BACKWARD BIFURCATION IN NEUTROPHIL-PATHOGEN INTERACTION

Bacterial infections elicit immune responses including neutrophils, whose recruitment is stimulated by the bacteria’s presence but which die after eliminating those bacteria. This dual interaction between bacteria and neutrophil concentrations, more complicated than the simple predator-prey relationship that describes macrophage-bacteria interactions, creates an environment in which neutrophils may only be able to clear sufficiently small infections. This study describes this relationship using a simple nonlinear dynamical system which exhibits bistability behavior known as a backward bifurcation. Bacterial growth is assumed limited by a key nutrient. In contrast to a previous study which held neutrophil and nutrient levels constant and required saturation terms to produce bistability, our model shows that simple bilinear terms support bistability when nutrient and neutrophil densities are allowed to vary in response to bacterial density. An example application involving Borrelia burgdorferi, which feeds on manganese, illustrates why neutrophils’ rapid response is key to their ability to contain bacterial infections.

The analytical one-loop contributions to Higgs boson mass in the Supersymmetric Standard Model with vector-like particles

In this paper, we extend the Minimal Supersymmetric Standard Model (MSSM) with additional vector-like particles (VLPs) and compared the differences of mass spectrum and Feynman rules between the MSSM and MSSMV. We analytically calculate the one loop contributions to the Higgs boson mass from the fermions and sfermions in the on shell renormalization scheme. After discussing and numerically analyzing cases without bilinear terms and a case with a (partial) decoupling limit, we find: (i) the corrections depend on the mass splittings between quarks and squarks and between vector-like fermions and their sfermions; (ii) there exists the (partial) decoupling limit, where the VLPs decouple from the electroweak (EW) energy scale, even when one of the VLPs is light around the EW scale. The reason is that the contributions to Higgs mass can be suppressed by the (or partial) decoupling effects, which can make the EW phenomenology different from the MSSM. Moreover, we present some numerical analysis to understand these unique features.

Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment

This paper proposes an inverse structural modification method for eigenstructure assignment (EA), which allows to assign the desired mode shapes only at the parts of interest of the system. The presence of unimposed eigenvector entries leads to a nonconvex problem. Therefore, to boost the convergence to a global optimal solution, a homotopy optimization strategy is implemented based on the convex approximation of the cost function. Such a relaxation is performed through some auxiliary variables and through the McCormick's relaxation of the occurring bilinear terms. The approach handles general assignment tasks, with an arbitrary number of modification parameters and prescribed eigenpairs.