Abstract:
Spinocerebellar ataxia type 1 (SCA1) is a dominantly inherited neurodegenerative disease caused by expansion of a CAG repeat that encodes a polyglutamine tract in ATAXIN1 (ATXN1). Molecular and genetic data indicate that SCA1 is mainly caused by a gain-of-function mechanism. However, deletion of wild-type ATXN1 enhances SCA1 pathogenesis, whereas increased levels of an evolutionarily conserved paralog of ATXN1, Ataxin 1-Like, ameliorate it. These data suggest that a partial loss of ATXN1 function contributes to SCA1. To address this possibility, we set out to determine if the SCA1 disease model (Atxn1154Q/+ mice) and the loss of Atxn1 function model (Atxn1？/？ mice) share molecular changes that could potentially contribute to SCA1 pathogenesis. To identify transcriptional changes that might result from loss of function of ATXN1 in SCA1, we performed gene expression microarray studies on cerebellar RNA from Atxn1？/？ and Atxn1154Q/+ cerebella and uncovered shared gene expression changes. We further show that mild overexpression of Ataxin-1-Like rescues several of the molecular and behavioral defects in Atxn1？/？ mice. These results support a model in which Ataxin 1-Like overexpression represses SCA1 pathogenesis by compensating for a partial loss of function of Atxn1. Altogether, these data provide evidence that partial loss of Atxn1 function contributes to SCA1 pathogenesis and raise the possibility that loss-of-function mechanisms contribute to other dominantly inherited neurodegenerative diseases.

Abstract:
Background Major basic protein released from eosinophils to airway parasympathetic nerves blocks inhibitory M2 muscarinic receptors on the parasympathetic nerves, increasing acetylcholine release and potentiating reflex bronchoconstriction. Recruitment of eosinophils to airway parasympathetic neurons requires neural expression of both intercellular adhesion molecular-1 (ICAM-1) and eotaxin. We have shown that inflammatory cytokines induce eotaxin and ICAM-1 expression in parasympathetic neurons. Objective To test whether the β2 agonist albuterol, which is used to treat asthma, changes TNF-alpha-induced eotaxin and ICAM-1 expression in human parasympathetic neurons. Methods Parasympathetic neurons were isolated from human tracheas and grown in serum-free medium for one week. Cells were incubated with either (R)-albuterol (the active isomer), (S)-albuterol (the inactive isomer) or (R,S)-albuterol for 90 minutes before adding 2 ng/ml TNF-alpha for another 4 hours (for mRNA) or 24 hours (for protein). Results and Conclusions Baseline expression of eotaxin and ICAM-1 were not changed by any isomer of albuterol as measured by real time RT-PCR. TNF-alpha induced ICAM-1 expression was significantly inhibited by (R)-albuterol in a dose dependent manner, but not by (S) or (R,S)-albuterol. Eotaxin expression was not changed by TNF-alpha or by any isomer of albuterol. The β-receptor antagonist propranolol blocked the inhibitory effect of (R)-albuterol on TNF-alpha-induced ICAM-1 expression. Clinical Implication The suppressive effect of (R)-albuterol on neural ICAM-1 expression may be an additional mechanism for decreasing bronchoconstriction, since it would decrease eosinophil recruitment to the airway nerves.

Abstract:
While many models have been proposed for GRBs, those currently favored are all based upon the formation of and/or rapid accretion into stellar mass black holes. We present population synthesis calculations of these models using a Monte Carlo approach in which the many uncertain parameters intrinsic to such calculations are varied. We estimate the event rate for each class of model as well as the propagation distance for those having significant delay between formation and burst production, i.e., double neutron star (DNS) mergers and black hole-neutron star (BH/NS) mergers. For reasonable assumptions regarding the many uncertainties in population synthesis, we calculate a daily event rate in the universe for i) merging neutron stars: ~100/day; ii) neutron-star black hole mergers: ~450/day; iii) collapsars: ~10,000/day; iv) helium star black hole mergers: ~1000/day; and v) white dwarf black hole mergers: ~20/day. The range of uncertainty in these numbers however, is very large, typically two to three orders of magnitude. These rates must additionally be multiplied by any relevant beaming factor and sampling fraction (if the entire universal set of models is not being observed). Depending upon the mass of the host galaxy, half of the DNS and BH/NS mergers will happen within 60kpc (for a Milky-Way massed galaxy) to 5Mpc (for a galaxy with negligible mass) from the galactic center. Because of the delay time, neutron star and black hole mergers will happen at a redshift 0.5 to 0.8 times that of the other classes of models. Information is still lacking regarding the hosts of short hard bursts, but we suggest that they are due to DNS and BH/NS mergers and thus will ultimately be determined to lie outside of galaxies and at a closer mean distance than long complex bursts (which we attribute to collapsars).

Abstract:
The recent detection of a transient absorption feature in the prompt emission of GRB 990705 has sparked multiple attempts to fit this feature in terms of photoelectric absorption or resonance scattering out of the line of sight to the observer. However, the physical conditions required to reproduce the observed absorption feature turn out to be rather extreme compared to the predictions of current GRB progenitor models. In particular, strong clumping of ejecta from the GRB progenitor seems to be required. Using detailed 3D hydrodynamic simulations of supernova explosions as a guideline, we have investigated the dynamics and structure of pre-GRB ejecta predicted in various GRB progenitor models. Based on our results, combined with population synthesis studies relevant to the He-merger model, we estimate the probability of observing X-ray absorption features as seen in GRB 990705 to << 1 %. Alternatively, if the supranova model is capable of producing highly collimated long-duration GRBs, it may be a more promising candidate to produce observable, transient X-ray absorption features.

Abstract:
It is firmly established that the stellar mass distribution is smooth, covering the range 0.1-100 Msun. It is to be expected that the masses of the ensuing compact remnants correlate with the masses of their progenitor stars, and thus it is generally thought that the remnant masses should be smoothly distributed from the lightest white dwarfs to the heaviest black holes. However, this intuitive prediction is not borne out by observed data. In the rapidly growing population of remnants with observationally determined masses, a striking mass gap has emerged at the boundary between neutron stars and black holes. The heaviest neutron stars reach a maximum of two solar masses, while the lightest black holes are at least five solar masses. Over a decade after the discovery, the gap has become a significant challenge to our understanding of compact object formation. We offer new insights into the physical processes that bifurcate the formation of remnants into lower mass neutron stars and heavier black holes. Combining the results of stellar modeling with hydrodynamic simulations of supernovae, we both explain the existence of the gap, and also put stringent constraints on the inner workings of the supernova explosion mechanism. In particular, we show that core-collapse supernovae are launched within 100-200 milliseconds of the initial stellar collapse, implying that the explosions are driven by instabilities with a rapid (10-20 ms) growth time. Alternatively, if future observations fill in the gap, this will be an indication that these instabilities develop over a longer (>200 milliseconds) timescale.

Abstract:
Periodically, research articles emerge arguing the economic benefits of peritoneal dialysis, or PD, over the traditional in-center hemo dialysis for patients suffering from End Stage Renal Disease. Resulting conclusions indentify PD as the ideal therapy to reduce Medicare expenditures for this expensive treatment. However, despite this possible economic benefit to the United States taxpayer, the number of PD patients remains relatively flat with an increasing amount of patients being prescribed in-center hemo dialysis. A simplistic view of controlling the rising costs, on a per treatment basis, associated with the treatment of this disease would be to increase the number of patients from in-center hemo dialysis to peritoneal dialysis. This paper will argue why this shift is both unlikely and unrealistic, and why the resulting potential cost savings to this segment of the Medicare program is a myth.

Abstract:
We study the commutative algebras $Z_{JK}$ appearing in the Brown-Goodearl conjecture, and show that if $A$ is the single parameter quantized coordinate ring of $M_{m,n}$, $GL_n$ or $SL_n$, then these algebras can always be constructed in terms of centres of localizations. The main purpose of the algebras $Z_{JK}$ is to study the structure of the topological space $spec(A)$, which remains unknown for all but a few low-dimensional examples. We explicitly construct the required Ore sets using several different techniques: restricted permutations, Grassmann necklaces, and a graphical method which allows us to read off generating sets for the Ore sets directly from the Cauchon diagrams. By showing that all of these techniques agree with each other, we obtain as a corollary a simple formula for the Grassmann necklace associated to a cell of totally nonnegative real $m\times n$ matrices.

Abstract:
A bijection $\psi$ is defined between the prime spectrum of quantum $SL_3$ and the Poisson prime spectrum of $SL_3$, and we verify that $\psi$ and $\psi^{-1}$ both preserve inclusions of primes, i.e. that $\psi$ is in fact a homeomorphism between these two spaces. This is accomplished by developing a Poisson analogue of Brown and Goodearl's framework for describing the Zariski topology of spectra of quantum algebras, and then verifying directly that in the case of $SL_3$ these give rise to identical pictures on both the quantum and Poisson sides. As part of this analysis, we study the Poisson primitive spectrum of $\mathcal{O}(SL_3)$ and obtain explicit generating sets for all of the Poisson primitive ideals.

Abstract:
We prove that the fixed ring of the $q$-division ring $k_q(x,y)$ under any finite group of monomial automorphisms is isomorphic to $k_q(x,y)$ for the same $q$. In a similar manner, we also show that this phenomenon extends to an automorphism that is defined only on $k_q(x,y)$ and does not restrict to $k_q[x^{\pm1},y^{\pm1}]$. We then use these results to answer several questions posed by Artamonov and Cohn about the endomorphisms and automorphisms of $k_q(x,y)$.

Abstract:
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative algebras (upon which a Poisson structure is induced) using existing results for the non-commutative ones. We consider two main cases: firstly, the division ring of fractions of the quantum plane, which we view as a deformation of the commutative field of rational functions in two variables with respect to the bracket $\{x,y\} = xy$, and secondly, quantum matrices and their semi-classical limits. In particular, we use the theory of $H$-stratification to study the Poisson-prime and Poisson-primitive ideals of $\mathcal{O}(GL_3)$ and $\mathcal{O}(SL_3)$, and compare this to the corresponding results for quantum matrices.