Sums and products along sparse graphs

In their seminal paper from 1983, Erdős and Szemerédi showed that any n distinct integers induce either n ^1+ɛ distinct sums of pairs or that many distinct products, and conjectured a lower bound of n ^2−o(1). They further proposed a generalization of this problem, in which the sums and products are taken along the edges of a given graph G on n labeled vertices. They conjectured a version of the sum-product theorem for general graphs that have at least n ^1+ɛ edges.     

Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part I

(Accepted July 23, 1996)     

Theorems of ergodic type for ρ-nonexpansive mappings in the Hilbert ball

Summary We present two types of ergodic theorems for contractive iterations in the Hilbert ball. Both explicit and implicit iterations are discussed.     

The approximate fixed point property in Banach and hyperbolic spaces

A geometrical characterization is given for those convex subsets of a Banach space (more generally a hyperbolic space) which possess the approximate fixed point property for nonexpansive mappings.     

A fast and simple randomized parallel algorithm for the maximal independent set problem

A simple parallel randomized algorithm to find a maximal independent set in a graph G = (V, E) on n vertices is presented. Its expected running time on a concurrent-read concurrent-write PRAM with O(|E|d_max) processors is O(log n), where d_max denotes the maximum degree. On an exclusive-read exclusive-write PRAM with O(|E|) processors the algorithm runs in O(log²n). Previously, an O(log⁴n) deterministic algorithm was given by Karp and Wigderson for the EREW-PRAM model. This was recently (independently of our work) improved to O(log²n) by M. Luby. In both cases randomized algorithms depending on pairwise independent choices were turned into deterministic algorithms. We comment on how randomized combinatorial algorithms whose analysis only depends on d-wise rather than fully independent random choices (for some constant d) can be converted into deterministic algorithms. We apply a technique due to A. Joffe (1974) and obtain deterministic construction in fast parallel time of various combinatorial objects whose existence follows from probabilistic arguments.     

Optimum heat treatment conditions for masking the bitterness of the clarithromycin wax matrix

The effects of the contents of aminoalkyl methacrylate copolymer E (AMCE) in a wax matrix on the mechanism of polymorphic transformation of glyceryl monostearate (GM) were clarified by evaluating the enthalpy change defined as 1.51 (DeltaH(1)-DeltaH(2))/DeltaH(2), where DeltaH(1) and DeltaH(2) denote the enthalpies in the first and second thermal analyses, respectively. Using this value, K(1), the rate constant of transformation from alpha-form to beta'-form, and K(2), the rate constant of transformation from beta'-form to beta-form, could be obtained. As the ratio of AMCE increased, K(2) increased, but a minimum point existed for K(1). K(1) was always larger than K(2), but gradually approached K(2) as the ratio of AMCE increased. The optimum temperature for the transformation of GM was 50 degrees C, at which the enthalpy change was maximum. To prepare the wax matrix preparation of clarithromycin (CAM), we considered 40 degrees C the optimum treatment temperature for the transformation of GM in a CAM wax matrix compounded from CAM, GM and AMCE, since the matrices were mutually welded at above 45 degrees C during the spray congealing process. Although K(1) and K(2) were almost the same at 40 degrees C, the rate of transformation was accelerated by tumbling. By applying the tumbling that accelerated the transformation of GM in a CAM wax matrix, almost all of the alpha-form disappeared, and the release of CAM from the wax matrix diminished when the enthalpy change was more than 0.8.     

A method for fast energy estimation and visualization of protein-ligand interaction

Summary A new computational and graphical method for facilitating ligand-protein docking studies is developed on a three-dimensional computer graphics display. Various physical and chemical properties inside the ligand binding pocket of a receptor protein, whose structure is elucidated by X-ray crystal analysis, are calculated on three-dimensional grid points and are stored in advance. By utilizing those tabulated data, it is possible to estimate the non-bonded and electrostatic interaction energy and the number of possible hydrogen bonds between protein and ligand molecules in real time during an interactive docking operation. The method also provides a comprehensive visualization of the local environment inside the binding pocket.With this method, it becomes easier to find a roughly stable geometry of ligand molecules, and one can therefore make a rapid survey of the binding capability of many drug candidates. The method will be useful for drug design as well as for the examination of protein-ligand interactions.     

The nature of NOx species on BaO(100): an ab initio molecular dynamics study

The dynamics of NO(x) species adsorbed on BaO(100) have been investigated with ab initio molecular dynamics simulations at a temperature of 300 degrees C. Nitrites are found to continuously interconvert between different adsorption configurations. For both nitrites and nitrates, diffusion events between anion sites are observed. These findings support the use of spillover mechanisms often postulated in mechanistic models of catalysts based on the NO(x)() storage and reduction concept. The large number of possible adsorption configurations are reflected in broad calculated vibrational signatures. These results explain the corresponding property observed in experimental infrared measurements of NO(x)() species on BaO. The dynamic response of the BaO(100) surface is found to strongly depend on the nature of the surface-adsorbate interaction. The largest distortions are predicted for nitrite adsorption.     

Retinoidal pyrimidinecarboxylic acids. Unexpected diaza-substituent effects in retinobenzoic acids

Several pyridine- and pyrimidine-carboxylic acids were synthesized as ligand candidates for retinoid nuclear receptors, retinoic acid receptors (RARs) and retinoic X receptors (RXRs). Although the pyridine derivatives, 6-[(5,6,7,8-tetrahydro-5,5,8,8-tetramethyl-2-naphthalenyl)carbamoyl]pyri dine-3-carboxylic acid (2b) and 6-[(5,6,7,8-tetrahydro-5,5,8,8-tetramethyl-2-naphthalenyl)carboxamido]py ridine-3-carboxylic acid (5b) are more potent than the corresponding benzoic acid-type retinoids, Am80 (2a) and Am580 (5a), the replacement of the benzene ring of Am580 (5a), Am555 (6a), or Am55 (7a) with a pyrimidine ring caused loss of the retinoidal activity both in HL-60 cell differentiation assay and in RAR transactivation assay using COS-1 cells. On the other hand, pyrimidine analogs (PA series, 10 and 11) of potent RXR agonists (retinoid synergists) with a diphenylamine skeleton (DA series, 8 and 9) exhibited potent retinoid synergistic activity in HL-60 cell differentiation assay and activated RXRs. Among the synthesized compounds, 2-[N-n-propyl-N-(5,6,7,8-tetrahydro-5,5,8,8-tetramethyl-2-naphthalenyl)a mino]pyrimidine-5-carboxylic acid (PA013, 10e) is most active retinoid synergist in HL-60 assay.