Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs

Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Gal\'{a}n recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion channel models, such as the Hodgkin-Huxley or other conductance based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Gal\'{a}n's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.Comment: Added one reference, typos corrected in Equation 6 and Appendix C, added the assumption that the graph is irreducible to the main theorem (results unchanged

One-Pot Synthesis of Single-Source Precursors for Nanocrystalline LED Phosphors M2Si5N8:Eu2+ (M = Sr, Ba)

Highly efficient red-emitting nitridosilicate phosphors Sr2Si5N8:Eu2+ and Ba1.5Sr0.5Si5N8:Eu2+ (doping level 1%) applicable to phosphor converted pc-LEDs were synthesized in nanocrystalline form at low temperatures employing a novel single-source precursor approach. Synthesis starts from nanocrystalline silicon and uses mixed metal amides M(NH2)2 with M = Sr, Ba, Eu as reactive intermediates. In a second approach, a single-source precursor mixture obtained from a one-pot reaction of the corresponding elements (Sr/Ba, Eu, Si) was obtained in supercritical ammonia. Thermoanalytical in situ investigations gain a deeper insight into the degradation mechanism of the mixed metal amide precursors and revealed the onset for the formation of the 2-5-8 phosphor materials at temperatures slightly above 900°C. Formation of the products is complete below 1400°C. Under these conditions, the nitridosilicate phosphors form spherically shaped particles with crystallites of 200 nm in size. Spherical particles are desirable for phosphor application because light extraction may be improved by decreased light trapping and re-absorption losses. As a major advantage of the one-pot precursor approach, the exact Sr/Ba content in the solid solution series Sr2−xBaxSi2N8:Eu2+ and the doping concentration of Eu2+ can easily be controlled in a wide range by the relative amount of the elemental starting materials (Sr, Ba, Eu, Si). Simultaneously, thorough mixing of these elements down to an atomic level (Sr, Ba, Eu) or at least at nanoscopic dimensions (silicon) is achieved by the solution approach. As a consequence, no milling and pre-reaction steps are necessary which might give rise to contamination. Advantageously, this approach can easily be extended to large-scale processes by simultaneously preserving complete mixing. Furthermore, the influence of the starting materials (single-source precursor, nanocrystalline silicon) and the reaction conditions on the crystal shape and finally on the luminescence properties of the products was investigated. The obtained nanophosphors exhibit luminescence properties comparable to coarsely crystalline nitridosilicate phosphor powders prepared by conventional high-temperature processing

Synthesis and Characterization of Tb[N(CN)2]3·2H2O and Eu[N(CN)2]3·2H2O:

Two new rare-earth dicyanamides, namely, Tb[N(CN)2]3·2H2O and Eu[N(CN)2]3·2H2O, have been prepared by ion exchange in aqueous solution, followed by evaporation of the solvent at room temperature. The structures of both compounds have been solved and refined from single-crystal and powder X-ray diffraction data, respectively. The two compounds are isostructural and are built up from irregular quadratic antiprismatic LnN6O2 polyhedra connected to each other by three crystallographically independent dicyanamide ([N(CN)2]3-) ions (Tb[N(CN)2]3·2H2O, P21/n, Z = 4, a = 7.4632(15) Å, b = 11.523(2) Å, c = 13.944(3) Å, β = 94.06(3)°, V = 1196.2(4) Å3; Eu[N(CN)2]3·2H2O, P21/n, Z = 4, a = 7.4780(3) Å, b = 11.5429(5) Å, c = 13.9756(7) Å, β = 93.998(4)°, V = 1203.41(10) Å3). Annealing of the hydrated phases of Ln[N(CN)2]3·2H2O (Ln = Eu, Tb) at 150 °C under an argon atmosphere leads to the formation of nonhydrated Ln[N(CN)2]3 (Ln = Eu, Tb). Both the hydrated (Eu[N(CN)2]3·2H2O) and nonhydrated (Eu[N(CN)2]3) europium(III) dicyanamides show red luminescence due to the dominant intensity of 5D0−7FJ (J = 1, 2, 4) emission lines by excitation at 365 nm. The broad excitation band of europium(III) dicyanamide (fwhm = 8000 cm-1) ranging between 260 and 420 nm with λmax ≈ 30000 cm-1 is ascribed to a Eu−N charge-transfer transition, which is significantly shifted to lower energy compared to that of oxo compounds due to the nephalauxetic effect. Similarly, both the hydrated (Tb[N(CN)2]3·2H2O) and nonhydrated (Tb[N(CN)2]3) terbium(III) dicyanamides show green emission at λexc = 365 nm, arising mainly from the dominant 5D0−7F4 transition. However, unlike europium(III) dicyanamide, the broad excitation band of terbium(III) dicyanamide ranging between 250 and 400 nm with a maximum at 33000 cm-1 can be assigned to the 4f8−4f75d1 transition of Tb3+

Structure of the ATP-Synthase from Chloroplasts and Mitochondria Studied by Electron Microscopy

The structure of the ATP-synthase, F0F1 , from spinach chloroplasts and beef heart mitochondria has been investigated by electron microscopy with negatively stained specimens. The detergent-solubilized ATP-synthase forms string-like structures in which the F0 parts are aggregated. In most cases, the F, parts are arranged at alternating sides along the string. The F0 part has an approximate cylindrical shape with heights of 8.3 and 8.9 nm and diameters of 6.2 and 6.4 nm for the chloroplast and mitochondrial enzyme, respectively. The F, parts are disk-like structures with a diameter of about 11.5 nm and a height of about 8.5 nm. The F, parts are attached to the strings, composed of Fn parts, in most cases, with their smallest dimension parallel to the strings. The stalk connecting F0 and F, has a length of 3.7 nm and 4.3 nm and a diameter of 2.7 nm and 4.3 nm for the chloroplast and mitochondrial enzyme, respectively

Otto Stern (1888-1969): The founding father of experimental atomic physics

We review the work and life of Otto Stern who developed the molecular beam technique and with its aid laid the foundations of experimental atomic physics. Among the key results of his research are: the experimental determination of the Maxwell-Boltzmann distribution of molecular velocities (1920), experimental demonstration of space quantization of angular momentum (1922), diffraction of matter waves comprised of atoms and molecules by crystals (1931) and the determination of the magnetic dipole moments of the proton and deuteron (1933).Comment: 39 pages, 8 figure