Probability & incompressible Navier-Stokes equations: An overview of some recent developments

This is largely an attempt to provide probabilists some orientation to an important class of non-linear partial differential equations in applied mathematics, the incompressible Navier-Stokes equations. Particular focus is given to the probabilistic framework introduced by LeJan and Sznitman [Probab. Theory Related Fields 109 (1997) 343-366] and extended by Bhattacharya et al. [Trans. Amer. Math. Soc. 355 (2003) 5003-5040; IMA Vol. Math. Appl., vol. 140, 2004, in press]. In particular this is an effort to provide some foundational facts about these equations and an overview of some recent results with an indication of some new directions for probabilistic consideration.Comment: Published at http://dx.doi.org/10.1214/154957805100000078 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Large Deviation Rate and Central Limit Theorem for Horton Ratios

Although originating in hydrology, the classical Horton analysis is based on a geometric progression that is widely used in the empirical analysis of branching patterns found in biology, atmospheric science, plant pathology, etc., and more recently in tree register allocation in computer science. The main results of this paper are a large deviation rate and a central limit theorem for Horton bifurcation ratios in a standard network model. The methods are largely self-contained. In particular, derivations of some previously known results of the theory are indicated along the way

Scaling and Multiscaling Exponents in Networks and Flows

The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchical structures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unit scale. Thus proper data analysis and inference require a mathematical framework which couples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the research in this area of applied probability over the past twenty years

Indiana Biobank and INresearch.org

poster abstractIndiana Biobank was established in July 2010 as a resource for all investigators throughout the state of Indiana. The biobank seeks to develop a statewide collection of bio specimens as a research tool to enhance translational research, to improve Hoosier health, and to promote personalized therapy. This large collection of samples is stored, catalogued, characterized and delivered to scientists to carry out translational research to improve the health of Hoosiers. INresearch.org is a secure, password-protected registry of Indiana resident volunteers who want to participate in health-related research. The goal of this registry is to match interested volunteers with researchers. The goal of INresearch.org is to improve health care by discovering new treatments and cures

Corrections for "Occupation and local times for skew Brownian motion with applications to dispersion across an interface"

We are making corrections and acknowledging colleagues that pointed out mistakes in our recent paper titled "Occupation and local times for skew Brownian motion with applications to dispersion across an interface" which was published in Annals of Applied Probability (2011) 21(1) 183-214. Specifically the corrections are: 1. The restriction of $\gamma$ to non negative values in Theorem 1.3 is not needed. But one has probabilistic interpretation only when $\gamma$ is non negative. 2. State the correct formulas in Corollary 3.3 as their were computational errors in the original formulas. We thank Pierre Etoir\'e and Miguel Martinez for pointing out these errors.Comment: Published in at http://dx.doi.org/10.1214/11-AAP775 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bitter taste preference and psychopathy: A partial replication of Sagioglou and Greitemeyer, 2016

In this study, we did a partial replication of Sagioglou and Greitemeyer’s 2016 study concerning bitter taste preferences and malevolent personality traits. Undergraduate students (n=40, mean age=19.40, 75% females) completed a laboratory component consisting of 24 samples of 8 different solutions (sucrose, sodium chloride, quinine, and citric acid with a higher and lower concentration of each) for 3 iterations, as well as PTC testing and tongue staining in order to count fungiform papillae. This was followed by a survey component that utilized HEXACO (which assesses six major domains of personality) and the IPIP-NEO scale for psychopathy (measured with the factors of “fearless dominance” and “impulsive antisociality”). While this study failed to support the link between bitter taste preference and psychopathy, there was a significant positive correlation (p\u3c.01) between psychopathy and extraversion as well as a significant negative correlation (p\u3c.01) between psychopathy and honesty-humility. Taste and personality correlates included significant negative correlation (p\u3c.05) existed between extraversion and the perceived intensity of sucrose, and also between agreeableness and perceived quinine intensity. While power and procedural issues warrant caution, the results we did achieve are promising and could have greater future applications as more studies are done to assess causal links between genetics and personality