Investigations of potential mechanisms underlying spinal cord injury-induced polyuria.

Spinal cord injury (SCI) results in neurological impairments including motor, sensory, and autonomic dysfunction. These neurological deficits result in a litany of complications apart from muscular paralysis, including bladder, bowel, cardiovascular, and sexual function. SCI-induced polyuria (the overproduction/passage of urine) remains understudied, and therefore mechanisms behind it are largely unknown and require extensive investigation for potential targeted therapies to improve quality of life. The objective of this dissertation was to investigate potential mechanisms of SCI-induced polyuria and explore potential therapies to improve quality of life in the SCI population. Metabolic cages, Western blot, enzyme-linked immunoassay, and immunostaining were first used to determine the timing of fluctuations in biomarkers associated with SCI-induced polyuria, including arginine vasopressin (AVP), atrial natriuretic peptide (ANP), vasopressin 2 receptor (V2R), natriuretic peptide receptor A (NPRA), and epithelial sodium channel (ENaC). Next, to identify which neural substrates induce polyuria with a T9-level SCI, a higher level (T3) contusion above the local sympathetic supply to the kidneys were also examined. Lastly, the effect of anantin (NPRA antagonist) on SCI-induced polyuria was explored, in addition to utilizing an established treadmill activity-based recovery training (ABRT) program. There were significant alterations of multiple biomarkers after SCI, beginning at 7 days post injury (dpi), in addition to a lower number of AVP-labeled neurons in the hypothalamus. By 7 dpi, continuing through 6 weeks post-SCI, T3 contused rats showed a significant increase in 24-hour void volume as well as significant changes in ANP and AVP like the T9 injury. There was also a significant decrease in AVP-labelled cells in the suprachiasmatic nucleus post-T9 and T3 contusion relative to controls. A reduction in void volume was found for rats having ABRT but not anantin treatment. A significant decrease in mean arterial pressure was measured in all animal groups lasting chronically, and there was a significant increase in serum potassium at 14 dpi in addition to a significant decrease in serum sodium at the chronic time point. Together, these studies provide a detailed account of systemic responses to SCI that are associated with SCI-induced polyuria and fluid homeostasis

Modeling temporal fluctuations in avalanching systems

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh's SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, and a drift term reflecting the tendency for small avalanches to grow and large avalanches to be constricted by the finite system size. If one defines avalanching to take place when the toppling activity exceeds a certain threshold the stochastic model allows us to compute the avalanche exponents in the continum limit as functions of the Hurst exponent of the noise. The results are found to agree well with numerical simulations in the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also provides a method for computing the probability density functions of the fluctuations in the toppling activity itself. We show that the sandpiles do not belong to the class of phenomena giving rise to universal non-Gaussian probability density functions for the global activity. Moreover, we demonstrate essential differences between the fluctuations of total kinetic energy in a two-dimensional turbulence simulation and the toppling activity in sandpiles.Comment: 14 pages, 11 figure

Renormalization group theory for finite-size scaling in extreme statistics

We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Anisotropy studies with multiscale autocorrelation function

We present a novel method, based on a multiscale approach, for detecting anisotropy signatures in the arrival direction distribution of the highest energy cosmic rays. This method is catalog independent, i.e. it does not depend on the choice of a particular catalog of candidate sources, and it provides a good discrimination power even in presence of contaminating isotropic background. We present applications to simulated data sets of events corresponding to plausible scenarios for events detected, in the last decades, by world-wide surface detector-based observatories for charged particles.Comment: 8 pages, 4 figures, proceed. of conferenc

Role of disorder in the size-scaling of material strength

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.Comment: 4 pages 5 figure

Diffusion of Tagged Particle in an Exclusion Process

We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the distribution and the mean square displacement of the tagged center particle valid for rather general external force fields and initial conditions. A wide range of physical behaviors emerge which are very different than the classical single file sub-diffusion $ \sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields. For symmetric initial conditions and potential fields we find $ = {{\cal R} (1 - {\cal R})\over 2 N {\it r} ^2} $ where $2 N$ is the (large) number of particles in the system, ${\cal R}$ is a single particle reflection coefficient obtained from the single particle Green function and initial conditions, and $r$ its derivative. We show that this equation is related to the mathematical theory of order statistics and it can be used to find even when the motion between collision events is not Brownian (e.g. it might be ballistic, or anomalous diffusion). As an example we derive the Percus relation for non Gaussian diffusion

Level Density of a Bose Gas and Extreme Value Statistics

We establish a connection between the level density of a gas of non-interacting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution function for the number of excited particles follows the three universal distribution laws of extreme value statistics, namely Gumbel, Weibull and Fr\'echet. Implications of this result, as well as general properties of the level density at different energies, are discussed.Comment: 4 pages, no figure

Roughness correction to the Casimir force at short separations: Contact distance and extreme value statistics

So far there has been no reliable method to calculate the Casimir force at separations comparable to the root-mean-square of the height fluctuations of the surfaces. Statistical analysis of rough gold samples has revealed the presence of peaks considerably higher than the root-mean-square roughness. These peaks redefine the minimum separation distance between the bodies and can be described by extreme value statistics. Here we show that the contribution of the high peaks to the Casimir force can be calculated with a pairwise additive summation, while the contribution of asperities with normal height can be evaluated perturbatively. This method provides a reliable estimate of the Casimir force at short distances, and it solves the significant, so far unexplained discrepancy between measurements of the Casimir force between rough surfaces and the results of perturbation theory. Furthermore, we illustrate the importance of our results in a technologically relevant situation.Comment: 29 pages, 11 figures, to appear in Phys. Rev.

Chemical fracture and distribution of extreme values

When a corrosive solution reaches the limits of a solid sample, a chemical fracture occurs. An analytical theory for the probability of this chemical fracture is proposed and confirmed by extensive numerical experiments on a two dimensional model. This theory follows from the general probability theory of extreme events given by Gumbel. The analytic law differs from the Weibull law commonly used to describe mechanical failures for brittle materials. However a three parameters fit with the Weibull law gives good results, confirming the empirical value of this kind of analysis.Comment: 7 pages, 5 figures, to appear in Europhysics Letter

On the Role of Global Warming on the Statistics of Record-Breaking Temperatures

We theoretically study long-term trends in the statistics of record-breaking daily temperatures and validate these predictions using Monte Carlo simulations and data from the city of Philadelphia, for which 126 years of daily temperature data is available. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperatures distribution in Philadelphia, as a function of the number of elapsed years from the start of the data. We further consider the case of global warming, where the mean temperature systematically increases with time. We argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events over the time range of the observations, a conclusion that is supported by numerical simulations and the Philadelphia temperature data.Comment: 11 pages, 6 figures, 2-column revtex4 format. For submission to Journal of Climate. Revised version has some new results and some errors corrected. Reformatted for Journal of Climate. Second revision has an added reference. In the third revision one sentence that explains the simulations is reworded for clarity. New revision 10/3/06 has considerable additions and new results. Revision on 11/8/06 contains a number of minor corrections and is the version that will appear in Phys. Rev.