The patchy Method for the Infinite Horizon Hamilton-Jacobi-Bellman Equation and its Accuracy

We introduce a modification to the patchy method of Navasca and Krener for solving the stationary Hamilton Jacobi Bellman equation. The numerical solution that we generate is a set of polynomials that approximate the optimal cost and optimal control on a partition of the state space. We derive an error bound for our numerical method under the assumption that the optimal cost is a smooth strict Lyupanov function. The error bound is valid when the number of subsets in the partition is not too large.Comment: 50 pages, 5 figure

Simplicial Nonlinear Principal Component Analysis

We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have implemented the algorithm in the case where the input data can be triangulated. We provide triangulations of data sets that fall on the surface of a torus, sphere, swiss roll, and creased sheet embedded in a fifty dimensional space. We also discuss the theoretical justification of our algorithm.Comment: 21 pages, 6 figure

Financial Benefits of Florida Generic Orange Juice Marketing

The benefits to Florida orange growers of generic orange juice advertising are assessed using additive, nonlinear, regional econometric models, measuring the impact of category and brand marketing efforts on category demand while controlling for pricing and various other factors. The study shows that generic marketing efforts increased orange juice category demand by 8.3 percent, resulting in increased orange prices and a benefit-to-cost ratio to Florida growers of 3.5 to 1. Branded promotional activity was found to primarily fuel brand switching and pantry-loading, with only modest impacts on overall category demand.marketing mix, marketing spend optimization, checkoff program, orange juice, benefit to cost ratio, Marketing,

Basic Filters for Convolutional Neural Networks Applied to Music: Training or Design?

When convolutional neural networks are used to tackle learning problems based on music or, more generally, time series data, raw one-dimensional data are commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients, which are then used as input to the actual neural network. In this contribution, we investigate, both theoretically and experimentally, the influence of this pre-processing step on the network's performance and pose the question, whether replacing it by applying adaptive or learned filters directly to the raw data, can improve learning success. The theoretical results show that approximately reproducing mel-spectrogram coefficients by applying adaptive filters and subsequent time-averaging is in principle possible. We also conducted extensive experimental work on the task of singing voice detection in music. The results of these experiments show that for classification based on Convolutional Neural Networks the features obtained from adaptive filter banks followed by time-averaging perform better than the canonical Fourier-transform-based mel-spectrogram coefficients. Alternative adaptive approaches with center frequencies or time-averaging lengths learned from training data perform equally well.Comment: Completely revised version; 21 pages, 4 figure

Development of a ninety string solar array simulator

A power source was developed to support testing for the Space Station Freedom Power Management and Distribution (PMAD) DC Testbed. The intent was to simulate as closely as possible the steady-state and transient responses of a solar array. Several breadboards and one thermal prototype were built and tested. Responses were successfully verified and improved upon during successive breadboards. The completed 90-string simulator consists of four power MOSFETs, four 25 watt source resistors, and four 250 watt drain source bypass resistors per string, in addition to the control circuitry