-relevant weather extremes, largely improved over a deterministic AI baseline. The system performs well with forcing data from other models (GDAS/FNL) and can produce detailed eyewall, rainband, and landfall structures in TC case studies. The study provides a good example of how AI-based dynamical downscaling systems can be designed to resolve small-scale extreme weather events.

physics.ao-ph↗

arXiv2026

AI-Based Regional Emulation for Kilometer-Scale Dynamical Downscaling

An AI-based Limited-Area Model (LAM) is developed for dynamical downscaling over the Southern Great Plains and the southeastern United States, with strong generalization abilities under diverse boundary conditions. The model is trained using 0.25-degree, 3-hourly ERA5 as forcings and CONUS404 as targets in 1980--2019, producing 4-km, hourly dynamical downscaling outputs; it is also connected to a post-processing model to derive additional diagnostic variables. The model is evaluated across multiple forcing datasets, time periods, and climate regimes. For present-day downscaling in the 2021--2024 water years, the model produces stable multi-year simulations with no unrealistic drift; its deterministic verification scores are comparable to other weather-forecasting-oriented AI models. The model also generalizes robustly to a 1.0-degree, 6-hourly non-ERA5 forcing dataset, yielding only minor performance changes. Frontal cyclone and hurricane case studies further demonstrate that the model reconstructs realistic, interpretable weather-scale dynamical and thermodynamic structure from coarse boundary information. The AI-based LAM is further tested by downscaling 30-year global climate model runs in 1980--2010 and 2070--2100, and climate model ensembles in 2025-2027. In this application, the model remains stable at hourly downscaling frequencies for all 30 years and effectively captures future climate-change signals, indicating meaningful generalization across different climate regimes. When downscaling ensembles, the model produces well-posed ensemble distributions without collapsing the ensemble spread. Overall, the AI-based LAM of this study offers good downscaling performance and generalization abilities. It provides a practical and transferable example of adapting AI weather prediction models for regional climate applications.

physics.ao-ph↗

arXiv2025

How an AI-ready National Data Library would help UK science

In this paper, we provide a technical vision for key enabling elements for the architecture of the UK National Data Library (NDL) with a strong focus on building it as an AI-ready data infrastructure through standardised vocabularies, automated analysis tools, and interoperability services. We follow the ODI Multilayer Interoperability Framework (MIF) for data stewardship, covering central socio-technical aspects for the NDL including user-centric approaches to service design and governance.

cs.DL↗

arXiv2024

Youden's Demon is Sylvester's Problem

If four people with Gaussian-distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are $\frac 6 \pi \arcsin\left(\frac{1}{3}\right)\approx .649$. We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian random points on the real line ("Youden's demon problem") is the same as a natural generalization of Sylvester's Four Point problem to Gaussian points in $\mathbb{R}^d$. Our main tool is the observation that the Gale dual of independent samples in $\mathbb{R}^d$ itself can be taken to be a set of independent points (conditioned on barycenter at the origin) when the distribution of the points is Gaussian.

math.PR↗

arXiv2024

A conditional lower bound for the Tur\'an number of spheres

We consider the hypergraph Tur\'an problem of determining $\mathrm{ex}(n, S^d)$, the maximum number of facets in a $d$-dimensional simplicial complex on $n$ vertices that does not contain a simplicial $d$-sphere (a homeomorph of $S^d$) as a subcomplex. We show that if there is an affirmative answer to a question of Gromov about sphere enumeration in high dimensions, then $\mathrm{ex}(n, S^d) \geq \Omega(n^{d + 1 - (d + 1)/(2^{d + 1} - 2)})$. Furthermore, this lower bound holds unconditionally for 2-LC spheres, which includes all shellable spheres and therefore all polytopes. We also prove an upper bound on $\mathrm{ex}(n, S^d)$ of $O(n^{d + 1 - 1/2^{d - 1}})$ using a simple induction argument. We conjecture that the upper bound can be improved to match the conditional lower bound.

math.CO↗

arXiv2023

Chromatic numbers of flag 3-spheres

A recent conjecture of Chudnovsky and Nevo asserts that flag triangulations of spheres always have linear-sized independent sets, with a precisely conjectured proportion depending on the dimension. For dimensions one and two, the lower bound of their conjecture basically follow from constant bounds on the chromatic number of flag triangulations of $S^1$ and $S^2$. This raises a natural question that does not appear to have been considered: For each $d$ is there a constant upper bound for the chromatic number of flag triangulations of $S^d$? Here we show that the answer to this question is no, and use results from Ramsey theory to construct flag triangulations of 3-spheres on $n$ vertices with chromatic number at least $\widetilde{\Omega}(n^{1/4})$.

math.CO↗

arXiv2023

On the intersecting family process

We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\ldots,r$. We prove some new results for the case where $k=cn^{1/3}$ and for the case where $k\gg n^{1/2}$.

math.CO↗

arXiv2022

Linear embeddings of random complexes

For $X \sim X(n; 1, n^{-\alpha_1}, n^{-\alpha_2}, ...)$ in the multiparameter random simplicial complex model we establish necessary and sufficient strict inequalities on the $\alpha_i$'s to linearly embed the complex into $\mathbb{R}^{2d}$.

math.CO↗

arXiv2022

Random complexes with free involution

We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for random simplicial complexes with fundamental group $\mathbb{Z}/2\mathbb{Z}$. We establish results about the typical asymptotic topology of these complexes. As a consequence we give bounds for the dimension $d$ such that $\mathbb{Z}/2\mathbb{Z}$-equivariant maps from the double cover to $\mathbb{R}^d$ have zeros with high probability, thus establishing a random Borsuk--Ulam theorem. We apply this to derive a structural result for pairs of non-adjacent cliques in Erd\H{o}s--R\'{e}nyi random graphs.

math.CO↗

arXiv2022

Complexes of nearly maximum diameter

The diameter of a strongly connected $d$-dimensional simplicial complex is the diameter of its dual graph. We provide a probabilistic proof of the existence of $d$-dimensional simplicial complexes with diameter $ (\frac{1}{d \cdot d!} - (\log n)^{-\epsilon}) n^d$. Up to the first order term, this is the best possible lower bound for the maximum diameter of a $d$-complex on $n$ vertices as a simple volume argument shows that the diameter of a $d$-dimensional simplicial complex is at most $ \frac{1}{d} \binom{n}{d}$. We also find the right first-order asymptotics for the maximum diameter of a $d$-pseudomanifold on $n$ vertices.

math.CO↗

arXiv2021

Abelian groups from random hypergraphs

For a $k$-uniform hypergraph $\mathcal{H}$ on vertex set $\{1, ..., n\}$ we associate a particular signed incidence matrix $M(\mathcal{H})$ over the integers. For $\mathcal{H} \sim \mathcal{H}_k(n, p)$ an Erd\H{o}s--R\'{e}nyi random $k$-uniform hypergraph, $\text{coker}(M(\mathcal{H}))$ is then a model for random abelian groups. Motivated by conjectures from the study of random simplicial complexes we show that for $p = \omega(1/n^{k - 1})$, $\text{coker}(M(\mathcal{H}))$ is torsion-free.

math.CO↗

arXiv2021

One-sided sharp thresholds for homology of random flag complexes

We prove that the random flag complex has a probability regime where the probability of nonvanishing homology is asymptotically bounded away from zero and away from one. Related to this main result we also establish new bounds on a sharp threshold for the fundamental group of a random flag complex to be a free group. In doing so we show that there is an intermediate probability regime in which the random flag complex has fundamental group which is neither free nor has Kazhdan's property (T).

math.AT↗

arXiv2021

Random subcomplexes and Betti numbers of random edge ideals

We study homological properties of random quadratic monomial ideals in a polynomial ring $R = {\mathbb K}[x_1, \dots x_n]$, utilizing methods from the Erd\"{o}s-R\'{e}nyi model of random graphs. Here for a graph $G \sim G(n, p)$ we consider the `coedge' ideal $I_G$ corresponding to the missing edges of $G$, and study Betti numbers of $R/I_G$ as $n$ tends to infinity. Our main results involve setting the edge probability $p = p(n)$ so that asymptotically almost surely the Krull dimension of $R/I_G$ is fixed. Under these conditions we establish various properties regarding the Betti table of $R/I_G$, including sharp bounds on regularity and projective dimension, and distribution of nonzero normalized Betti numbers. These results extend work of Erman and Yang, who studied such ideals in the context of conjectured phenomena in the nonvanishing of asymptotic syzygies. Along the way we establish results regarding subcomplexes of random clique complexes as well as notions of higher-dimensional vertex $k$-connectivity that may be of independent interest.

math.AC↗

arXiv2020

The worst way to collapse a simplex

In general a contractible complex need not be collapsible. Moreover, there exist complexes which are collapsible but even so admit a collapsing sequence where one "gets stuck", that is one can choose the collapses in such a way that one arrives at a nontrivial complex which admits no collapsing moves. Here we examine this phenomenon in the case of a simplex. In particular we characterize all values of $n$ and $d$ so that the n-simplex may collapse to a d-complex from which no further collapses are possible. Equivalently and in the language of high-dimensional generalizations of trees, we construct hypertrees that are anticollapsible, but not collapsible. Furthermore we examine anticollapsibility in random simplicial complexes.

math.CO↗

arXiv2020

Graph invariants from the topology of rigid isotopy classes

We define a new family of graph invariants, studying the topology of the moduli space of their geometric realizations in Euclidean spaces, using a limiting procedure reminiscent of Floer homology. Given a labeled graph $G$ on $n$ vertices and $d \geq 1$, $W_{G, d} \subseteq \mathbb{R}^{d \times n}$ denotes the space of nondegenerate realizations of $G$ in $\mathbb{R}^d$.The set $W_{G, d}$ might not be connected, even when it is nonempty, and we refer to its connected components as rigid isotopy classes of $G$ in $\mathbb{R}^d$. We study the topology of these rigid isotopy classes. First, regarding the connectivity of $W_{G, d}$, we generalize a result of Maehara that $W_{G, d}$ is nonempty for $d \geq n$ to show that $W_{G, d}$ is $k$-connected for $d \geq n + k + 1$, and so $W_{G, \infty}$ is always contractible. While $\pi_k(W_{G, d}) = 0$ for $G$, $k$ fixed and $d$ large enough, we also prove that, in spite of this, when $d\to \infty$ the structure of the nonvanishing homology of $W_{G, d}$ exhibits a stabilization phenomenon: it consists of $(n-1)$ equally spaced clusters whose shape does not depend on $d$, for $d$ large enough. This leads to the definition of a family of graph invariants, capturing this structure. For instance, the sum of the Betti numbers of $W_{G,d}$ does not depend on $d$, for $d$ large enough; we call this number the Floer number of the graph $G$. Finally, we give asymptotic estimates on the number of rigid isotopy classes of $\mathbb{R}^d$--geometric graphs on $n$ vertices for $d$ fixed and $n$ tending to infinity. When $d=1$ we show that asymptotically as $n\to \infty$ each isomorphism class corresponds to a constant number of rigid isotopy classes, on average. For $d>1$ we prove a similar statement at the logarithmic scale.

math.AT↗

arXiv2020

Doubly random polytopes

A two-step model for generating random polytopes is considered. For parameters $d$, $m$, and $p$, the first step is to generate a simple polytope $P$ whose facets are given by $m$ uniform random hyperplanes tangent to the unit sphere in $\mathbb{R}^d$, and the second step is to sample each vertex of $P$ independently with probability $p$ and let $Q$ be the convex hull of the sampled vertices. We establish results on how well $Q$ approximates the unit sphere in terms of $m$ and $p$ as well as asymptotics on the combinatorial complexity of $Q$ for certain regimes of $p$.

math.CO↗

arXiv2020

Topology and geometry of random 2-dimensional hypertrees

A hypertree, or $\mathbb{Q}$-acyclic complex, is a higher-dimensional analogue of a tree. We study random $2$-dimensional hypertrees according to the determinantal measure suggested by Lyons. We are especially interested in their topological and geometric properties. We show that with high probability, a random $2$-dimensional hypertree $T$ is apsherical, i.e. that it has a contractible universal cover. We also show that with high probability the fundamental group $π_1(T)$ is hyperbolic and has cohomological dimension $2$.

math.AT↗

arXiv2019

A lower bound on the number of homotopy types of simplicial complexes on $n$ vertices

For $n \in \mathbb{N}$, let $h(n)$ denote the number of simplicial complexes on $n$ vertices up to homotopy equivalence. Here we prove that $h(n) \geq 2^{2^{0.02n}}$ when $n$ is large enough. Together with the trivial upper bound of $2^{2^n}$ on the number of labeled simplicial complexes on $n$ vertices this proves a conjecture of Kalai that $h(n)$ is doubly exponential in $n$.

math.AT↗