Global MRI with Braginskii viscosity in a galactic profile

We present a global-in-radius linear analysis of the axisymmetric magnetorotational instability (MRI) in a collisional magnetized plasma with Braginskii viscosity. For a galactic angular velocity profile $\Omega$ we obtain analytic solutions for three magnetic field orientations: purely azimuthal, purely vertical and slightly pitched (almost azimuthal). In the first two cases the Braginskii viscosity damps otherwise neutrally stable modes, and reduces the growth rate of the MRI respectively. In the final case the Braginskii viscosity makes the MRI up to $2\sqrt{2}$ times faster than its inviscid counterpart, even for \emph{asymptotically small} pitch angles. We investigate the transition between the Lorentz-force-dominated and the Braginskii viscosity-dominated regimes in terms of a parameter \sim \Omega \nub/B^2 where \nub is the viscous coefficient and $B$ the Alfv\'en speed. In the limit where the parameter is small and large respectively we recover the inviscid MRI and the magnetoviscous instability (MVI). We obtain asymptotic expressions for the approach to these limits, and find the Braginskii viscosity can magnify the effects of azimuthal hoop tension (the growth rate becomes complex) by over an order of magnitude. We discuss the relevance of our results to the local approximation, galaxies and other magnetized astrophysical plasmas. Our results should prove useful for benchmarking codes in global geometries.Comment: 14 pages, 5 figure

Improving accuracy and efficiency of mutual information for multi-modal retinal image registration using adaptive probability density estimation

Mutual information (MI) is a popular similarity measure for performing image registration between different modalities. MI makes a statistical comparison between two images by computing the entropy from the probability distribution of the data. Therefore, to obtain an accurate registration it is important to have an accurate estimation of the true underlying probability distribution. Within the statistics literature, many methods have been proposed for finding the 'optimal' probability density, with the aim of improving the estimation by means of optimal histogram bin size selection. This provokes the common question of how many bins should actually be used when constructing a histogram. There is no definitive answer to this. This question itself has received little attention in the MI literature, and yet this issue is critical to the effectiveness of the algorithm. The purpose of this paper is to highlight this fundamental element of the MI algorithm. We present a comprehensive study that introduces methods from statistics literature and incorporates these for image registration. We demonstrate this work for registration of multi-modal retinal images: colour fundus photographs and scanning laser ophthalmoscope images. The registration of these modalities offers significant enhancement to early glaucoma detection, however traditional registration techniques fail to perform sufficiently well. We find that adaptive probability density estimation heavily impacts on registration accuracy and runtime, improving over traditional binning techniques. © 2013 Elsevier Ltd

Excitability in autonomous Boolean networks

We demonstrate theoretically and experimentally that excitable systems can be built with autonomous Boolean networks. Their experimental implementation is realized with asynchronous logic gates on a reconfigurabe chip. When these excitable systems are assembled into time-delay networks, their dynamics display nanosecond time-scale spike synchronization patterns that are controllable in period and phase.Comment: 6 pages, 5 figures, accepted in Europhysics Letters (epljournal.edpsciences.org

Speeding up Simplification of Polygonal Curves using Nested Approximations

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.Comment: 12 pages + figure

Possible Treatment of Parkinson's Disease with Intrathecal Medication in the MPTP Model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73916/1/j.1749-6632.1988.tb31828.x.pd

Application of the Fisher-Rao metric to ellipse detection

The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm

Transient dynamics and their control in time-delay autonomous Boolean ring networks

Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation. To address this issue, we have developed an experimental test bed to realize a time-delay autonomous Boolean network with three inhibitory nodes, known as a repressilator, and use it to study the dynamics that arise as time delays along the links vary. We observe various nearly periodic oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay, and which are distinct from the eventual asymptotically stable periodic attractors. For repeated experiments with a given network, we find that stochastic processes give rise to a broad distribution of transient times with an exponential tail. In some cases, the transients are so long that it is doubtful the attractors will ever be approached in a biological system that has a finite lifetime. To counteract the long transients, we show experimentally that small, occasional perturbations applied to the time delays can force the trajectories to rapidly approach the attractors

A Categorization and Parametric Modeling Approach Using Open Geodata Enabling Building Vulnerability Assessment

Due to the increase in the frequency and intensity of natural disasters such as heavy rainfall events, the evaluation of the vulnerability of the built environment is becoming increasingly important. Evaluation techniques for each separate building often require detailed geometric models of the supporting structures and time-consuming simulations. One possibility to overcome this problem is to categorize the buildings in a first step and use representative building models for each category. This paper presents a semi-automated approach for categorizing buildings and creating parametric models for the respective building categories. Using these models, the buildings of a category can be collectively examined for their vulnerability to various impacts. First, this paper introduces open geodata that can be used for this process. For the categorization of the buildings, the collected data is further processed to extract additional information such as building age classes or floor plan geometries of the buildings. This results in a data set, with the help of which the buildings can be categorized. However, information about the load-bearing structure is often missing in the different data sources. By including information on typical construction methods that are associated with the previously determined characteristics (age, floor plan geometry, usage), representative models can be created for individual building categories. In this study, the approach was tested in a selected reference area in Berlin. The results indicate that the presented approach is a promising first step towards deriving geometrical models from open geodata that can be used to evaluate the vulnerability of buildings

Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design