Parameter Estimation and the CRLB with Uncertain Origin Measurements

Parameter estimation in the presence of false measurements due to false alarms and missed true detections, i.e., in the presence of measurement origin uncertainty, is a difficult problem because of the need for data association, the process of deciding which, if any, is the true measurement and which are false. An additional aspect of estimation is performance evaluation via, for example, the Cramer-Rao Lower Bound (CRLB), which quantifies the achievable performance. With measurement origin uncertainty and the ensuing data association, the CRLB has to be modified to account for the loss of information due to false alarms and missed true detections. This is the focus of our paper—we show that the loss of information can be accounted for by a single scalar, known as the information reduction factor, under certain conditions. We illustrate the evaluation of the generalized CRLB on parameter estimation from direction-of-arrival measurements with applications to target tracking, communications and signal processing. Simulation results on a realistic scenario show that the lower bounds quantified via the information reduction factor are statistically compatible with the observed errors.     

A clinical study of failure in microchannel cooled diodes used in large laser systems

In this paper we investigate the source of failure in commercial, microchannel cooled CW diode bars placed in 12 bar horizontal arrays. The arrays were used to pump Nd:YAG rods in our 10 kW developmental laser. The laser was operated at low duty factor over a period of over 2 years. Experimental evidence indicated that the sudden, catastrophic failure was because of degraded cooling. We used optical microscopes, an X-ray microfocus imager, and a thermal neutron scattering camera to look inside the microcoolers. Our investigations revealed only one possible failure mechanism: cooling flow reduction because of delamination of the Au coating the walls of the microcoolers and the entrapment of Au flakes within the microchannel structures. We observed blisters in the microcoolers under working bars, and flake-like structures in the microcoolers under burnt-out bars (all taken from the laser). We observed no evidence of either massive blockages because of electrochemical deposits, or of corrosion/erosion in the microchannel walls. Integral operation times of the high flow-rate cooling system and of the diodes themselves were too short by one and two orders of magnitude, respectively, to explain the observed failures. Microchannel immersion times in the deionized water were, however, long enough to allow for corrosion of metals that may have been exposed through defects in the Au coatings. Three-dimensional heat flow simulations showed that blockage of multiple microchannels towards the edge of a bar can easily lead to catastrophic temperature increases.     

Signal feature recognition based on lightwave neuromorphic signal processing

We developed a hybrid analog/digital lightwave neuromorphic processing device that effectively performs signal feature recognition. The approach, which mimics the neurons in a crayfish responsible for the escape response mechanism, provides a fast and accurate reaction to its inputs. The analog processing portion of the device uses the integration characteristic of an electro-absorption modulator, while the digital processing portion employ optical thresholding in a highly Ge-doped nonlinear loop mirror. The device can be configured to respond to different sets of input patterns by simply varying the weights and delays of the inputs. We experimentally demonstrated the use of the proposed lightwave neuromorphic signal processing device for recognizing specific input patterns.     

On the existence of a combinatorial Schlegel diagram of a simplical unstacked 3-polytope with a prescribed set of vertices

It is shown that, except for two well defined configurations, any finite set with exactly three points on ∂V is the vertex set of a triangulation of [V] which is combinatorially the Schlegel diagram of a simplicial unstacked 3-polytope.     

Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable the relativistic dynamic equation for systems with an invariant plane becomes a non-linear analytic equation in one complex variable. We obtained explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock hypothesis and using these solutions, we were able to describe the space-time transformations between two uniformly accelerated and rotating systems. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Additivity of melting curves

Universality of some melting indicators, in the context of two successful models of the solid and the liquid, gives rise to simple semi-empirical melting equations that describe additivity of melting curves. Computer inverse power melting results are used to reproduce the melting characteristics of argon to a good accuracy.     

Super-Resolved Raman Spectra of Toluene and Toluene–Chlorobenzene Mixture

In this paper, we present a method for “super-resolved” Raman spectroscopy which improves the resolution of obtained spectra. Experimental investigations were carried out on the spectra of toluene and a toluene–chlorobenzene mixture. A tunable Fabry–Perot filter is added to the detection channel and by measuring the spectra for several states of the filter a spectrum of higher resolution can be obtained after a decoding process. We demonstrate both a reduced linewidth in the pure toluene spectra and partial separation of the two overlapping peaks in the mixture.     

The Fermat–Torricelli Problem, Part I: A Discrete Gradient-Method Approach

We give a discrete geometric (differential-free) proof of the theorem underlying the solution of the well known Fermat–Torricelli problem, referring to the unique point having minimal distance sum to a given finite set of non-collinear points in d-dimensional space. Further on, we extend this problem to the case that one of the given points is replaced by an affine flat, and we give also a partial result for the case where all given points are replaced by affine flats (of various dimensions), with illustrative applications of these theorems.