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Richard Parker

Publications and source records attributed to Richard Parker.

11 recordsLinked to original sources
arXiv2023

Mixed-effects location scale models for joint modelling school value-added effects on the mean and variance of student achievement

School value-added models are widely applied to study, monitor, and hold schools to account for school differences in student learning. The traditional model is a mixed-effects linear regression of student current achievement on student prior achievement, background characteristics, and a school random intercept effect. The latter is referred to as the school value-added score and measures the mean student covariate-adjusted achievement in each school. In this article, we argue that further insights may be gained by additionally studying the variance in this quantity in each school. These include the ability to identify both individual schools and school types that exhibit unusually high or low variability in student achievement, even after accounting for differences in student intakes. We explore and illustrate how this can be done via fitting mixed-effects location scale versions of the traditional school value-added model. We discuss the implications of our work for research and school accountability systems.

stat.AP↗
arXiv2023

Photoevaporation versus enrichment in the cradle of the Sun

The presence of short-lived radioisotopes (SLRs) 26-Al and 60-Fe in the Solar system places constraints on the initial conditions of our planetary system. Most theories posit that the origin of 26-Al and 60-Fe is in the interiors of massive stars, and they are either delivered directly to the protosolar disc from the winds and supernovae of the massive stars, or indirectly via a sequential star formation event. However, massive stars that produce SLRs also emit photoionising far and extreme ultraviolet radiation, which can destroy the gas component of protoplanetary discs, possibly precluding the formation of gas giant planets like Jupiter and Saturn. Here, we perfom N-body simulations of star-forming regions and determine whether discs that are enriched in SLRs can retain enough gas to form Jovian planets. We find that discs are enriched and survive the photoionising radiation only when the dust radius of the disc is fixed and not allowed to move inwards due to the photoevaporation, or outwards due to viscous spreading. Even in this optimal scenario, not enough discs survive until the supernovae of the massive stars and so have zero or very little enrichment in 60-Fe. We therefore suggest that the delivery of SLRs to the Solar system may not come from the winds and supernovae of massive stars.

astro-ph.EP↗
arXiv2023

Critical density triplets for the arrestment of a sphere falling in a sharply stratified fluid

We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20 to 450 indicate that a sphere with the precise critical density, higher than the bottom layer density, can display behaviors such as bounce or arrestment after crossing the interface. We experimentally demonstrate that such a critical sphere density increases linearly as the bottom fluid density increases with a fixed top fluid density. Additionally, the critical density approaches the bottom layer fluid density as the thickness of density transition layer increases. We propose an estimation of the critical density based on the potential energy. With assuming the zero layer thickness, the estimation constitutes an upper bound of the critical density with less than 0.043 relative difference within the experimental density regime 0.997 $g/cm^{3}$ $\sim $ 1.11 $g/cm^{3}$ under the zero layer thickness assumption. By matching the experimental layer thickness, we obtain a critical density estimation with less than 0.01 relative difference within the same parameter regime.

physics.flu-dyn↗
arXiv2022

Orthogonal Stability

A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are no odd-degree orthogonal constituents. We further show that if the reduction mod p of an ordinary character is orthogonally stable, this determinant is the reduction mod p of the ordinary one. In particular, if the characteristic does not divide the group order, we immediately see in which orthogonal group it lies. We sketch methods for computing this determinant, and give some examples.

math.RT↗
arXiv2022

Equivariant quadratic forms in characteristic 2

Let $G$ be a finite group and $K$ a finite field of characteristic $2$. Denote by $t$ the $2$-rank of the commutator factor group $G/G'$ and by $s$ the number of self-dual simple $KG$-modules. Then the Witt group of equivariant quadratic forms $\WQ (K,G)$ is isomorphic to an elementary abelian $2$-group of rank $s+t$.

math.NT↗
arXiv2020

Polynomial-time proofs that groups are hyperbolic

It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kampen diagrams, which represent groups as quotients of virtually free groups. We then present a polynomial-time procedure which analyses these diagrams, and either returns an explicit linear Dehn function for the presentation, or returns fail, together with its reasons for failure. Furthermore, if our procedure succeeds we are often able to produce in polynomial time a word problem solver for the presentation that runs in linear time. Our algorithms have been implemented, and are often many orders of magnitude faster than KBMAG, the only comparable publicly available software.

math.GR↗
arXiv2019

Computational Modular Character Theory

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character tables of sporadic simple groups.

math.RT↗
arXiv2019

Estimating the association between blood pressure variability and cardiovascular disease: An application using the ARIC Study

The association between visit-to-visit systolic blood pressure variability and cardiovascular events has recently received a lot of attention in the cardiovascular literature. But blood pressure variability is usually estimated on a person-by-person basis, and is therefore subject to considerable measurement error. We demonstrate that hazard ratios estimated using this approach are subject to bias due to regression dilution and we propose alternative methods to reduce this bias: a two-stage method and a joint model. For the two-stage method, in stage one repeated measurements are modelled using a mixed effects model with a random component on the residual standard deviation. The mixed effects model is used to estimate the blood pressure standard deviation for each individual, which in stage two is used as a covariate in a time-to-event model. For the joint model, the mixed effects sub-model and time-to-event sub-model are fitted simultaneously using shared random effects. We illustrate the methods using data from the Atherosclerosis Risk in Communities (ARIC) study.

stat.AP↗
arXiv2018

A parallel algorithm for Gaussian elimination over finite fields

In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both rows and columns into roughly square blocks sized so that computing with individual blocks on individual processors provides adequate concurrency. The algorithm also returns the transformation matrix, which encodes the row operations used. We go to some lengths to avoid storing any unnecessary data as we keep track of the row operations, such as block columns of the transformation matrix known to be zero. The algorithm is accompanied by a concurrency analysis which shows that the improvement in concurrency is of the same order of magnitude as the number of blocks. An implementation of the algorithm has been tested on matrices as large as $1 000 000\times 1 000 000$ over small finite fields.

math.RA↗
arXiv2014

The Dynamical Fate of Self-Gravitating Disc Fragments After Tidal Downsizing

The gravitational instability model of planet/brown dwarf formation proposes that protostellar discs can fragment into objects with masses above a few Jupiter masses at large semimajor axis. Tidal downsizing may reduce both the object mass and semimajor axis. However, most studies of tidal downsizing end when the protostellar disc disperses, while the system is embedded in its parent star-forming region. To compare disc fragment descendants with exoplanet and brown dwarf observations, the subsequent dynamical evolution must be explored. We carry out N-Body integrations of fragment-fragment scattering in multi-object star systems, and star systems embedded in substructured clusters. In both cases, we use initial conditions generated by population synthesis models of tidal downsizing. The scattering simulations produce a wide range of eccentricities. The ejection rate is around 25%. The ejecta mass distribution is similar to that for all objects, with a velocity dispersion consistent with those produced by full hydrodynamic simulations. The semimajor axis distribution after scattering extends to parsec scales. In the cluster simulations, 13% of objects are ejected from their planetary system, and around 10% experience significant orbit modification. A small number of objects are recaptured on high eccentricity, high inclination orbits. The velocity distribution of ejecta is similar to that produced by fragment-fragment scattering. If fragment-fragment scattering and cluster stripping act together, then disc fragmentation should be efficient at producing free-floating substellar objects, and hence characterising the free-floating planet population will provide strong constraints on the frequency of disc fragmentation.

astro-ph.EP↗