arXiv subjects

James Taylor

Publications and source records attributed to James Taylor.

At least 19 recordsLinked to original sources

arXiv2026

Imprints of Mass Accretion History on Galaxy Cluster Morphology

Variations in dynamical states of galaxy clusters can introduce biases and scatter in observable-mass relations. The dynamical state of a cluster is an emergent feature of its mass accretion history (MAH), it is therefore useful to constrain the MAH of the cluster. In this work, we characterize 305 massive clusters from The300 project by connecting features from their projected stellar distributions to their mass accretion histories (MAH). As a baseline, we first correlate host dark matter halo dynamical state indicators at $z=0$ with their MAH via the Spearman rank correlation coefficient $\rho_{\mathrm{sp}}$. Both substructure mass fraction and center-of-mass offset measurements correlate strongly with the MAH measured between $0.1\lesssim z\lesssim 1$. We repeat this exercise with morphological measurements of projected stellar density maps, many of which exhibit moderate correlation strength with different times in the MAH. Broadly, core morphological measurements ($r \leq 30\,\mathrm{kpc}$) correlate better with early-time MAH. Core-excised ($50\,\mathrm{kpc} \leq r \leq 1\,\mathrm{Mpc}$) morphological measurements correlate better with late-time MAH. We further quantify the MAH prediction power of both traditional dynamical state indicators and morphological parameters using Multivariable Conditional Abundance Matching (MultiCAM). MultiCAM employs simple rank-ordering operations, making it straightforward to translate to observed datasets. We find reasonable ($\rho_{\mathrm{sp}} \geq 0.6$) performance for predictions of the mass fraction between $1\lesssim z\lesssim 0.1$, though with notable information loss when using projected quantities. In one example application of our methodology, we use the coefficients of the MultiCAM models to select subsamples of galaxy clusters that have accreted more (or less) of their $z = 0$ mass budget over a given time frame.

astro-ph.CO↗

arXiv2026

MassSpecGym in the Wild: Uncovering and Correcting Evaluation Pitfalls in AI-Driven Molecule Discovery

Reliable benchmarking is critical for developing machine learning models for tandem mass spectrometry (MS/MS) based molecule discovery. Subtle issues in experimental design and model evaluation procedures can degrade the trustworthiness of such benchmarks and lead to erroneous conclusions. We conduct a thorough review of model evaluation issues in the recent MS/MS machine learning literature, using the standard MassSpecGym benchmark suite as a case study to illustrate the impact of these issues. We find evaluation issues in at least 17 of 26 papers reporting MassSpecGym benchmark results in the first year of its adoption. We isolate three classes of failures: (i) data leakage, (ii) shortcut learning, and (iii) implementation bugs and metric divergence. Through extensive experimentation and code replication, we quantify the impact of these issues and show how they corrupt the evaluation standards MassSpecGym was designed to enforce. We distill our findings into recommendations generalizable to MS/MS challenges, benchmarks, and custom evaluation setups. We also release MassSpecGym v1.5, an implementation of our recommendations in the MassSpecGym benchmarking suite which addresses the failure modes identified in this audit. MassSpecGym v1.5 is publicly available at https://github.com/pluskal-lab/MassSpecGym.

cs.LG↗

arXiv2025

Character Theory for Semilinear Representations

Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$, the kernel of the map $G \rightarrow \mathrm{Aut}(L)$. When $G$ is finite and $L$ has characteristic 0 this provides a character theory for semilinear representations of $G$ over $L$, which recovers ordinary character theory when the action of $G$ on $L$ is trivial.

math.RT↗

arXiv2025

Fast 360-Degree 3D Metrology for Directed Energy Deposition

Directed Energy Deposition (DED) is a metal additive manufacturing process capable of building and repairing large, complex metal parts from a wide range of alloys. Its flexibility makes it attractive for multiple industrial applications, e.g., in aerospace, automotive and biomedical fields. However, errors or defects introduced at any stage of the printing process can, if undetected, significantly impact the final result, rendering the printed part unusable. Potential in-situ correction methods of printing defects require fast and high-resolution on-the-fly 3D inspection inside the machine, but existing 3D monitoring methods often lack full 360{\deg} 3D coverage, require bulky setups, or are too slow for real-time layer-wise feedback. In this paper, we present a single-shot, multi-view polarized fringe projection profilometry (FPP) system designed for real-time in-situ 3D inspection during DED printing. Multiple camera-projector pairs are arranged around the deposition surface to measure depth from different viewpoints in single-shot, while cross-polarized image filtering suppresses specular reflections caused by varying surface reflectance across different alloys. The final 360{\deg} reconstruction is obtained via joint registration of the captured multi-view measurements. Our prototype has been deployed in a DED system and our first experiments demonstrate a depth precision better than $\delta z < 60\,\mu\mathrm{m}$ on partially reflective and "shiny" metal surfaces, enabling accurate, layer-wise monitoring for closed-loop DED control.

physics.optics↗

arXiv2025

A Personalized Exercise Assistant using Reinforcement Learning (PEARL): Results from a four-arm Randomized-controlled Trial

Consistent physical inactivity poses a major global health challenge. Mobile health (mHealth) interventions, particularly Just-in-Time Adaptive Interventions (JITAIs), offer a promising avenue for scalable, personalized physical activity (PA) promotion. However, developing and evaluating such interventions at scale, while integrating robust behavioral science, presents methodological hurdles. The PEARL study was the first large-scale, four-arm randomized controlled trial to assess a reinforcement learning (RL) algorithm, informed by health behavior change theory, to personalize the content and timing of PA nudges via a Fitbit app. We enrolled and randomized 13,463 Fitbit users into four study arms: control, random, fixed, and RL. The control arm received no nudges. The other three arms received nudges from a bank of 155 nudges based on behavioral science principles. The random arm received nudges selected at random. The fixed arm received nudges based on a pre-set logic from survey responses about PA barriers. The RL group received nudges selected by an adaptive RL algorithm. We included 7,711 participants in primary analyses (mean age 42.1, 86.3% female, baseline steps 5,618.2). We observed an increase in PA for the RL group compared to all other groups from baseline to 1 and 2 months. The RL group had significantly increased average daily step count at 1 month compared to all other groups: control (+296 steps, p=0.0002), random (+218 steps, p=0.005), and fixed (+238 steps, p=0.002). At 2 months, the RL group sustained a significant increase compared to the control group (+210 steps, p=0.0122). Generalized estimating equation models also revealed a sustained increase in daily steps in the RL group vs. control (+208 steps, p=0.002). These findings demonstrate the potential of a scalable, behaviorally-informed RL approach to personalize digital health interventions for PA.

cs.LG↗

arXiv2025

Improving Audio Classification by Transitioning from Zero- to Few-Shot

State-of-the-art audio classification often employs a zero-shot approach, which involves comparing audio embeddings with embeddings from text describing the respective audio class. These embeddings are usually generated by neural networks trained through contrastive learning to align audio and text representations. Identifying the optimal text description for an audio class is challenging, particularly when the class comprises a wide variety of sounds. This paper examines few-shot methods designed to improve classification accuracy beyond the zero-shot approach. Specifically, audio embeddings are grouped by class and processed to replace the inherently noisy text embeddings. Our results demonstrate that few-shot classification typically outperforms the zero-shot baseline.

cs.SD↗

arXiv2025

The Categories of Lubin-Tate and Drinfeld Bundles

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, we show that the category of Lubin-Tate bundles on the $(n-1)$-dimensional Drinfeld symmetric space is equivalent to the category of finite-dimensional smooth representations of the group of units of the division algebra of invariant $1/n$ over $F$.

math.NT↗

arXiv2025

Brauer's 14th Problem and Dyson's Tenfold Way

We consider Brauer's 14th Problem in the context of "Real" structures on finite groups and their antilinear representations. The problem is to count the number of characters of each different type using "group theory". While Brauer's original problem deals only with three types (real, complex and quaternionic), here we consider the ten types coming from Dyson's tenfold way.

math.GR↗

arXiv2024

Prime Gaps In The Gaussian Integers

In this paper we create a definition for prime gaps in the Gaussian integers using a boxcar metric. From this we used numerical methods to derive an asymptotic upper bound for the gaps in this scenario, namely O(log^2|p_{n}|).

math.NT↗

arXiv2024

Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of $D^\times$ on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of $D^\times$ to $G^0$-finite $\text{GL}_n(F)$-equivariant vector bundles with connection on $\Omega$, the $(n-1)$-dimensional Drinfeld symmetric space.

math.NT↗

arXiv2023

Event-based Motion-Robust Accurate Shape Estimation for Mixed Reflectance Scenes

Event-based structured light systems have recently been introduced as an exciting alternative to conventional frame-based triangulation systems for the 3D measurements of diffuse surfaces. Important benefits include the fast capture speed and the high dynamic range provided by the event camera - albeit at the cost of lower data quality. So far, both low-accuracy event-based and high-accuracy frame-based 3D imaging systems are tailored to a specific surface type, such as diffuse or specular, and can not be used for a broader class of object surfaces ("mixed reflectance scenes"). In this work, we present a novel event-based structured light system that enables fast 3D imaging of mixed reflectance scenes with high accuracy. On the captured events, we use epipolar constraints that intrinsically enable decomposing the measured reflections into diffuse, two-bounce specular, and other multi-bounce reflections. The diffuse surfaces in the scene are reconstructed using triangulation. Then, the reconstructed diffuse scene parts are leveraged as a "display" to evaluate the specular scene parts via deflectometry. This novel procedure allows us to use the entire scene as a virtual screen, using only a scanning laser and an event camera. The resulting system achieves fast and motion-robust (14Hz) reconstructions of mixed reflectance scenes with < 600 ${\mu}m$ depth error. Moreover, we introduce an "ultrafast" capture mode (250Hz) for the 3D measurement of diffuse scenes.

cs.CV↗

arXiv2023

Line Bundles on The First Drinfeld Covering

Let $\Omega^d$ be the $d$-dimensional Drinfeld symmetric space for a finite extension $F$ of $\mathbb{Q}_p$. Let $\Sigma^1$ be a geometrically connected component of the first Drinfeld covering of $\Omega^d$ and let $\mathbb{F}$ be the residue field of the unique degree $d+1$ unramified extension of $F$. We show that the natural homomorphism determined by the second Drinfeld covering from the group of characters of $(\mathbb{F}, +)$ to $\text{Pic}(\Sigma^1)[p]$ is injective. In particular, $\text{Pic}(\Sigma^1)[p] \neq 0$. We also show that all vector bundles on $\Omega^1$ are trivial, which extends the classical result that $\text{Pic}(\Omega^1) = 0$.

math.RT↗

arXiv2023

Defining Real Numbers as Oracles

A real number is a rule that, when provided with a rational interval, answers Yes or No depending on if the real number ought to be considered to be in the given interval. Since the goal is to define the real numbers, this can only motivate the definition of which rules should be considered a real number. The rule must satisfy five properties and any rule that does so we call an oracle. Three of the properties ensure that we do not have multiple oracles representing the same real number. The other two properties ensure that the oracle does narrow down to a single real number. The most important property is the Separating property which ensures that if we divide a Yes interval into two parts, then one part is a Yes interval while the other is a No interval; the exception is if the division point, which is a rational number, happens to be the desired real number in which case both intervals are Yes intervals. We explore various examples and algorithms in using oracles in addition to establishing that the oracles do, in fact, form the field of real numbers. The concept of a Family of Overlapping, Notionally Shrinking Intervals is defined and found to be an essential tool in working with oracle arithmetic. Mediant approximations, which are related to continued fraction representations, naturally arise from an oracle perspective. We also compare and contrast with other common definitions of real numbers, such as Cauchy sequences and Dedekind cuts, in which the conclusion is that the oracle perspective is somewhat of a master map to the other definitions. We do an explicit example to contrast oracle arithmetic with decimal arithmetic and continued fraction arithmetic.

math.GM↗

arXiv2023

Rationally Querying the Reals

A new definition of a real number is that it is a rule which says Yes or No based on whether the real number ought to be in a given rational interval. This is a teaser paper for formalizing, exploring, and generalizing this definition. The full exploration is given in the paper "Defining Real Numbers as Oracles".

math.GM↗

arXiv2023

RxRx1: A Dataset for Evaluating Experimental Batch Correction Methods

High-throughput screening techniques are commonly used to obtain large quantities of data in many fields of biology. It is well known that artifacts arising from variability in the technical execution of different experimental batches within such screens confound these observations and can lead to invalid biological conclusions. It is therefore necessary to account for these batch effects when analyzing outcomes. In this paper we describe RxRx1, a biological dataset designed specifically for the systematic study of batch effect correction methods. The dataset consists of 125,510 high-resolution fluorescence microscopy images of human cells under 1,138 genetic perturbations in 51 experimental batches across 4 cell types. Visual inspection of the images alone clearly demonstrates significant batch effects. We propose a classification task designed to evaluate the effectiveness of experimental batch correction methods on these images and examine the performance of a number of correction methods on this task. Our goal in releasing RxRx1 is to encourage the development of effective experimental batch correction methods that generalize well to unseen experimental batches. The dataset can be downloaded at https://rxrx.ai.

cs.CV↗

arXiv2021

The Picard Group of Vertex Affinoids in the First Drinfeld Covering

Let $F$ be a finite extension of $\mathbb{Q}_p$. Let $\Omega$ be the Drinfeld upper half plane, and $\Sigma^1$ the first Drinfeld covering of $\Omega$. We study the affinoid open subset $\Sigma^1_v$ of $\Sigma^1$ above a vertex of the Bruhat-Tits tree for $\text{GL}_2(F)$. Our main result is that $\text{Pic}(\Sigma^1_v)[p] = 0$, which we establish by showing that $\text{Pic}(\mathbf{Y})[p] = 0$ for $\mathbf{Y}$ the Deligne-Lusztig variety of $\text{SL}_2(\mathbb{F}_q)$. One formal consequence is a description of the representation $H^1_{\text{\'{e}t}}(\Sigma^1_v, \mathbb{Z}_p(1))$ of $\text{GL}_2(\mathcal{O}_F)$ as the $p$-adic completion of $\mathcal{O}(\Sigma^1_v)^\times$.

math.RT↗

arXiv2020

Real Representations of $C_2$-Graded Groups: The Linear and Hermitian Theories

We study linear and hermitian representations of finite $C_2$-graded groups. We prove that the category of linear representations is equivalent to a category of antilinear representations as an $\infty$-category. We also prove that the category hermitian representations, as an $\infty$-category, is equivalent to a category of usual representations.

math.RT↗

arXiv2020

Real Representations of $C_2$-Graded Groups: The Antilinear Theory

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite $C_2$-graded groups. A finite $C_2$-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial component of the theory. Among other things, we study characters and Frobenius-Schur indicators. As an example, we describe the antilinear representations of the $C_2$-graded group $A_n \leq S_n$.

math.RT↗