Aggregative movement and front propagation for bi-stable population models

Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation

Diffusion-aggregation processes with mono-stable reaction terms

This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $v \in[0,1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $v$ at time $\tau$ and position $x$. The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both

Heteroclinic Orbits in Plane Dynamical Systems

We consider general second order boundary value problems on the whole line of the type u''=h(t, u, u'), u(-∞)=0, u(+∞)=1, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the (u, u') plane dynamical system

Existence and multiplicity of heteroclinic solutions for non-autonomous boundary eigenvalue problem

In this paper we investigate the boundary eigenvalue problem x''-b(c,t,x)x'+g(t,x)=0, x(-∞)=0, x(+∞)=1 depending on the real parameter c. We take the function b continuous and positive and assume that g is bounded and becomes active and positive only when it exceeds a threshold value theta in (0,1). At the point theta we allow g to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when b=c+h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included

Continuous dependence in front propagation of convective reaction-diffusion equations

Continuous dependence of the threshold wave speed and of thetravelling wave profiles for reaction-diffusion-convection equationsis here studied with respect to the diffusion, reaction and convection terms

XANES Study of Structural Disorder in Amorphous Silicon

An investigation of the structure of several amorphous silicon (a-Si) films is presented. Samples were prepared by using the ion beam sputtering technique at different substrate deposition temperatures. X-ray absorption spectroscopy and multiple scattering formalism have been used to detect structural variations of the a-Si films. The analysis of the XANES (X-ray absorption near-edge structure) spectra shows that increasing the substrate deposition temperature leads to a structural change toward a higher-level short-range order.

The androgen receptor and signal-transduction pathways in hormone-refractory prostate cancer. Part 1: modifications to the androgen receptor

Prostate cancer is the second most common male malignancy in the western world an increasing incidence in an ageing population. Treatment of advanced prostate cancer relies on androgen deprivation. Although the majority of patients initially respond favourably to androgen deprivation therapy, the mean time to relapse is 12-18 months. Currently there are few treatments available for men who have developed resistance to hormone therapy, due to the lack of understanding of the molecular mechanisms underlying development of this disease. Recently, however, major advances have been made in understanding both androgen receptor (AR) dependent and independent pathways which promote development of hormone resistant prostate cancer. This review will focus on modifications to the AR and associated pathways. Molecular modifications to the androgen receptor itself, e.g. mutations and/or amplification, although involved in the development of hormone resistance cannot explain all cases. Phosphorylation of AR, via either Ras/MAP kinase or PI3K/Akt signal transduction pathways, have been shown to activate AR in both a ligand (androgen) dependent and independent fashion. During this review we will discuss the clinical evidence to support AR dependent pathways as mediators of hormone resistance

Train vs. play: Evaluating the effects of gamified and non-gamified wheelchair skills training using virtual reality

This study compares the influence of a gamified and a non-gamified virtual reality (VR) environment on wheelchair skills training. In specific, the study explores the integration of gamification elements and their influence on wheelchair driving performance in VR-based training. Twenty-two non-disabled participants volunteered for the study, of whom eleven undertook the gamified VR training, and eleven engaged in the non-gamified VR training. To measure the efficacy of the VR-based wheelchair skills training, we captured the heart rate (HR), number of joystick movements, completion time, and number of collisions. In addition, an adapted version of the Wheelchair Skills Training Program Questionnaire (WSTP-Q), the Igroup Presence Questionnaire (IPQ), and the Simulator Sickness Questionnaire (SSQ) questionnaires were administered after the VR training. The results showed no differences in wheelchair driving performance, the level of involvement, or the ratings of presence between the two environments. In contrast, the perceived cybersickness was statistically higher for the group of participants who trained in the non-gamified VR environment. Remarkably, heightened cybersickness symptoms aligned with increased HR, suggesting physiological connections. As such, while direct gamification effects on the efficacy of VR-based wheelchair skills training were not statistically significant, its potential to amplify user engagement and reduce cybersickness is evident

Lorenz integrable system moves \`a la Poinsot

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.Comment: 14 pages, 6 figure

First Ex Vivo Animal Study of a Biological Heart Valve Prosthesis Sensorized with Intravalvular Impedance

IntraValvular Impedance (IVI) sensing is an innovative concept for monitoring heart valve prostheses after implant. We recently demonstrated IVI sensing feasible in vitro for biological heart valves (BHVs). In this study, for the first time, we investigate ex vivo the IVI sensing applied to a BHV when it is surrounded by biological tissue, similar to a real implant condition. A commercial model of BHV was sensorized with three miniaturized electrodes embedded in the commissures of the valve leaflets and connected to an external impedance measurement unit. To perform ex vivo animal tests, the sensorized BHV was implanted in the aortic position of an explanted porcine heart, which was connected to a cardiac BioSimulator platform. The IVI signal was recorded in different dynamic cardiac conditions reproduced with the BioSimulator, varying the cardiac cycle rate and the stroke volume. For each condition, the maximum percent variation in the IVI signal was evaluated and compared. The IVI signal was also processed to calculate its first derivative (dIVI/dt), which should reflect the rate of the valve leaflets opening/closing. The results demonstrated that the IVI signal is well detectable when the sensorized BHV is surrounded by biological tissue, maintaining the similar increasing/decreasing trend that was found during in vitro experiments. The signal can also be informative on the rate of valve opening/closing, as indicated by the changes in dIVI/dt in different dynamic cardiac conditions