Inequality and Network Structure

This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.inequality;networks;coalitional deviations;power;centrality

Sparsity-Based Error Detection in DC Power Flow State Estimation

This paper presents a new approach for identifying the measurement error in the DC power flow state estimation problem. The proposed algorithm exploits the singularity of the impedance matrix and the sparsity of the error vector by posing the DC power flow problem as a sparse vector recovery problem that leverages the structure of the power system and uses $l_1$-norm minimization for state estimation. This approach can provably compute the measurement errors exactly, and its performance is robust to the arbitrary magnitudes of the measurement errors. Hence, the proposed approach can detect the noisy elements if the measurements are contaminated with additive white Gaussian noise plus sparse noise with large magnitude. The effectiveness of the proposed sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE 118-bus and 300-bus test systems

DG algebras with exterior homology

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page

Esterification of succinic anhydride to di-(p-cresyl) succinate over M n+-montmorillonite clay catalysts

Esterification of succinic anhydride to di-(p-cresyl) succinate over heterogeneous acid clay catalysts is reported. Montmorillonite clay samples exchanged with different cations were prepared and catalytic activity of the resulting materials was investigated in the synthesis of di-(p-cresyl) succinate esters. Among the exchanged clay catalysts, Al3+ and H +-mont were found to be more active for the esterification of succinic anhydride with p-cresol. The activity of Mn+-mont was found to be directly related to the charge to radius ratio of Mn+-ions. The influence of molar ratio of reactants, reaction time, and catalyst amount on the esterification reaction was investigated. The esterification was found to follow the second order rate kinetics and the kinetic parameters such as rate constant (k), equilibrium constant (K) and Gibbs free energy (ÎG°) for the reaction have been determined. The activity of Al3+-mont clay catalyst for the esterification of succinic anhydride with phenol, m-cresol, o-cresol, p-nitrophenol and resorcinol have been studied. Regeneration and reusability of the clay catalyst has also been investigated. © 2004 Elsevier B.V. All rights reserved

Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement ~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0<alpha<=2) give rise to subdiffusion of the form ~t^{alpha/(1+alpha)}. In contrast correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.Comment: 6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communicatio

Synthesis of phenylacetates using aluminium-exchanged montmorillonite clay catalyst

Liquid phase esterification of phenylacetic acid with phenol and substituted phenols has been investigated over montmorillonite clay exchanged with H + - Al 3+ - and aluminium polyhydroxy oligomer cations. Among the catalysts studied, Al 3+ - montmorillonite dried at 100°C showed 67 conversion, while the same catalyst dried at 200deg;C showed reduced conversion of 36. Al 3+ - montmorillonite dried at 400°C and montmorillonite exchanged with aluminium polyhydroxy oligomer cations dried at 100°C and calcined at 500°C failed to bring about the reaction. Effects of mole ratio of reactants, reaction period and catalyst amount on yield of the ester and catalyst regeneration are also investigated. Esterification of phenylacetic acid with phenol, cresols, nitrophenols and resorcinol has been carried out in the presence of montmorillonite clay exchanged with H +-ions, Al 3+-ions and polyhydroxy oligomer cations of Al. Na +-montmorillonite (raw clay) was inactive, H +- and Al 3+-montmorillonites, dried at 100°C, showed 52 and 67 conversions to ester, respectively, upon refluxing the phenylacetic acid (20 mmol) and p-cresol (40 mmol) for 6 h. While Al 3+- montmorillonite dried at 200°C showed a conversion of 36 the same catalyst when dried at 400°C showed no conversion. Montmorillonite exchanged with aluminium polyhydroxy oligomers dried at 100°C and calcined at 500°C to get pillared clay (d 0 0 1=17.5 à ) failed to bring about the esterification. Effect of concentration of reactants, amount of catalyst and the reaction time on the yield of p-cresyl phenylacetate has been investigated. The esterification of phenylacetic acid with phenol and substituted phenols like m-cresol, o-cresol, p-nitro phenol and o-nitro phenol showed reduced yield due to steric factors. The activity of the clay catalyst after regeneration has also been studied. © 2004 Published by Elsevier B.V

Patterns of Individual Shopping Behavior

Much of economic theory is built on observations of aggregate, rather than individual, behavior. Here, we present novel findings on human shopping patterns at the resolution of a single purchase. Our results suggest that much of our seemingly elective activity is actually driven by simple routines. While the interleaving of shopping events creates randomness at the small scale, on the whole consumer behavior is largely predictable. We also examine income-dependent differences in how people shop, and find that wealthy individuals are more likely to bundle shopping trips. These results validate previous work on mobility from cell phone data, while describing the unpredictability of behavior at higher resolution.Comment: 4 pages, 5 figure