On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

Objective: This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography. Materials and methods: We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification. Results: Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A z = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A z value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A z value. Conclusion: FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

A three-dimensional magnetometer for motion sensing of a balloon-carried atmospheric measurement package

An instrument is described which carries three orthogonal geomagnetic field sensors on a standard meteorological balloon package, to sense rapid motion and position changes during ascent through the atmosphere. Because of the finite data bandwidth available over the UHF radio link, a burst sampling strategy is adopted. Bursts of 9s of measurements at 3.6Hz are interleaved with periods of slow data telemetry lasting 25s. Calculation of the variability in each channel is used to determine position changes, a method robust to periods of poor radio signals. During three balloon ascents, variability was found repeatedly at similar altitudes, simultaneously in each of three orthogonal sensors carried. This variability is attributed to atmospheric motions. It is found that the vertical sensor is least prone to stray motions, and that the use of two horizontal sensors provides no additional information over a single horizontal sensor

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. (c) 2007 American Institute of Physics

Fusion of motion segmentation algorithms

Many algorithms have been developed to achieve motion segmentation for video surveillance. The algorithms produce varying performances under the infinite amount of changing conditions. It has been recognised that individually these algorithms have useful properties. Fusing the statistical result of these algorithms is investigated, with robust motion segmentation in mind.

Comparison of balloon-carried atmospheric motion sensors with Doppler lidar turbulence measurements

Magnetic sensors have been added to a standard weather balloon radiosonde package to detect motion in turbulent air. These measure the terrestrial magnetic field and return data over the standard uhf radio telemetry. Variability in the magnetic sensor data is caused by motion of the instrument package. A series of radiosonde ascents carrying these sensors has been made near a Doppler lidar measuring atmospheric properties. Lidar-retrieved quantities include vertical velocity (w) profile and its standard deviation (w). w determined over 1 h is compared with the radiosonde motion variability at the same heights. Vertical motion in the radiosonde is found to be robustly increased when w>0.75 m s−1 and is linearly proportional to w. ©2009 American Institute of Physics

Non-radial solar wind flows induced by the motion of interplanetary coronal mass ejections

A survey of the non-radial flows (NRFs) during nearly five years of interplanetary observations revealed the average non-radial speed of the solar wind flows to be �30 km/s, with approximately one-half of the large (>100 km/s) NRFs associated with ICMEs. Conversely, the average non-radial flow speed upstream of all ICMEs is �100 km/s, with just over one-third preceded by large NRFs. These upstream flow deflections are analysed in the context of the large-scale structure of the driving ICME. We chose 5 magnetic clouds with relatively uncomplicated upstream flow deflections. Using variance analysis it was possible to infer the local axis orientation, and to qualitatively estimate the point of interception of the spacecraft with the ICME. For all 5 events the observed upstream flows were in agreement with the point of interception predicted by variance analysis. Thus we conclude that the upstream flow deflections in these events are in accord with the current concept of the large scale structure of an ICME: a curved axial loop connected to the Sun, bounded by a curved (though not necessarily circular)cross section.

HMS - Harmonic Motion by Shadows

A problem is discussed which is generated by shadows and which is a generalization of simple harmonic motion.

Potential energy for slantwise parcel motion

Two formulations for the potential energy for slantwise motion are compared: one which applies strictly only to two-dimensional flows (SCAPE) and a three-dimensional formulation based on a Bernoulli equation. The two formulations share an identical contribution from the vertically integrated buoyancy anomaly and a contribution from different Coriolis terms. The latter arise from the neglect of (different) components of the total change in kinetic energy along a trajectory in the two formulations. This neglect is necessary in order to quantify the potential energy available for slantwise motion relative to a defined steady environment. Copyright © 2000 Royal Meteorological Society.