arXiv subjects

Andrew Baker

Publications and source records attributed to Andrew Baker.

At least 19 recordsLinked to original sources

arXiv2026

Poincar\'e duality spaces related to the Joker

The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By attaching an extra cell we obtain an $8$-dimensional Poincar\'e duality space whose mod~$2$ cohomology realising is an unstable $\mathcal{A}$-algebra. We use obstruction theory to show that this admits a $PL$-structure. Although we are unable to show it is smoothable, it turns out that the cohomology can be realised as that of a homogeneous space.

math.AT↗

arXiv2025

INTELLECT-3: Technical Report

We present INTELLECT-3, a 106B-parameter Mixture-of-Experts model (12B active) trained with large-scale reinforcement learning on our end-to-end RL infrastructure stack. INTELLECT-3 achieves state of the art performance for its size across math, code, science and reasoning benchmarks, outperforming many larger frontier models. We open-source the model together with the full infrastructure stack used to create it, including RL frameworks, complete recipe, and a wide collection of environments, built with the verifiers library, for training and evaluation from our Environments Hub community platform. Built for this effort, we introduce prime-rl, an open framework for large-scale asynchronous reinforcement learning, which scales seamlessly from a single node to thousands of GPUs, and is tailored for agentic RL with first-class support for multi-turn interactions and tool use. Using this stack, we run both SFT and RL training on top of the GLM-4.5-Air-Base model, scaling RL training up to 512 H200s with high training efficiency.

cs.LG↗

arXiv2025

Difference-in-Differences Designs: A Practitioner's Guide

Difference-in-differences (DiD) is arguably the most popular quasi-experimental research design. Its canonical form, with two groups and two periods, is well-understood. However, empirical practices can be ad hoc when researchers go beyond that simple case. This article provides an organizing framework for discussing different types of DiD designs and their associated DiD estimators. It discusses covariates, weights, handling multiple periods, and staggered treatments. The organizational framework, however, applies to other extensions of DiD methods as well.

econ.EM↗

arXiv2024

Key Science Goals for the Next Generation Very Large Array (ngVLA): Update from the ngVLA Science Advisory Council (2024)

In 2017, the next generation Very Large Array (ngVLA) Science Advisory Council, together with the international astronomy community, developed a set of five Key Science Goals (KSGs) to inform, prioritize and refine the technical capabilities of a future radio telescope array for high angular resolution operation from 1.2 - 116 GHz with 10 times the sensitivity of the Jansky VLA and ALMA. The resulting KSGs, which require observations at centimeter and millimeter wavelengths that cannot be achieved by any other facility, represent a small subset of the broad range of astrophysical problems that the ngVLA will be able address. This document presents an update to the original ngVLA KSGs, taking account of new results and progress in the 7+ years since their initial presentation, again drawing on the expertise of the ngVLA Science Advisory Council and the broader community in the ngVLA Science Working Groups. As the design of the ngVLA has also matured substantially in this period, this document also briefly addresses initial expectations for ngVLA data products and processing that will be needed to achieve the KSGs. The original ngVLA KSGs endure as outstanding problems of high priority. In brief, they are: (1) Unveiling the Formation of Solar System Analogues; (2) Probing the Initial Conditions for Planetary Systems and Life with Astrochemistry; (3) Charting the Assembly, Structure, and Evolution of Galaxies from the First Billion Years to the Present; (4) Science at the Extremes: Pulsars as Laboratories for Fundamental Physics; (5) Understanding the Formation and Evolution of Stellar and Supermassive Black Holes in the Era of Multi-Messenger Astronomy.

astro-ph.IM↗

arXiv2024

Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs

Large Language Models (LLMs) generate text by sampling the next token from a probability distribution over the vocabulary at each decoding step. Popular sampling methods like top-p (nucleus sampling) often struggle to balance quality and diversity, especially at higher temperatures which lead to incoherent or repetitive outputs. We propose min-p sampling, a dynamic truncation method that adjusts the sampling threshold based on the model's confidence by using the top token's probability as a scaling factor. Our experiments on benchmarks including GPQA, GSM8K, and AlpacaEval Creative Writing show that min-p sampling improves both the quality and diversity of generated text across different model families (Mistral and Llama 3) and model sizes (1B to 123B parameters), especially at higher temperatures. Human evaluations further show a clear preference for min-p sampling, in both text quality and creativity. Min-p sampling has been adopted by popular open-source LLM frameworks, including Hugging Face Transformers, VLLM, and many others, highlighting its considerable impact on improving text generation quality.

cs.CL↗

arXiv2023

Characterisation of Herschel-selected strong lens candidates through HST and sub-mm/mm observations

We have carried out HST snapshot observations at 1.1 $\mu$m of 281 candidate strongly lensed galaxies identified in the wide-area extragalactic surveys conducted with the Herschel space observatory. Our candidates comprise systems with flux densities at $500\,\mu$m$ S_{500}\geq 80$ mJy. We model and subtract the surface brightness distribution for 130 systems, where we identify a candidate for the foreground lens candidate. After combining visual inspection, archival high-resolution observations, and lens subtraction, we divide the systems into different classes according to their lensing likelihood. We confirm 65 systems to be lensed. Of these, 30 are new discoveries. We successfully perform lens modelling and source reconstruction on 23 systems, where the foreground lenses are isolated galaxies and the background sources are detected in the HST images. All the systems are successfully modelled as a singular isothermal ellipsoid. The Einstein radii of the lenses and the magnifications of the background sources are consistent with previous studies. However, the background source circularised radii (between 0.34 kpc and 1.30 kpc) are $\sim$3 times smaller than the ones measured in the sub-mm/mm for a similarly selected and partially overlapping sample. We compare our lenses with those in the SLACS survey, confirming that our lens-independent selection is more effective at picking up fainter and diffuse galaxies and group lenses. This sample represents the first step towards characterising the near-IR properties and stellar masses of the gravitationally lensed dusty star-forming galaxies.

astro-ph.GA↗

arXiv2023

Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory

The algebraic Joker module was originally described in the 1970s by Adams and Priddy and is a $5$-dimensional module over the subHopf algebra $\mathcal{A}(1)$ of the mod $2$ Steenrod algebra. It is a self-dual endotrivial module, i.e., an invertible object in the stable module category of $\mathcal{A}(1)$. Recently it has been shown that no analogues exist for $\mathcal{A}(n)$ with $n>1$. Using iterated doubling this also gives an iterated double which is an $\mathcal{A}(n)$-module but not stably invertible. In previous work the author showed that for $n=1,2,3$ these iterated doubles were realisable as cohomology of CW spectra, but no such realisation existed for $n>3$. The main point of the paper is to show that in the height $2$ chromatic context, the Morava $K$-theory of double Jokers realise an exceptional endotrivial module over the quaternion group of order $8$ that only exists over a field of characteristic $2$ containing a primitive cube root of unity. This has connections with certain Massey products in the cohomology of the quaternion group.

math.AT↗

arXiv2022

Locally Frobenius algebras and Hopf algebras

We develop a theory of \emph{locally Frobenius algebras} which are colimits of certain directed systems of Frobenius algebras. A major goal is to obtain analogues of the work of Moore \& Peterson and Margolis on \emph{nearly Frobenius algebras} and \emph{$P$-algebras} which was applied to graded Hopf algebras such as the Steenrod algebra for a prime. Such locally Frobenius algebras are coherent and in studying their modules we are naturally led to focus on coherent and finite dimensional modules. Indeed, the category of coherent modules over locally Frobenius algebra $A$ is abelian with enough projectives and injectives since $A$ is injective relative to the coherent modules; however it only has finite limits and colimits. The finite dimensional modules also form an abelian category but finite dimensional modules are never coherent. The minimal ideals of a locally Frobenius algebra are precisely the ones which are isomorphic to coherent simple modules; in particular it does not contain a copy of any finite dimensional simple module so it is not a Kasch algebra. We discuss possible versions of stable module categories for such algebras. We also discuss possible monoidal structures on module categories of a locally Frobenius Hopf algebra: for example tensor products of coherent modules turn out to be pseudo-coherent. Examples of locally Frobenius Hopf algebras include group algebras of locally finite groups, already intensively studied in the literature.

math.RA↗

arXiv2022

A new technique to isolate kinematically anomalous gas in HI data cubes

HI line observations of nearby galaxies often reveal the presence of extraplanar and/or kinematically anomalous gas that deviates from the general circular flow. In this work, we study the dependence of kinematically anomalous HI gas in galaxies taken from the Simba cosmological simulation on galaxy properties such as HI mass fraction, specific star formation rate, and local environmental density. To identify kinematically anomalous gas, we use a simple yet effective decomposition method to separate it from regularly-rotating gas in the galactic disk; this method is well-suited for application to observational datasets but has been validated here using the simulation. We find that at fixed atomic gas mass fraction, the anomalous gas fraction increases with the specific star formation rate. We also find that the anomalous gas fraction does not have a significant dependence on a galaxy's environment. Our decomposition method has the potential to yield useful insights from future HI surveys.

astro-ph.GA↗

arXiv2022

On $P$-algebras and their duals

The notion of $P$-algebra due to Margolis, building on work of Moore and Peterson, was motivated by the case of the Steenrod algebra at a prime and its modules. We develop aspects of this theory further, focusing especially on coherent modules and finite dimensional modules. We also discuss the dual Hopf algebra of $P$-algebra and its comodules. One of our aims is provide a collection of techniques for calculating cohomology groups over $P$-algebras and their duals, in particular giving vanishing results. Much of our work is implicit in that of Margolis and others but we are unaware of systematic discussions in the literature. We give some examples illustrating topological applications which follow easily from our results.

math.AT↗

arXiv2022

Asymptotics, Tur\'an inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions

Let $j,n$ be even positive integers, and let $\overline{p}_j(n)$ denote the number of partitions with BG-rank $j$, and $\overline{p}_j(a,b;n)$ to be the number of partitions with BG-rank $j$ and $2$-quotient rank congruent to $a \pmod{b}$. We give asymptotics for both statistics, and show that $\overline{p}_j(a,b;n)$ is asymptotically equidistributed over the congruence classes modulo $b$. We also show that each of $\overline{p}_j(n)$ and $\overline{p}_j(a,b;n)$ asymptotically satisfy all higher-order Tur\'{a}n inequalities.

math.NT↗

arXiv2021

On the dual of a $P$-algebra and its comodules, with applications to comparison of some Bousfield classes

In his seminal work on localisation of spectra, Ravenel initiated the study of Bousfield classes of spectra related to the chromatic perspective. In particular he showed that there were infinitely many distinct Bousfield classes between $\langle MU\rangle$ and $\langle S^0\rangle$. The main topological goal of this paper is investigate how these Bousfield classes are related to that of another classical Thom spectrum $MSp$, and in particular how $\langle MSp\rangle$ is related to $\langle MU\rangle$. We follow the approach of Ravenel, but adapt it using the theory of $P$-algebras to give vanishing results for cohomology. Our work involves dualising and considering comodules over duals of $P$-algebras; these ideas are then applied to the mod~$2$ Steenrod algebra and certain subHopf algebras.

math.AT↗

arXiv2020

Homotopy theory of modules over a commutative $S$-algebra: some tools and examples

Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These have categories of modules which are generalisations of the classical categories of spectra that correspond to modules over the sphere spectrum; passing to their derived or homotopy categories leads to new contexts in which homotopy theory can be explored. In this paper we describe some of the tools available for studying these `brave new homotopy theories' and demonstrate them by considering modules over the $K$-theory spectrum, closely related to Mahowald's theory of $bo$-resolutions. In a planned sequel we will apply these techniques to the much less familiar context of modules over the $2$-local connective spectrum of topological modular forms.

math.AT↗

arXiv2019

The realizability of some finite-length modules over the Steenrod algebra by spaces

The Joker is an important finite cyclic module over the mod-$2$ Steenrod algebra $\mathcal A$. We show that the Joker, its first two iterated Steenrod doubles, and their linear duals are realizable by spaces of as low a dimension as the instability condition of modules over the Steenrod algebra permits. This continues and concludes prior work by the first author and yields a complete characterization of which versions of Jokers are realizable by spaces or spectra and which are not. The constructions involve sporadic phenomena in homotopy theory ($2$-compact groups, topological modular forms) and may be of independent interest.

math.AT↗

arXiv2017

Iterated doubles of the Joker and their realisability

Let $\mathcal{A}(1)^*$ be the subHopf algebra of the mod~$2$ Steenrod algebra $\mathcal{A}^*$ generated by $\mathrm{Sq}^1$ and $\mathrm{Sq}^2$. The \emph{Joker} is the cyclic $\mathcal{A}(1)^*$-module $\mathcal{A}(1)^*/\mathcal{A}(1)^*\{\mathrm{Sq}^3\}$ which plays a special r\^ole in the study of $\mathcal{A}(1)^*$-modules. We discuss realisations of the Joker both as an $\mathcal{A}^*$-module and as the cohomology of a spectrum. We also consider analogous $\mathcal{A}(n)^*$-modules for $n\geq2$ and prove realisability results (both stable and unstable) for $n=2,3$ and non-realisability results for $n\geq4$.

math.AT↗

arXiv2017

MERGHERS: An SZ-selected cluster survey with MeerKAT

The MeerKAT telescope will be one of the most sensitive radio arrays in the pre-SKA era. Here we discuss a low-frequency SZ-selected cluster survey with MeerKAT, the MeerKAT Extended Relics, Giant Halos, and Extragalactic Radio Sources (MERGHERS) survey. The primary goal of this survey is to detect faint signatures of diffuse cluster emission, specifically radio halos and relics. SZ-selected cluster samples offer a homogeneous, mass-limited set of targets out to higher redshift than X-ray samples. MeerKAT is sensitive enough to detect diffuse radio emission at the faint levels expected in low-mass and high-redshift clusters, thereby enabling radio halo and relic formation theories to be tested with a larger statistical sample over a significantly expanded phase space. Complementary multiwavelength follow-up observations will provide a more complete picture of any clusters found to host diffuse emission, thereby enhancing the scientific return of the MERGHERS survey.

astro-ph.CO↗

arXiv2015

$\mathcal{E}_\infty$ ring spectra and elements of Hopf invariant $1$

The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain iterated mapping cones by applying the free algebra functor. In fact, these are equivalent to Thom spectra over infinite loop spaces related to the classifying spaces $B\mathrm{SO},\,B\mathrm{Spin},\,B\mathrm{String}$. We show that the homology of these Thom spectra are all extended comodule algebras of the form $\mathcal{A}_*\square_{\mathcal{A}(r)_*}P_*$ over the dual Steenrod algebra $\mathcal{A}_*$ with $\mathcal{A}_*\square_{\mathcal{A}(r)_*}\mathbb{F}_2$ as an algebra retract. This suggests that these spectra might be wedges of module spectra over the ring spectra $H\mathbb{Z}$, $k\mathrm{O}$ or $\mathrm{tmf}$, however apart from the first case, we have no concrete results on this.

math.AT↗

arXiv2014

Power operations and coactions in highly commutative homology theories

Power operations in the homology of infinite loop spaces, and $H_\infty$ or $E_\infty$ ring spectra have a long history in Algebraic Topology. In the case of ordinary mod p homology for a prime p, the power operations of Kudo, Araki, Dyer and Lashof interact with Steenrod operations via the Nishida relations, but for many purposes this leads to complicated calculations once iterated applications of these functions are required.On the other hand, the homology coaction turns out to provide tractable formulae better suited to exploiting multiplicative structure. We show how to derive suitable formulae for the interaction between power operations and homology coactions in a wide class of examples; our approach makes crucial use of modern frameworks for spectra with well behaved smash products. In the case of mod $p$ homology, our formulae extend those of Bisson and Joyal to odd primes. We also show how to exploit our results in sample calculations, and produce some apparently new formulae for the Dyer-Lashof action on the dual Steenrod algebra.

math.AT↗