Reducing rear-end crashes with cooperative systems

This paper presents an evaluation of the effectiveness of a cooperative Intelligent Transport System (C-ITS) to reduce rear-end crashes. Two complementary simulation techniques are used to demonstrate the benefits of the C-ITS. A traffic (VEINS) and sensor (SiVIC) simulations use realistic data related to traffic/road in Brisbane’s Pacific Motorway, driver’s reaction time and injury severity to evaluate benefits. The results of our simulations show that C-ITS could reduce rear-end crash risk by providing several seconds of additional warning to drivers.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Platelet endothelial cell adhesion molecule 1 (PECAM-1) and its interactions with glycosaminoglycans: 2. Biochemical analyses

Platelet endothelial cell adhesion molecule 1 (PECAM-1) (CD31), a member of the immunoglobulin (Ig) superfamily of cell adhesion molecules with six Ig-like domains, has a range of functions, notably its contributions to leukocyte extravasation during inflammation and in maintaining vascular endothelial integrity. Although PECAM-1 is known to mediate cell adhesion by homophilic binding via domain 1, a number of PECAM-1 heterophilic ligands have been proposed. Here, the possibility that heparin and heparan sulfate (HS) are ligands for PECAM-1 was reinvestigated. The extracellular domain of PECAM-1 was expressed first as a fusion protein with the Fc region of human IgG1 fused to domain 6 and second with an N-terminal Flag tag on domain 1 (Flag-PECAM-1). Both proteins bound heparin immobilized on a biosensor chip in surface plasmon resonance (SPR) binding experiments. Binding was pH-sensitive but is easily measured at slightly acidic pH. A series of PECAM-1 domain deletions, prepared in both expression systems, were tested for heparin binding. This revealed that the main heparin-binding site required both domains 2 and 3. Flag-PECAM-1 and a Flag protein containing domains 1-3 bound HS on melanoma cell surfaces, but a Flag protein containing domains 1-2 did not. Heparin oligosaccharides inhibited Flag-PECAM-1 from binding immobilized heparin, with certain structures having greater inhibitory activity than others. Molecular modeling similarly identified the junction of domains 2 and 3 as the heparin-binding site and further revealed the importance of the iduronic acid conformation for binding. PECAM-1 does bind heparin/HS but by a site that is distinct from that required for homophilic binding.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.