Parametric Euler sum identities

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums.     

A representation of acoustic waves in unbounded domains

Compact, time‐harmonic, acoustic sources produce waves that decay too slowly to be square‐integrable on a line away from the sources. We introduce an inner product, arising directly from Green's second theorem, to form a Hilbert space of these waves and present examples of its computation.¹ © 2005 Wiley Periodicals, Inc.     

Inducing models of behavior from expert task performance in virtual environments

We developed an end-to-end process for inducing models of behavior from expert task performance through in-depth case study. A subject matter expert (SME) performed navigational and adversarial tasks in a virtual tank combat simulation, using the dTank and Unreal platforms. Using eye tracking and Cognitive Task Analysis, we identified the key goals pursued by and attributes used by the SME, including reliance on an egocentric spatial representation, and on the fly re-representation of terrain in qualitative terms such as “safe” and “risky”. We demonstrated methods for automatic extraction of these qualitative higher-order features from combinations of surface features present in the simulation, producing a terrain map that was visually similar to the SME annotated map. The application of decision-tree and instance-based machine learning methods to the transformed task data supported prediction of SME task selection with greater than 95 % accuracy, and SME action selection at a frequency of 10 Hz with greater than 63 % accuracy, with real time constraints placing limits on algorithm selection. A complete processing model is presented for a path driving task, with the induced generative model deviating from the SME chosen path by less than 2 meters on average. The derived attributes also enabled environment portability, with path driving models induced from dTank performance and deployed in Unreal demonstrating equivalent accuracy to those induced and deployed completely within Unreal.     

Genetic algorithms applied to the solution of hybrid optimal control problems in astrodynamics

Many space mission planning problems may be formulated as hybrid optimal control problems, i.e. problems that include both continuous-valued variables and categorical (binary) variables. There may be thousands to millions of possible solutions; a current practice is to pre-prune the categorical state space to limit the number of possible missions to a number that may be evaluated via total enumeration. Of course this risks pruning away the optimal solution. The method developed here avoids the need for pre-pruning by incorporating a new solution approach using nested genetic algorithms; an outer-loop genetic algorithm that optimizes the categorical variable sequence and an inner-loop genetic algorithm that can use either a shape-based approximation or a Lambert problem solver to quickly locate near-optimal solutions and return the cost to the outer-loop genetic algorithm. This solution technique is tested on three asteroid tour missions of increasing complexity and is shown to yield near-optimal, and possibly optimal, missions in many fewer evaluations than total enumeration would require.     

A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly \(\alpha \)-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.     

Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications

Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center, we use operator-valued periodization to give a range-function type characterization of shift-invariant spaces of function on the group. We then give characterizations of frame and Riesz families for shift-invariant spaces.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

T-ray computed tomography

We demonstrate a tomographic imaging modality that uses pulsed terahertz (THz) radiation to probe the optical properties of three-dimensional (3D) structures in the far-infrared. This THz-wave computed tomography (T-ray CT) system provides sectional images of objects in a manner analogous to conventional CT techniques such as x-ray CT. The transmitted amplitude and phase of broadband pulses of THz radiation are measured at multiple projection angles. The filtered backprojection algorithm is then used to reconstruct the target object, including both its 3D structure and its frequency-dependent far-infrared optical properties.     

On the relationship between signal bandwidth and frequency correlation for ocean surface forward scattered signals

The relationship between the bandwidth of a signal and the correlation of that signal with its ocean surface reflected arrival, a quantity we term frequency correlation, has been investigated experimentally and compared with two theories. Decorrelation of wideband surface scattered signals is a direct consequence of time spread. The acoustic measurement utilized a very short pure tone signal, from which time spread has been estimated, and four broadband signals with different bandwidths, for which correlation with the transmitted signal has been measured. An environment-driven model developed by Dahl was used to predict time spread, which agreed favorably with our time spread measurements. The model was also employed in two theories that predict frequency correlation. The first, a theory published by Reeves in 1974, is based upon the ratio of signal temporal resolution to total time spread. This theory compared well with our measurements for 1 kHz bandwidth signals, but is not applicable for signal bandwidths greater than about 2 kHz. The second, a theory developed by Ziomek, models ocean acoustic propagation as transmission through a linear system. This theory agreed well with our frequency correlation measurements for signal bandwidths of 1-22 kHz.