Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.Comment: 40 pages, 4 figure

Percolation in the Sherrington-Kirkpatrick Spin Glass

We present extended versions and give detailed proofs of results concerning percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The proofs involve comparison inequalities between SK multireplica bond occupation variables and the independent variables of standard Erdos-Renyi random graphs.Comment: 18 page

Propulsion Study for Small Transport Aircraft Technology (STAT)

Propulsion requirements were determined for 0.5 and 0.7 Mach aircraft. Sensitivity studies were conducted on both these aircraft to determine parametrically the influence of propulsion characteristics on aircraft size and direct operating cost (DOC). Candidate technology elements and design features were identified and parametric studies conducted to select the STAT advanced engine cycle. Trade off studies were conducted to determine those advanced technologies and design features that would offer a reduction in DOC for operation of the STAT engines. These features were incorporated in the two STAT engines. A benefit assessment was conducted comparing the STAT engines to current technology engines of the same power and to 1985 derivatives of the current technology engines. Research and development programs were recommended as part of an overall technology development plan to ensure that full commercial development of the STAT engines could be initiated in 1988

Q-space analysis of the light scattering phase function of particles with any shape

Citation: Sorensen, C. M., Heinson, Y. W., Heinson, W. R., Maughan, J. B., & Chakrabarti, A. (2017). Q-space analysis of the light scattering phase function of particles with any shape. Atmosphere, 8(4). doi:10.3390/atmos8040068Q-space analysis is applied to the light scattering phase function of a wide variety of non-spherical and irregularly shaped particles including a great many types of dusts, fractal aggregates, spheroids, irregular spheres, Gaussian random spheres, thickened clusters and nine types of ice crystals. The phase functions were either experimental data or calculations. This analysis method uncovers many specific and quantitative similarities and differences between the scattering by various shapes and also when compared to spheres. From this analysis a general description for scattering by a particle of any shape emerges with specific details assigned to various shapes. © 2017 by the authors. Licensee MDPI, Basel, Switzerland