Separation of variables in quasi-potential systems of bi-cofactor form

We perform variable separation in the quasi-potential systems of equations of the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$ and $\tilde{A}$ are Killing tensors, by embedding these systems into a bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis coordinates on the symplectic leaves of one of the Hamiltonian structures of the system. We also present examples of the corresponding separation coordinates in two and three dimensions.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge

Exploring the impact of participative place-based community archaeology in rural Europe: Community archaeology in rural environments meeting societal challenges

This paper reviews the aims, context, approach and early outcomes of a new transnational participative archaeology project focussed on rural village communities. ‘Community Archaeology in Rural Environments Meeting Societal Challenges’ (CARE-MSoC) includes three European countries where participative community archaeology is new- the Czech Republic, the Netherlands and Poland. CARE-MSoC aims to explore the feasibility, value and impact of excavation by rural residents within their home communities by using a method which can be deployed anywhere and which in the UK has been shown to advance knowledge of the past while also delivering a wide range of social and heritage benefits: multiple test pit excavation within inhabited villages. Data presented here from the Czech Republic, the Netherlands and Poland show the activity to be popular and effective here in benefitting people while also attracting, sustaining and growing local interest in heritage participation in all three countries

Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization

We present modeling of the incompressible viscous flows in the domain containing an unconfined fluid and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface condition was undertaken by J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we justify rigorously the pressure jump condition using the corresponding boundary layer

2-Sulfonylpyrimidines as Privileged Warheads for the Development of S. aureus Sortase A Inhibitors

Staphylococcus aureus is one of the most frequent causes of nosocomial and community-acquired infections, with emerging multiresistant isolates causing a significant burden to public health systems. We identified 2-sulfonylpyrimidines as a new class of potent inhibitors against S. aureus sortase A acting by covalent modification of the active site cysteine 184. Series of derivatives were synthesized to derive structure-activity relationship (SAR) with the most potent compounds displaying low micromolar K(I) values. Studies on the inhibition selectivity of homologous cysteine proteases showed that 2-sulfonylpyrimidines reacted efficiently with protonated cysteine residues as found in sortase A, though surprisingly, no reaction occurred with the more nucleophilic cysteine residue from imidazolinium-thiolate dyads of cathepsin-like proteases. By means of enzymatic and chemical kinetics as well as quantum chemical calculations, it could be rationalized that the S ( N )Ar reaction between protonated cysteine residues and 2-sulfonylpyrimidines proceeds in a concerted fashion, and the mechanism involves a ternary transition state with a conjugated base. Molecular docking and enzyme inhibition at variable pH values allowed us to hypothesize that in sortase A this base is represented by the catalytic histidine 120, which could be substantiated by QM model calculation with 4-methylimidazole as histidine analog

Integrating glycolysis, citric acid cycle, pentose phosphate pathway, and fatty acid beta‑oxidation into a single computational model

The metabolic network of a living cell is highly intricate and involves complex interactions between various pathways. In this study, we propose a computational model that integrates glycolysis, the pentose phosphate pathway (PPP), the fatty acids beta-oxidation, and the tricarboxylic acid cycle (TCA cycle) using queueing theory. The model utilizes literature data on metabolite concentrations and enzyme kinetic constants to calculate the probabilities of individual reactions occurring on a microscopic scale, which can be viewed as the reaction rates on a macroscopic scale. However, it should be noted that the model has some limitations, including not accounting for all the reactions in which the metabolites are involved. Therefore, a genetic algorithm (GA) was used to estimate the impact of these external processes. Despite these limitations, our model achieved high accuracy and stability, providing real-time observation of changes in metabolite concentrations. This type of model can help in better understanding the mechanisms of biochemical reactions in cells, which can ultimately contribute to the prevention and treatment of aging, cancer, metabolic diseases, and neurodegenerative disorders