A numerical study of SSP time integration methods for hyperbolic conservation laws

he method of lines approach for solving hyperbolic conservation laws is based on the idea of splitting the discretization process in two stages. First, the spatial discretization is performed by leaving the system continuous in time. This approximation is usually developed in a non-oscillatory manner with a satisfactory spatial accuracy. The obtained semi-discrete system of ordinary differential equations (ODE) is then solved by using some standard time integration method. In the last few years, a series of papers appeared, dealing with the high order strong stability preserving (SSP) time integration methods that maintain the total variation diminishing (TVD) property of the first order forward Euler method. In this work the optimal SSP Runge--Kutta methods of different order are considered in combination with the finite volume weighted essentially non-oscillatory (WENO) discretization. Furthermore, a new semi--implicit WENO scheme is presented and its properties in combination with different optimal implicit SSP Runge--Kutta methods are studied. Analysis is made on linear and nonlinear scalar equations and on Euler equations for gas dynamics

Rapid Endosomal Recycling

Peripheral membrane proteins are endocytosed by constitutive processes of membrane invaginations, followed by internalization driven by diverse endocytic machinery available at the cell surface. It is believed that after endocytic uptake, cargo proteins proceed either through the endosomal recycling circuit of the cell or travel toward late endosomes for degradation. In this chapter, we analyzed trafficking of seven cargo molecules (transferrin receptor, fully conformed MHC-I, non-conformed MHC-I, cholera-toxin B subunit, CD44, ICAM1, and G-protein-coupled receptor Rae-1) known to use the distinct endocytic route. For that purpose, we developed the software for multicompartment analysis of intracellular trafficking. We demonstrate that all endocytosed molecules are rapidly recycled and propose that the rapid recycling is a constitutive process that should be considered in the analysis of intracellular trafficking of peripheral membrane proteins

Late Endosomal Recycling of Open MHC-I Conformers

With an increasing number of endosomal cargo molecules studied, it is becoming clear that endocytic routes are diverse, and the cell uses more pathways to adjust expression of cell surface proteins. Intracellular itinerary of integral membrane proteins that avoid the early endosomal recycling route is not enough studied. Therefore, we studied endocytic trafficking of empty Ld (eLd ) molecules, an open form of murine MHC-I allele, in fibroblast-like cells. Pulse labeling of cell surface eLd with mAbs and internalization kinetics suggest two steps of endosomal recycling: rapid and late. The same kinetics was also observed for human open MHC-I conformers. Kinetic modeling, using in-house developed software for multicompartment analysis, colocalization studies and established protocols for enriched labeling of the late endosomal (LE) pool of eLd demonstrated that the late step of recycling occurs from an LE compartment. Although the majority of eLd distributed into pre-degradative multivesicular bodies (MVBs), these LE subsets were not a source for eLd recycling. The LE recycling of eLd did not require Rab7 membrane domains, as demonstrated by Rab7-silencing, but required vectorial LE motility, suggesting that LE recycling occurs from dynamic tubulovesicular LE domains prior segregation of eLd in MVBs. Thus, our study indicates that LE system should not be simply considered as a feeder for loading of the degradative tract of the cell but also as a feeder for loading of the plasma membrane and thereby contribute to the maintenance of homeostasis of plasma membrane proteins

Temporal variations analyses and predictive modeling of microbiological seawater quality

Bathing water quality is a major public health issue, especially for tourism-oriented regions. Currently used methods within EU allow at least a 2.2 day period for obtaining the analytical results, making outdated the information forwarded to the public. Obtained results and beach assessment are influenced by the temporal and spatial characteristics of sample collection, and numerous environmental parameters, as well as by differences of official water standards. This paper examines the temporal variation of microbiological parameters during the day, as well as the influence of the sampling hour, on decision processes in the management of the beach. Apart from the fecal indicators stipulated by the EU Bathing Water Directive (E. coli and enterococci), additional fecal (C. perfringens) and non-fecal (S. aureus and P. aeriginosa) parameters were analyzed. Moreover, the effects of applying different evaluation criteria (national, EU and U.S. EPA) to beach ranking were studied, and the most common reasons for exceeding water-quality standards were investigated. In order to upgrade routine monitoring, a predictive statistical model was developed. The highest concentrations of fecal indicators were recorded early in the morning (6 AM) due to the lack of solar radiation during the night period. When compared to enterococci, E. coli criteria appears to be more stringent for the detection of fecal pollution. In comparison to EU and U.S. EPA criteria, Croatian national evaluation criteria provide stricter public health standards. Solar radiation and precipitation were the predominant environmental parameters affecting beach water quality, and these parameters were included in the predictive model setup. Predictive models revealed great potential for the monitoring of recreational water bodies, and with further development can become a useful tool for the improvement of public health protection

A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases

Abstract Future state prediction for nonlinear dynamical systems is a challenging task. Classical prediction theory is based on a, typically long, sequence of prior observations and is rooted in assumptions on statistical stationarity of the underlying stochastic process. These algorithms have trouble predicting chaotic dynamics, “Black Swans” (events which have never previously been seen in the observed data), or systems where the underlying driving process fundamentally changes. In this paper we develop (1) a global and local prediction algorithm that can handle these types of systems, (2) a method of switching between local and global prediction, and (3) a retouching method that tracks what predictions would have been if the underlying dynamics had not changed and uses these predictions when the underlying process reverts back to the original dynamics. The methodology is rooted in Koopman operator theory from dynamical systems. An advantage is that it is model-free, purely data-driven and adapts organically to changes in the system. While we showcase the algorithms on predicting the number of infected cases for COVID-19 and influenza cases, we emphasize that this is a general prediction methodology that has applications far outside of epidemiology