Neural networks,rational functions,and realization theory

The problem of parametrizing single hidden layer scalar neural networks with continuous activation functions is investigated. A connection is drawn between realization theory for linear dynamical systems, rational functions, and neural networks that appears to be new. A result of this connection is a general parametrization of such neural networks in terms of strictly proper rational functions. Some existence and uniqueness results are derived. Jordan decompositions are developed, which show how the general form can be expressed in terms of a sum of canonical second order sections. The parametrization may be useful for studying learning algorithms.This work was supported by the Australian Research Council, the Australian Telecommunications and Electronics Research Board, and the Boeing Commencai Aircraft Company (thanks to John Moore).     

Prednisolone therapy of idiopathic feline lower urinary tract disease: a double-blind clinical study

A double-blind clinical study was performed to evaluate prednisolone as treatment for idiopathic feline lower urinary tract disease. No differences in response were observed in prednisolone- and placebo-treated cats.     

Decision support in early development phases—A case study from machine engineering

In the case study presented in this paper we consider early development phases of a mechanical product. We want to evaluate different concepts and decide which one(s) to pursue. A problem in early phases is that usually no test runs are available. In our case study, based on a standard, there are ways to compute the lifetime distributions of the components of the different concepts. Some parameters needed for these computations are not known precisely. Unfortunately, the lifetime distributions of the components are highly sensitive to these parameters. Our approach is to equip these parameters with distributions. These distributions would be called prior distributions in Bayesian terminology, but no update is possible since no test runs are available. Our approach implies that the distribution of the system lifetime for each concept is random, i.e. we get random elements in the space of lifetime distributions. Using Monte-Carlo simulations, we demonstrate several ways to compare the random lifetime distributions of the concepts. Some of these comparisons use stochastic orderings. We also introduce a new stochastic ordering which is particularly suitable for reliability purposes. Our case study, consisting of three scenarios, allows us to demonstrate some conclusions that can be reached.     

Quantitative measurement of gas hold-up distribution in a stirred chemical reactor using X-ray cone-beam computed tomography

Cone-beam type X-ray computed tomography (CBCT) is a potential method to measure three-dimensional phase distributions in vessels. An example for that is the measurement of gas profiles in stirred chemical reactors. Such data are highly valuable for the assessment and evaluation of chemical processes, for optimisation of the reactor and stirrer design, and for evaluation of computational fluid dynamics codes used to model the fluid flow and heat transfer in reactive systems. However, there are considerable difficulties for accurate quantitative measurements due to beam hardening and radiation scattering effects. In a theoretical and experimental work we have investigated the non-linear effects of both physical phenomena and developed a suitable measurement setup as well as calibration and software correction methods to achieve a highly accurate measurement of void fraction profiles with CBCT.     

Smaller superconcentrators of density 28

An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. Here it is proved that such superconcentrators exist (by a random construction of certain expander graphs as building blocks) having density 28 (where the density is the number of edges divided by N). The best known density before this paper was 34.2 [U. Schöning, Construction of expanders and superconcentrators using Kolmogorov complexity, J. Random Structures Algorithms 17 (2000) 64-77] or 33 [L.A. Bassalygo, Personal communication, 2004].     

Photoacoustic ultrasound: pulse production and detection of 0.5% Liposyn

Theoretical predictions and experimental measurements of photoacoustic pulse production within a 0.5% solution of Liposyn, a highly scattering, optical propagation medium, are reported. A simple model for photoacoustic energetics is developed that predicts photoacoustic signal pressure as a function of depth within a turbid medium following surface irradiation from an infrared source. The model is valid for very short irradiation duration. The model predicts that the acoustic pressure produced at a distance r from the center of a small, highly absorbing sphere of radius R consists of two, opposite polarity pulses, one originating from the near and one from the far side of the sphere. The magnitude of these biphasic pulses is expected to be proportional to the energy fluence (E) incident on the surface of the sphere and to the ratio, R/r. Furthermore, the energy fluence (E) that reaches the sphere is roughly proportional to e-mu effZ, where mu eff is the effective attenuation coefficient of the turbid medium and Z is the depth of the embedded sphere below the irradiated surface. The variation of E with depth within the absorber and biphasic acoustic pulse production have been verified experimentally. Further experiments demonstrate that a small (3-mm diameter), highly absorbing sphere can be detected and localized at a depth of 37.5 mm within a 0.5% solution of Liposyn with a spatial resolution of 1 x 6 mm2, using a biologically safe level of infrared irradiation (lambda = 1064 nm) and a conventional ultrasound transducer (frequency = 2.25 MHz). These results suggest that photoacoustic ultrasound imaging may have application to biologic systems such as the human breast.     

A note on a local twist estimator

For the construction of composite surfaces interpolating a given curve net a new local twist estimator was proposed recently (Farin and Hagen, 1992). Some properties of this estimator—including an explicit representation for Gaussian curvature K at the knots of the curve net—are presented in this note.     

Improving sub-pixel accuracy for long range stereo

Dense stereo algorithms are able to estimate disparities at all pixels including untextured regions. Typically these disparities are evaluated at integer disparity steps. A subsequent sub-pixel interpolation often fails to propagate smoothness constraints on a sub-pixel level.We propose to increase the sub-pixel accuracy in low-textured regions in four possible ways: First, we present an analysis that shows the benefit of evaluating the disparity space at fractional disparities. Second, we introduce a new disparity smoothing algorithm that preserves depth discontinuities and enforces smoothness on a sub-pixel level. Third, we present a novel stereo constraint (gravitational constraint) that assumes sorted disparity values in vertical direction and guides global algorithms to reduce false matches, especially in low-textured regions. Finally, we show how image sequence analysis improves stereo accuracy without explicitly performing tracking. Our goal in this work is to obtain an accurate 3D reconstruction. Large-scale 3D reconstruction will benefit heavily from these sub-pixel refinements.Results based on semi-global matching, obtained with the above mentioned algorithmic extensions are shown for the Middlebury stereo ground truth data sets. The presented improvements, called ImproveSubPix, turn out to be one of the top-performing algorithms when evaluating the set on a sub-pixel level while being computationally efficient. Additional results are presented for urban scenes. The four improvements are independent of the underlying type of stereo algorithm.     

Topology of the moduli space for reachable linear dynamical systems: The complex case

This paper deals with the algebraic topology of the space _n,m of complex reachable linear dynamical systems. Topological invariants such as the singular homology groups of _n,m are explicitly computed and they are shown to coincide with those of a certain Grassmann manifold. From this some new results on the topology of rational transfer matrices with fixed McMillan degree are obtained.