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

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

Investigating exploration for deep reinforcement learning of concentric tube robot control

PURPOSE: Concentric tube robots are composed of multiple concentric, pre-curved, super-elastic, telescopic tubes that are compliant and have a small diameter suitable for interventions that must be minimally invasive like fetal surgery. Combinations of rotation and extension of the tubes can alter the robot's shape but the inverse kinematics are complex to model due to the challenge of incorporating friction and other tube interactions or manufacturing imperfections. We propose a model-free reinforcement learning approach to form the inverse kinematics solution and directly obtain a control policy. METHOD: Three exploration strategies are shown for deep deterministic policy gradient with hindsight experience replay for concentric tube robots in simulation environments. The aim is to overcome the joint to Cartesian sampling bias and be scalable with the number of robotic tubes. To compare strategies, evaluation of the trained policy network to selected Cartesian goals and associated errors are analyzed. The learned control policy is demonstrated with trajectory following tasks. RESULTS: Separation of extension and rotation joints for Gaussian exploration is required to overcome Cartesian sampling bias. Parameter noise and Ornstein-Uhlenbeck were found to be optimal strategies with less than 1 mm error in all simulation environments. Various trajectories can be followed with the optimal exploration strategy learned policy at high joint extension values. Our inverse kinematics solver in evaluation has 0.44 mm extension and [Formula: see text] rotation error. CONCLUSION: We demonstrate the feasibility of effective model-free control for concentric tube robots. Directly using the control policy, arbitrary trajectories can be followed and this is an important step towards overcoming the challenge of concentric tube robot control for clinical use in minimally invasive interventions

A method of staining Neurospora nuclei

Staining Neurospora nucle

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

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