On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Coarsening of intermetallic or compound precipitates in binary systems

A special form of equation r̄ -r̄ = 8x (∞)DσV /9RT 1-x (∞)/(x (∞)-x (∞)) t or equation r̄ -r̄ = 8DσV /9 G (x (∞)-x (∞)) t was presented for the coarsening of stoichiometric compound precipitates in a binary system. The modification is based on the facts that the Gibbs-Thomson equation for a compound precipitate and the mass balance equation for the growth of a compound precipitate are somewhat different from those for a solid-solution precipitates

Identifying the parametric occurrence of multiple steady states for some biological networks

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic and numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality / inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine semi-algebraic conditions for multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space. © 2019 Elsevier Lt

Novel phenanthridinone inhibitors of poly(adenosine 5'-diphosphate-ribose) synthetase: Potent cytoprotective and antishock agents

OBJECTIVE: To synthesize novel inhibitors of the nuclear enzyme poly(adenosine 5'-diphosphate [ADP]-ribose) synthetase (PARS), also known as poly(ADP-ribose) polymerase (PARP), and to test them in in vitro models of oxidant-induced cytotoxicity and in endotoxin and splanchnic occlusion-reperfusion-induced shock. DESIGN: Randomized, prospective laboratory study. SETTING: Research laboratory. SUBJECTS: Murine macrophages, thymocytes, and endothelial cells; Balb/c mice and Wistar rats. INTERVENTIONS: Macrophages and endothelial cells were treated with peroxynitrite and bleomycin to induce PARS activation, and thymocytes were treated with peroxynitrite to induce cell necrosis. Novel PARS inhibitors were synthesized and used to reduce PARS activation and to reverse cytotoxicity. Balb/c mice were subjected to splanchnic occlusion and reperfusion and were pretreated with various doses (1-10 mg/kg intraperitoneally) of PJ34, a selected, potent, water-soluble PARS inhibitor. The passage of fluorescein isothiocyanate-conjugated dextran (4 kDa) was analyzed in everted gut ileal sacs incubated ex vivo as an index of gut permeability. Wistar rats were subjected to Escherichia coli bacterial lipopolysaccharide (40 mg/kg intraperitoneally). PJ34 was also used at 10 mg/kg intraperitoneally, 1 hr before lipopolysaccharide or at 25 mg/kg intraperitoneally 1 hr after lipopolysaccharide treatment. Serum concentrations of indicators or multiple organ injury, concentrations of various proinflammatory mediators, and tissue concentrations of myeloperoxidase and malondialdehyde were measured. In addition, survival rates and vascular contractile and relaxant responses were recorded. MEASUREMENTS AND MAIN RESULTS: Appropriate modifications of the phenanthridinone core structure yielded significant increases in the potency of the compounds, both as PARS inhibitors and as cytoprotective agents. The compound N-(6-oxo-5,6-dihydro-phenanthridin-2-yl) -N,N-dimethylacetamide (designated as PJ34) was one of the potent PARS inhibitors of the series, and it dose-dependently protected against thymocyte necrosis, with a half-maximal restoration of cell viability of 35 nM and complete protection at 200 nM. PARS activation also was visualized by immunohistochemistry and was dose-dependently suppressed by PJ34. The effect of PJ34 was dose-dependently reversed by excess nicotinamide adenine dinucleotide (oxidized). The PARS inhibitors dose-dependently suppressed proinflammatory cytokine and chemokine production and restored viability in immunostimulated macrophages. PJ34 was selected for the subsequent in vivo studies. PJ34 significantly protected against splanchnic reperfusion-induced intestinal hyperpermeability in the mouse. PJ34 reduced peak plasma concentrations of tumor necrosis factor-alpha, interleukin-1beta, and nitrite/nitrate in the plasma of lipopolysaccharide-treated rats. PJ34 ameliorated the lipopolysaccharide-induced increases in indexes of liver and kidney failure and concentrations of myeloperoxidase and malondialdehyde in the lung and gut. Lipopolysaccharide elicited vascular dysfunction, which was normalized by PJ34. Lipopolysaccharide-induced mortality was reduced by PJ34 (both pre- and posttreatment). CONCLUSIONS: The novel series of phenanthridinone PARS inhibitors have potent cytoprotective effects in vitro and significant protective effects in shock and reperfusion injury in rodent models in vivo