On Embedding Singular Poisson Spaces

This dissertation investigates the problem of locally embedding singular Poisson spaces. Specifically, it seeks to understand when a singular symplectic quotient V/G of a symplectic vector space V by a group G \subseteq Sp_2n(R) is realizable as a Poisson subspace of some Poisson manifold (R^n,{.,.}). The local embedding problem is recast in the language of schemes and reinterpreted as a problem of extending the Poisson bracket to infinitesimal neighborhoods of an embedded singular space. Such extensions of a Poisson bracket near a singular point p of V/G are then related to the cohomology and representation theory of the cotangent Lie algebra at p. Using this framework, it is shown that the real 4-dimensional quotient V/\ZZ_n (n odd) is not realizable as a Poisson subspace of any (R^{2n+6},{.,.}), even though the underlying variety algebraically embeds into R^{2n+6}. The proof of this nonembedding result hinges on a refinement of the Levi decomposition for Poisson manifolds to partially linearize any extension with respect to the Levi decomposition of the cotangent Lie algebra of V/G at the origin. Moreover, in the case n=3, this nonembedding result is complemented by a concrete realization of V/\ZZ_3 as a Poisson subspace of R^78

Small-N Collisional Dynamics: Pushing Into the Realm of Not-So-Small-N

In this paper, we study small-N gravitational dynamics involving up to six objects. We perform a large suite of numerical scattering experiments involving single, binary, and triple stars. This is done using the FEWBODY numerical scattering code, which we have upgraded to treat encounters involving triple stars. We focus on outcomes that result in direct physical collisions between stars, within the low angular momentum and high absolute orbital energy regime. The dependence of the collision probability on the number of objects involved in the interaction, N, is found for fixed total energy and angular momentum. Our results are consistent with a collision probability that increases approximately as N^2. Interestingly, this is also what is expected from the mean free path approximation in the limit of very large N. A more thorough exploration of parameter space will be required in future studies to fully explore this potentially intriguing connection. This study is meant as a first step in an on-going effort to extend our understanding of small-N collisional dynamics beyond the three- and four-body problems and into the realm of larger-N.Comment: 11 pages, 6 figures, 2 tables; accepted for publication in MNRAS; updated to match published versio

Hepatotoxicity following administration of onasemnogene abeparvovec (AVXS-101) for the treatment of spinal muscular atrophy

BACKGROUND & AIMS: Spinal muscular atrophy (SMA) is an autosomal recessive, childhood-onset motor neuron disease. Onasemnogene abeparvovec (OA) is a gene therapy designed to address SMA\u27s root cause. In pivotal mouse toxicology studies, the liver was identified as a major site of OA toxicity. Clinical data reflect elevations in serum aminotransferase concentrations, with some reports of serious acute liver injury. Prophylactic prednisolone mitigates these effects. Herein, we aim to provide pragmatic, supportive guidance for identification, management, and risk mitigation of potential drug-induced liver injury. METHODS: Data from 325 patients with SMA who had received OA through 31 December 2019, in 5 clinical trials, a managed access program (MAP), and a long-term registry (RESTORE), and through commercial use, were analyzed. Liver-related adverse events, laboratory data, concomitant medications, and prednisolone use were analyzed. RESULTS: Based on adverse events and laboratory data, 90 of 100 patients had elevated liver function test results (alanine aminotransferase, and/or aspartate aminotransferase, and/or bilirubin concentrations). Of these, liver-associated adverse events were reported for 34 of 100 (34%) and 10 of 43 (23%) patients in clinical trials and MAP/RESTORE, respectively. Two patients in MAP had serious acute liver injury, which resolved completely. While all events in the overall population resolved, prednisolone treatment duration varied (range: 33-229 days), with a majority receiving prednisolone for 60-120 days. More than 60% had elevations in either alanine aminotransferase, aspartate aminotransferase, or bilirubin concentrations prior to dosing. Greater than 40% received potentially hepatotoxic concomitant medications. CONCLUSIONS: Hepatotoxicity is a known risk associated with OA use. Practitioners should identify contributing factors and mitigate risk through appropriate monitoring and intervention. LAY SUMMARY: Onasemnogene abeparvovec is a type of medicine called a gene therapy, which is used to treat babies and young children who have a rare, serious inherited condition called spinal muscular atrophy (SMA). It works by supplying a fully functioning copy of the survival motor neuron or SMN gene, which then helps the body produce enough SMN protein. However, it can cause an immune response that could lead to an increase in enzymes produced by the liver. This article provides information about the liver injury and how to prevent and recognize if it happens, so that it may be treated properly

Implementing Primordial Binaries in Simulations of Star Cluster Formation with a Hybrid MHD and Direct N-Body Method

The fraction of stars in binary systems within star clusters is important for their evolution, but what proportion of binaries form by dynamical processes after initial stellar accretion remains unknown. In previous work, we showed that dynamical interactions alone produced too few low-mass binaries compared to observations. We therefore implement an initial population of binaries in the coupled MHD and direct N-body star cluster formation code Torch. We compare simulations with, and without, initial binary populations and follow the dynamical evolution of the binary population in both sets of simulations, finding that both dynamical formation and destruction of binaries take place. Even in the first few million years of star formation, we find that an initial population of binaries is needed at all masses to reproduce observed binary fractions for binaries with mass ratios above the $q \geq 0.1$ detection limit. Our simulations also indicate that dynamical interactions in the presence of gas during cluster formation modify the initial distributions towards binaries with smaller primary masses, larger mass ratios, smaller semi-major axes and larger eccentricities. Systems formed dynamically do not have the same properties as the initial systems, and systems formed dynamically in the presence of an initial population of binaries differ from those formed in simulations with single stars only. Dynamical interactions during the earliest stages of star cluster formation are important for determining the properties of binary star systems.Comment: 15 pages, 14 figures, submitted to MNRAS and edited to address positive referee's repor

Cross-validation of single-step genetic evaluation in U.S. Katahdin sheep

Genomic information is used in genetic evaluation to improve prediction accuracy in most livestock species. Such is less so in sheep, particularly in the U.S. In this study, the impact of implementing singlestep genomic BLUP as compared to pedigree BLUP for weight and faecal egg count traits was evaluated in U.S. Katahdin sheep. Two methods of cross validation were utilised to compare the predictive ability and bias of estimated breeding values of these methods. Genomic information improved predictive ability for both traits, and reduced bias in the evaluation of faecal egg counts. Accuracies of estimated breeding values improved appreciably in genotyped animals. The benefit from including genomic information based on cross validation was minimal but is expected to improve as the reference population grows. Single-step genomic BLUP procedures developed will be used to update those applied in the routine genetic evaluation offered through the U.S. National Sheep Improvement Program