Explicit towers of Drinfeld modular curves

We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth.Comment: 10 pages. For mini-symposium on "curves over finite fields and codes" at the 3rd European Congress in Barcelona 7/2000 Revised to correct minor typographical and grammatical error

Differentially Private Distributed Optimization

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve $\epsilon$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{\epsilon^2})$

An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems

This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric vehicles. We cast the problem as an optimization program, where the objective is to minimize the losses in the network subject to constraints on bus voltage magnitudes, limits on active and reactive power injections, transmission line thermal limits and losses. We provide sufficient conditions under which the optimization problem can be solved via its convex relaxation. Using data from existing networks, we show that these sufficient conditions are expected to be satisfied by most networks. We also provide an efficient distributed algorithm to solve the problem. The algorithm adheres to a communication topology described by a graph that is the same as the graph that describes the electrical network topology. We illustrate the operation of the algorithm, including its robustness against communication link failures, through several case studies involving 5-, 34-, and 123-bus power distribution systems.Comment: To Appear in IEEE Transaction on Power System

Carbon burning in intermediate mass primordial stars

The evolution of a zero metallicity 9 M_s star is computed, analyzed and compared with that of a solar metallicity star of identical ZAMS mass. Our computations range from the main sequence until the formation of a massive oxygen-neon white dwarf. Special attention has been payed to carbon burning in conditions of partial degeneracy as well as to the subsequent thermally pulsing Super-AGB phase. The latter develops in a fashion very similar to that of a solar metallicity 9 M_s star, as a consequence of the significant enrichment in metals of the stellar envelope that ensues due to the so-called third dredge-up episode. The abundances in mass of the main isotopes in the final ONe core resulting from the evolution are X(^{16}O) approx 0.59, X(^{20}Ne) approx 0.28 and X(^{24}Mg) approx 0.05. This core is surrounded by a 0.05 M_s buffer mainly composed of carbon and oxygen, and on top of it a He envelope of mass 10^{-4} M_sComment: 11 pages, 11 figures, accepted for publication in A&

Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property automatically defines the delta distribution as the P-representation of such states. Then, in principle, there must be a classical analog for them. Among other examples, we construct a family of nonlinear coherent states for a representation of the su(1,1) Lie algebra that is realized as a deformation of the oscillator algebra. In (2), we use a beam splitter to show that the nonlinear coherent states exhibit properties like anti-bunching that prohibit a classical description for them. We also show that these states lack second order coherence. That is, although the P-representation of the nonlinear coherent states is a delta function, they are not full coherent. Therefore, the systems associated with the generalized oscillator algebras cannot be considered `classical' in the context of the quantum theory of optical coherence.Comment: 26 pages, 10 figures, minor changes, misprints correcte