Rumor spreading on random regular graphs and expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well‐studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d ‐regular graphs with n vertices. We show that with probability 1 ‐ o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d lnn rounds, where Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo‐random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 ‐ o(1), where \begin{align*}C = \lim_{d\to\infty}C_d = \frac{1}{\ln2} + 1\end{align*}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.     

Endogenous matching in a market with heterogeneous principals and agents

We employ the assignment game of Shapley and Shubik (Int J Game Theory 1:111–130, 1972) to study the endogenous matching patterns in a market that consists of heterogenous principals and agents. We show that, in general, the equilibrium matching is non-assortative. We then characterize the equilibrium relationship between risk and performance pay and risk and fixed compensation. This is the first paper that characterizes the equilibrium matching, to its fullest possible extent, building on the Holmstrom and Milgrom (Econometrica 55:303–328, 1987) principal-agent model. This model has been used extensively in the empirical literature and therefore we hope that our results will be of value to empirical researchers who wish to study a principal-agent market.     

Recovery rates in investment-grade pools of credit assets: A large deviations analysis

We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate function and show that it has a natural interpretation as the favored way to rearrange recoveries and losses among the different types. Numerical examples are also provided.     

Chemistry of organophosphonate scale growth inhibitors: two-dimensional, layered polymeric networks in the structure of tetrasodium 2-hydroxyethyl-amino-bis(methylenephosphonate)

Aminomethylene phosphonates are important scale inhibitors applied in diverse areas of technology. This study adds to the existing body of information on this subject and reports the crystal and molecular structures of tetrasodium 2-hydroxyethylamino-bis(methylene-phosphonate) decahydrate ([Na₄(HOCH₂CH₂N(CH₂PO₃)₂)]·10H₂O, 1). The crystal structure of 1 could be described as two-dimensional polymeric layered structure hydrogen bonded into a 3D supramolecular polymeric network. The structure of the tetraanion consists of a “three-arm” backbone stemming from the N atom. Two “arms” are deprotonated methylene phosphonate (-CH₂PO₃²⁻) moieties and the third is a hydroxyethyl (-CH₂CH₂OH) moiety. One Na cation forms an intramolecular complex with two oxygens from separate phosphonate groups, a hydroxyl oxygen, the nitrogen and two lattice water molecules. The position of this Na cation points to a possible coordination site for Ca in a proposed Ca-HEABMP complex (HEABMP=2-hydroxyethylamino-bis(methylene-phosphonate).     

Synthesis,Kinetic and Conformational Studies of 2-Substituted-5-(β-d-glucopyranosyl)-pyrimidin-4-ones as Potential Inhibitors of Glycogen Phosphorylase

Dysregulation of glycogen phosphorylase, an enzyme involved in glucose homeostasis, may lead to a number of pathological states such as type 2 diabetes and cancer, making it an important molecular target for the development of new forms of pharmaceutical intervention. Based on our previous work on the design and synthesis of 4-arylamino-1-(β-d-glucopyranosyl)pyrimidin-2-ones, which inhibit the activity of glycogen phosphorylase by binding at its catalytic site, we report herein a general synthesis of 2-substituted-5-(β-d-glucopyranosyl)pyrimidin-4-ones, a related class of metabolically stable, C-glucosyl-based, analogues. The synthetic development consists of a metallated heterocycle, produced from 5-bromo-2-methylthiouracil, in addition to protected d-gluconolactone, followed by organosilane reduction. The methylthio handle allowed derivatization through hydrolysis, ammonolysis and arylamine substitution, and the new compounds were found to be potent (μM) inhibitors of rabbit muscle glycogen phosphorylase. The results were interpreted with the help of density functional theory calculations and conformational analysis and were compared with previous findings.     

Über die Wirkung von Auxochromen in Flavyliumsalzen,II. 5,6-Benzo-flavyliumsalze

Analogously to the 7-hydroxyflavyliumion the 5,6-benzoflavyliumion affects auxochromes in 4′-position not as strongly as the flavylium ion. In the flavylium series the dimethyl-amino group e.g. causes a bathochromic effect of 137 nm; in the 5,6-benzoflavylium series however the bathochromic effect is only 109 nm. The absorption maxima of both series converge; in the case of the dimethylamino group the convergence amounts to 28 nm.