Approximation to the mean curve in the LCS problem

The problem of sequence comparison via optimal alignments occurs naturally in many areas of applications. The simplest such technique is based on evaluating a score given by the length of a longest common subsequence divided by the average length of the original sequences. In this paper we investigate the expected value of this score when the input sequences are random and their length tends to infinity. The corresponding limit exists but is not known precisely. We derive a theoretical large deviation, convex analysis and Monte Carlo based method to compute a consistent sequence of upper bounds on the unknown limit. An empirical practical version of our method produces promising numerical results.     

Pulse vaccination delayed SEIRS epidemic model with saturation incidence

A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using the discrete dynamical system determined by the stroboscopic map, we obtain the existence of the disease-free periodic solution and its exact expression. Further, using the comparison theorem, we establish the sufficient conditions of global attractivity of the disease-free periodic solution and the permanence of disease. Our results indicate that a long latent period of the disease or a proper pulse vaccination rate will lead to eradication of the disease.     

An integro-differential equation model for alignment and orientational aggregation

We study an integro-differential equation modeling angular alignment of interacting bundles of cells or filaments. A bifurcation analysis of the related stationary problem was done by Geigant and Stoll in [E. Geigant, M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol. 46 (6) (2003) 537-563]. Here we analyze the time-dependent problem and prove that the type of alignment (one- or multi-directional) depends on the initial distribution, the interaction potential, and the preferred optimal orientation of the bundles of cells or filaments. Our main technical tool is the analysis of the evolution of suitable functionals for the cell density, which allows to also specify the direction(s) where the final alignment takes place.     

Optimal Control for the Degenerate Elliptic Logistic Equation

We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results.     

Competition Between Radial Expansion and Thickening in the Enlargement of an Intracranial Saccular Aneurysm

Rupture of intracranial saccular aneurysms is the leading cause of spontaneous subarachnoid hemorrhage, which results in significant morbidity and mortality. Although many have suggested that saccular aneurysms enlarge and rupture due to mechanical instabilities, our recent nonlinear analyses suggest that at least certain classes of aneurysms do not exhibit a quasi-static limit point instability or dynamic instabilities in response to periodic loading. Based on an increased understanding of the ubiquitous role of growth and remodeling within the vasculature and recent histopathological data on saccular aneurysms, it is hypothesized that a stress-mediated regulation of collagen turnover causes their enlargement. There is a need, however, for a theoretical framework to explore this and competing hypotheses. In this paper, we present a 2-D constrained mixture model for growth and remodeling of an ellipsoidally shaped saccular aneurysm and numerically simulate enlargement and changes in material symmetry in the aneurysmal wall. Results suggest that ellipsoidal aneurysms tend toward spherical shapes, and a competition between radial expansion and wall thickening plays a critical role in determining the stability of an enlarging lesion.     

Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions

In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it has been noticed in previous works, there is a phase transition in the behavior of the process. Here, we examine the strongly and intermediately supercritical regimes The main result is a conditional limit theorem for the rescaled associated random walk in the intermediately case.     

On some free boundary problems of the prey–predator model

In this paper we investigate some free boundary problems for the Lotka–Volterra type prey–predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading via a free boundary. We prove a spreading–vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey–predator model on the whole real line without a free boundary.     

A BARRIER BOUNDARY VALUE PROBLEM FOR PARABOLIC AND ELLIPTIC EQUATIONS

Barrier type boundary conditions are modeled for describing the substance diffusion in a medium when obstacles in the medium are considered. The existence of solutions of parabolic and elliptic differential equations with barrier boundary condition is presented in this paper.