Robust Distributed Estimation over Multiple Access Channels with Constant Modulus Signaling

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case both for a per-sensor power constraint, and a total power constraint. When the distributions of the sensing noise are not identical, a bound on the variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with a variance (AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior. The robustness of the estimator to impulsive sensing noise distributions such as those with positive excess kurtosis, or those that do not have finite moments is shown. The proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario. The effect of fading is shown to not affect the consistency of the estimator, but to scale the asymptotic variance by a constant fading penalty depending on the fading statistics. Simulations corroborate our analytical results.Comment: 28 pages, 10 figures, submitted to IEEE Transactions on Signal Processing for consideratio

A Hierarchial Neural Network Implementation for Forecasting

In this paper, a hierarchical neural network architecture for forecasting time series is presented. The architecture is composed of two hierarchical levels using a maximum likelihood competitive learning algorithm. The first level of the system has three experts each using backpropagation and a gating network to partition the input space in order to map the input vectors to the output vectors. The second level of the hierarchical network has an expert using fuzzy ART for producing the correct trend coming from the first level. The experiments show that the resulting network is capable of forecasting the changes in the input and identifying the trends correctl

Generalization of Weierstrassian Elliptic Functions to Rn{\bf R}^{n}

The Weierstrassian $\wp, \zeta$ and $\sigma$ functions are generalized to ${\bf R}^{n}$. The $n=3$ and $n=4$ cases have already been used in gravitational and Yang-Mills instanton solutions which may be interpreted as explicit realizations of spacetime foam and the monopole condensate, respectively. The new functions satisfy higher dimensional versions of the periodicity properties and Legendre's relations obeyed by their familiar complex counterparts. For $n=4$, the construction reproduces functions found earlier by Fueter using quaternionic methods. Integrating over lattice points along all directions but two, one recovers the original Weierstrassian elliptic functions.Comment: pp. 9, Late

Type-tunable amplified spontaneous emission from core-seeded CdSe/CdS nanorods controlled by exciton-exciton interaction

Cataloged from PDF version of article.Type-tunable optical gain performance of core-seeded CdSe/CdS nanorods is studied via two-photon optical pumping. Controlling the exciton-exciton interaction by varying the core and shell size, blue-shifted and red-shifted modes of amplified spontaneous emission are systematically demonstrated and their type attributions are verified by time-resolved emission kinetics

Solutions of the Einstein-Dirac and Seiberg-Witten Monopole Equations

We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann surfaces of genuses p_1 and p_2. There are p_1 -1 magnetic vortices on one surface and p_2 - 1 electric ones on the other, with p_1 + p_2 \geq 2 p_1 = p_2= 1 being excluded). When p_1 = p_2, the electromagnetic fields are self-dual and one also has a solution of the coupled euclidean Einstein-Maxwell-Dirac equations, with the monopole condensate serving as cosmological constant. The metric is decomposable and the electromagnetic fields are covariantly constant as in the Bertotti-Robinson solution. The Einstein metric can also be derived from a K\"{a}hler potential satisfying the Monge-Amp\`{e}re equations.Comment: 22 pages. Rep. no: FGI-99-

Fake R^4's, Einstein Spaces and Seiberg-Witten Monopole Equations

We discuss the possible relevance of some recent mathematical results and techniques on four-manifolds to physics. We first suggest that the existence of uncountably many R^4's with non-equivalent smooth structures, a mathematical phenomenon unique to four dimensions, may be responsible for the observed four-dimensionality of spacetime. We then point out the remarkable fact that self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean signature without affecting the metric. As a specific example, we consider solutions of the Seiberg-Witten Monopole Equations in which the U(1) fields are covariantly constant, the monopole Weyl spinor has only a single constant component, and the 4-manifold M_4 is a product of two Riemann surfaces Sigma_{p_1} and Sigma_{p_2}. There are p_{1}-1(p_{2}-1) magnetic(electric) vortices on \Sigma_{p_1}(\Sigma_{p_2}), with p_1 + p_2 \geq 2 (p_1=p_2= 1 being excluded). When the two genuses are equal, the electromagnetic fields are self-dual and one obtains the Einstein space \Sigma_p x \Sigma_p, the monopole condensate serving as the cosmological constant.Comment: 9 pages, Talk at the Second Gursey Memorial Conference, June 2000, Istanbu

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 3.3.1 (r4302)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of five major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. • an inversion library. The current version supports parallelization through both MPI for distributed memory and OpenMP for distributed shared memory. In this release there are a number of small changes which are not backwards compatible. Please see Appendix B to see if your scripts will be affected. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D. For Python3 support, see Appendix E