Reverse Khas'minskii condition

The aim of this paper is to present and discuss some equivalent characterizations of p-parabolicity in terms of existence of special exhaustion functions. In particular, Khas'minskii in [K] proved that if there exists a 2-superharmonic function k defined outside a compact set such that $\lim_{x\to \infty} k(x)=\infty$, then R is 2-parabolic, and Sario and Nakai in [SN] were able to improve this result by showing that R is 2-parabolic if and only if there exists an Evans potential, i.e. a 2-harmonic function $E:R\setminus K \to \R^+$ with \lim_{x\to \infty} \E(x)=\infty. In this paper, we will prove a reverse Khas'minskii condition valid for any p>1 and discuss the existence of Evans potentials in the nonlinear case.Comment: final version of the article available at http://www.springer.co

Modeling the ballistic-to-diffusive transition in nematode motility reveals variation in exploratory behavior across species

A quantitative understanding of organism-level behavior requires predictive models that can capture the richness of behavioral phenotypes, yet are simple enough to connect with underlying mechanistic processes. Here we investigate the motile behavior of nematodes at the level of their translational motion on surfaces driven by undulatory propulsion. We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain $C. elegans$ N2 as well as wild strains and distant species. We focus on trajectory dynamics over timescales spanning the transition from ballistic (straight) to diffusive (random) movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed, bearing and reversal events. We show that the model parameters vary among species in a correlated, low-dimensional manner suggestive of a common mode of behavioral control and a trade-off between exploration and exploitation. The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these nematode lineages employ contrasting ``bet-hedging'' strategies for foraging.Comment: 46 pages, 18 figures, 6 table

A Fascinating Polynomial Sequence arising from an Electrostatics Problem on the Sphere

A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a negatively charged spherical cap to appear. The determination of the smallest distance $\rho(d)$ ($d$ is the dimension of the unit sphere) from the point charge to the sphere where still all of the sphere is positively charged is known as Gonchar's problem. Using classical potential theory for the harmonic case, we show that $1+\rho(d)$ is equal to the largest positive zero of a certain sequence of monic polynomials of degree $2d-1$ with integer coefficients which we call Gonchar polynomials. Rather surprisingly, $\rho(2)$ is the Golden ratio and $\rho(4)$ the lesser known Plastic number. But Gonchar polynomials have other interesting properties. We discuss their factorizations, investigate their zeros and present some challenging conjectures.Comment: 12 pages, 6 figures, 1 tabl

Response of selected microorganisms to experimental planetary environments

The anaerobic utilization of phosphite or phosphine and the significance of this conversion to potential contamination of Jupiter were investigated. A sporeforming organism was isolated from Cape Canaveral soil which anaerobically converts hypophosphite to phosphate. This conversion coincides with an increase in turbidity of the culture and with phosphate accumulation in the medium. Investigations of omnitherms (organisms which grow over a broad temperature range, i.e. 3 -55 C were also conducted. The cellular morphology of 28 of these isolates was investigated, and all were demonstrated to be sporeformers. Biochemical characterizations are also presented. Procedures for replicate plating were evaluated, and those results are also presented. The procedures for different replicate-plating techniques are presented, and these are evaluated on the basis of reproducibility, percentage of viable transfer, and ease of use. Standardized procedures for the enumeration of microbial populations from ocean-dredge samples from Cape Canaveral are also presented

Adequate Levels of Adherence with Controller Medication Is Associated with Increased Use of Rescue Medication in Asthmatic Children

Peer reviewedPublisher PD

Brain tissue properties differentiate between motor and limbic basal ganglia circuits

Despite advances in understanding basic organizational principles of the human basal ganglia, accurate in vivo assessment of their anatomical properties is essential to improve early diagnosis in disorders with corticosubcortical pathology and optimize target planning in deep brain stimulation. Main goal of this study was the detailed topological characterization of limbic, associative, and motor subdivisions of the subthalamic nucleus (STN) in relation to corresponding corticosubcortical circuits. To this aim, we used magnetic resonance imaging and investigated independently anatomical connectivity via white matter tracts next to brain tissue properties. On the basis of probabilistic diffusion tractography we identified STN subregions with predominantly motor, associative, and limbic connectivity. We then computed for each of the nonoverlapping STN subregions the covariance between local brain tissue properties and the rest of the brain using high-resolution maps of magnetization transfer (MT) saturation and longitudinal (R1) and transverse relaxation rate (R2*). The demonstrated spatial distribution pattern of covariance between brain tissue properties linked to myelin (R1 and MT) and iron (R2*) content clearly segregates between motor and limbic basal ganglia circuits. We interpret the demonstrated covariance pattern as evidence for shared tissue properties within a functional circuit, which is closely linked to its function. Our findings open new possibilities for investigation of changes in the established covariance pattern aiming at accurate diagnosis of basal ganglia disorders and prediction of treatment outcom

Current research into brain barriers and the delivery of therapeutics for neurological diseases: a report on CNS barrier congress London, UK, 2017.

This is a report on the CNS barrier congress held in London, UK, March 22-23rd 2017 and sponsored by Kisaco Research Ltd. The two 1-day sessions were chaired by John Greenwood and Margareta Hammarlund-Udenaes, respectively, and each session ended with a discussion led by the chair. Speakers consisted of invited academic researchers studying the brain barriers in relation to neurological diseases and industry researchers studying new methods to deliver therapeutics to treat neurological diseases. We include here brief reports from the speakers

New tissue priors for improved automated classification of subcortical brain structures on MRI.

Despite the constant improvement of algorithms for automated brain tissue classification, the accurate delineation of subcortical structures using magnetic resonance images (MRI) data remains challenging. The main difficulties arise from the low gray-white matter contrast of iron rich areas in T1-weighted (T1w) MRI data and from the lack of adequate priors for basal ganglia and thalamus. The most recent attempts to obtain such priors were based on cohorts with limited size that included subjects in a narrow age range, failing to account for age-related gray-white matter contrast changes. Aiming to improve the anatomical plausibility of automated brain tissue classification from T1w data, we have created new tissue probability maps for subcortical gray matter regions. Supported by atlas-derived spatial information, raters manually labeled subcortical structures in a cohort of healthy subjects using magnetization transfer saturation and R2* MRI maps, which feature optimal gray-white matter contrast in these areas. After assessment of inter-rater variability, the new tissue priors were tested on T1w data within the framework of voxel-based morphometry. The automated detection of gray matter in subcortical areas with our new probability maps was more anatomically plausible compared to the one derived with currently available priors. We provide evidence that the improved delineation compensates age-related bias in the segmentation of iron rich subcortical regions. The new tissue priors, allowing robust detection of basal ganglia and thalamus, have the potential to enhance the sensitivity of voxel-based morphometry in both healthy and diseased brains