On the Conjecture of Kochar and Korwar

In this paper, we solve for some cases a conjecture by Kochar and Korwar (1996) in relation with the normalized spacings of the order statistics related to a sample of independent exponential random variables with different scale parameter. In the case of a sample of size n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all n. We give the proof of this conjecture for n=4 and for both spacing and normalized spacings. We also generalize some results to n>

Regulation Of Hippocampal NMDA Receptor Signaling, Memory And Synaptic Plasticity By The JIP1 Scaffold Protein

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2018

Dimethyl Fumarate Alleviates Dextran Sulfate Sodium-Induced Colitis, through the Activation of Nrf2-Mediated Antioxidant and Anti-inflammatory Pathways.

Oxidative stress and chronic inflammation play critical roles in the pathogenesis of ulcerative colitis (UC) and inflammatory bowel diseases (IBD). A previous study has demonstrated that dimethyl fumarate (DMF) protects mice from dextran sulfate sodium (DSS)-induced colitis via its potential antioxidant capacity, and by inhibiting the activation of the NOD-, LRR- and pyrin domain-containing protein 3 (NLRP3) inflammasome. This study aims to clarify the nuclear factor erythroid 2-related factor 2/antioxidant responsive element (Nrf2/ARE) pathway pharmacological activation and anti-inflammatory effect by DMF, through focusing on other crucial antioxidant enzymes and inflammatory mediator, including glutamate-cysteine ligase catalytic subunit (GCLC), glutathione peroxidase (GPX) and cyclooxygenase-2 (COX-2), in a DSS-induced colitis mouse model. The oral administration of DMF attenuated the shortening of colons and alleviated colonic inflammation. Furthermore, the expression of key antioxidant enzymes, including GCLC and GPX, in the colonic tissue were significantly increased by DMF administration. In addition, protein expression of the inflammatory mediator, COX-2, was reduced by DMF administration. Our results suggest that DMF alleviates DSS-induced colonic inflammatory damage, likely via up-regulating GCLC and GPX and down-regulating COX-2 protein expression in colonic tissue

Improved Treatment of Dark Matter Capture in Neutron Stars II: Leptonic Targets

Neutron stars harbour matter under extreme conditions, providing a unique testing ground for fundamental interactions. We recently developed an improved treatment of dark matter (DM) capture in neutron stars that properly incorporates many of the important physical effects, and outlined useful analytic approximations that are valid when the scattering amplitude is independent of the centre of mass energy. We now extend that analysis to all interaction types. We also discuss the effect of going beyond the zero-temperature approximation, which provides a boost to the capture rate of low mass dark matter, and give approximations for the dark matter up-scattering rate and evaporation mass. We apply these results to scattering of dark matter from leptonic targets, for which a correct relativistic description is essential. We find that the potential neutron star sensitivity to DM-lepton scattering cross sections greatly exceeds electron-recoil experiments, particularly in the sub-GeV regime, with a sensitivity to sub-MeV DM well beyond the reach of future terrestrial experiments.Comment: 32 pages, 9 figures, 3 tables, 2 appendices. References added, matches published versio

Improved Treatment of Dark Matter Capture in Neutron Stars

Neutron stars provide a cosmic laboratory to study the nature of dark matter particles and their interactions. Dark matter can be captured by neutron stars via scattering, where kinetic energy is transferred to the star. This can have a number of observational consequences, such as the heating of old neutron stars to infra-red temperatures. Previous treatments of the capture process have employed various approximation or simplifications. We present here an improved treatment of dark matter capture, valid for a wide dark matter mass range, that correctly incorporates all relevant physical effects. These include gravitational focusing, a fully relativistic scattering treatment, Pauli blocking, neutron star opacity and multi-scattering effects. We provide general expressions that enable the exact capture rate to be calculated numerically, and derive simplified expressions that are valid for particular interaction types or mass regimes and that greatly increase the computational efficiency. Our formalism is applicable to the scattering of dark matter from any neutron star constituents, or to the capture of dark matter in other compact objects.Comment: 52 pages, 17 figures, 3 tables, 3 appendices. Discussion extended, references added, matches JCAP published versio

On stochastic properties between some ordered random variables

A great number of articles have dealt with stochastic comparisons of ordered random variables in the last decades. In particular, distributional and stochastic properties of ordinary order statistics have been studied extensively in the literature. Sequential order statistics are proposed as an extension of ordinary order statistics. Since sequential order statistics models unify various models of ordered random variables, it is interesting to study their distributional and stochastic properties. In this work, we consider the problem of comparing sequential order statistics according to magnitude and location orders