Differences Between an Aerobic and Yoga Group Exercise on Measures of Mood, Stress, and Group Cohesion

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Spectra of sparse non-Hermitian random matrices: an analytical solution

We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends upon the degree of symmetry of the edges in a non-monotonous way.Comment: 5 pages, 5 figures, 12 pages supplemental materia

Balanced growth for solutions of nonautonomous partial differential equations

We show balanced growth for solutions of some nonautonomous partial differential equations which in certain cases also describe the dynamics of structured populations

Fisher Waves and Front Roughening in a Two-Species Invasion Model with Preemptive Competition

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of non-equilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of ${\cal O}(t^{-2/3})$.Comment: 8 pages, 5 figures; Papers on related work can be found at http://www.rpi.edu/~korniss/Researc

On the net reproduction rate of continuous structured populations with distributed states at birth

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

Therapeutic efficacy of microtube-embedded chondroitinase ABC in a canine clinical model of spinal cord injury

Many hundreds of thousands of people around the world are living with the long-term consequences of spinal cord injury and they need effective new therapies. Laboratory research in experimental animals has identified a large number of potentially translatable interventions but transition to the clinic is not straightforward. Further evidence of efficacy in more clinically-relevant lesions is required to gain sufficient confidence to commence human clinical trials. Of the many therapeutic candidates currently available, intraspinally applied chondroitinase ABC has particularly well documented efficacy in experimental animals. In this study we measured the effects of this intervention in a double-blinded randomized controlled trial in a cohort of dogs with naturally-occurring severe chronic spinal cord injuries that model the condition in humans. First, we collected baseline data on a series of outcomes: forelimb-hindlimb coordination (the prespecified primary outcome measure), skin sensitivity along the back, somatosensory evoked and transcranial magnetic motor evoked potentials and cystometry in 60 dogs with thoracolumbar lesions. Dogs were then randomized 1:1 to receive intraspinal injections of heat-stabilized, lipid microtube-embedded chondroitinase ABC or sham injections consisting of needle puncture of the skin. Outcome data were measured at 1, 3 and 6 months after intervention; skin sensitivity was also measured 24 h after injection (or sham). Forelimb-hindlimb coordination was affected by neither time nor chondroitinase treatment alone but there was a significant interaction between these variables such that coordination between forelimb and hindlimb stepping improved during the 6-month follow-up period in the chondroitinase-treated animals by a mean of 23%, but did not change in controls. Three dogs (10%) in the chondroitinase group also recovered the ability to ambulate without assistance. Sensitivity of the dorsal skin increased at 24 h after intervention in both groups but subsequently decreased to normal levels. Cystometry identified a non-significant improvement of bladder compliance at 1 month in the chondroitinase-injected dogs but this did not persist. There were no overall differences between groups in detection of sensory evoked potentials. Our results strongly support a beneficial effect of intraspinal injection of chondroitinase ABC on spinal cord function in this highly clinically-relevant model of chronic severe spinal cord injury. There was no evidence of long-term adverse effects associated with this intervention. We therefore conclude that this study provides strong evidence in support of initiation of clinical trials of chondroitinase ABC in humans with chronic spinal cord injury