Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Time delay estimation with hidden Markov models

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.

Estimation of functional connectivity from electromagnetic signals and the amount of empirical data required

An increasing number of neuroimaging studies are concerned with the identification of interactions or statistical dependencies between brain areas. Dependencies between the activities of different brain regions can be quantified with functional connectivity measures such as the cross-correlation coefficient. An important factor limiting the accuracy of such measures is the amount of empirical data available. For event-related protocols, the amount of data also affects the temporal resolution of the analysis. We use analytical expressions to calculate the amount of empirical data needed to establish whether a certain level of dependency is significant when the time series are autocorrelated, as is the case for biological signals. These analytical results are then contrasted with estimates from simulations based on real data recorded with magnetoencephalography during a resting-state paradigm and during the presentation of visual stimuli. Results indicate that, for broadband signals, 50-100 s of data is required to detect a true underlying cross-correlations coefficient of 0.05. This corresponds to a resolution of a few hundred milliseconds for typical event-related recordings. The required time window increases for narrow band signals as frequency decreases. For instance, approximately 3 times as much data is necessary for signals in the alpha band. Important implications can be derived for the design and interpretation of experiments to characterize weak interactions, which are potentially important for brain processing.

Signal processing techniques for ultrasonic inspection

This thesis discusses the need for nondestructive testing and highlights some of the limitations in present day techniques. Special interest has been given to ultrasonic examination techniques and the problems encountered when they are applied to thick welded plates. Some suggestions are given using signal processing methods. Chapter 2 treats the need for nondestructive testing as seen in the light of economy and safety. A short review of present day techniques in nondestructive testing is also given. The special problems using ultrasonic techniques for welded structures is discussed in Chapter 3 with some examples of elastic wave propagation in welded steel. The limitations in applying sophisticated signal processing techniques to ultrasonic NDT~ mainly found in the transducers generating or receiving the ultrasound. Chapter 4 deals with the different transducers used. One of the difficulties with ultrasonic testing is the interpretation of the signals encountered. Similar problems might be found with SONAR/RADAR techniques and Chapter 5 draws some analogies between SONAR/RADAR and ultrasonic nondestructive testing. This chapter also includes a discussion on some on the techniques used in signal processing in general. A special signal processing technique found useful is cross-correlation detection and this technique is treated in Chapter 6. Electronic digital compute.rs have made signal processing techniques easier to implement -Chapter 7 discusses the use of digital computers in ultrasonic NDT. Experimental equipment used to test cross-correlation detection of ultrasonic signals is described in Chapter 8. Chapter 9 summarises the conclusions drawn during this investigation.

Possibilities and limitations of coded aperture imaging

We have simulated the performance of various apertures used in Coded Aperture Imaging - optically. Coded pictures of extended and continuous-tone planar objects from the Annulus, Twin Annulus, Fresnel Zone Plate and the Uniformly Redundant Array have been decoded using a noncoherent correlation process. We have compared the tomographic capabilities of the Twin Annulus with the Uniformly Redundant Arrays based on quadratic residues and m-sequences. We discuss the ways of reducing the 'd. c.' background of the various apertures used. The non-ideal System-Point-Spread-Function inherent in a noncoherent optical correlation process produces artifacts in the reconstruction. Artifacts are also introduced as a result of unwanted cross-correlation terms from out-of-focus planes. We find that the URN based on m-sequences exhibits good spatial resolution and out-of-focus behaviour when imaging extended objects.

Autonomic, biometric and oculomotor correlates of myopia in young adults

The principal work reported in this thesis is the examination of autonomic profile of ciliary muscle innervation as a risk factor in myopia development. Deficiency in sympathetic inhibitory control of accommodation has been proposed as a contributory factor in the development of late onset myopia (LOM). Complementary measurements of ocular biometry, oculomotor function and dynamic accommodation response were carried out on the same subject cohort, thus allowing cross-correlation of these factors with. autonomic profile. Subjects were undergraduate and postgraduate students of Aston University. A 2.5 year longitudinal study of refractive error progression in 40 subjects revealed the onset of LOM in 10, initially emmetropic, young adult subjects (age range 18-24 years) undertaking substantial amounts of near work. A controlled, double blind experimental protocol was conducted concurrently to measure post-task open-loop accommodative regression following distance (0 D) or near (3 D above baseline tonic accommodation) closed-loop tasks of short (10 second) or long (3 minute) duration. Closed-loop tasks consisted of observation of a high contrast Maltese cross target; open-loop conditions were imposed by observation of a 0.2 c/deg Difference of Gaussian target. Accommodation responses were recorded continuously at 42 Hz using a modified Shin-Nippon SRW-5000 open-view infra-red optometer. Blockade of the sympathetic branch of accommodative control was achieved by topical instillation of the non-selective b-adrenoceptor antagonist timolol maleate. Betaxolol hydrochloride (non-selective b1-adrenoceptor antagonist) and normal saline were employed as control agents. Retarded open-loop accommodative regression under b2 blockade following the 3 minute near task indicated the presence of sympathetic facility. Sympathetic inhibitory facility in accommodation control was found in similar proportions between LOM and stable emmetropic subjects. A cross-sectional study (N=60) of autonomic profile showed that sympathetic innervation of ciliary muscle is present in similar proportions between emmetropes, early-, and late-onset myopes. Sympathetic facility was identified in 27% of emmetropes, 21% of EOMs and 29% of LOMs.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

The experimental evaluation of the dynamics of fluid-loaded microplates

An experimental testing system for the study of the dynamic behavior of fluid-loaded rectangular micromachined silicon plates is designed and presented in this paper. In this experimental system, the base-excitation technique combined with pseudo-random signal and cross-correlation analysis is applied to test fluid-loaded microstructures. Theoretical model is also derived to reveal the mechanism of such an experimental system in the application of testing fluid-loaded microstructures. The dynamic experiments cover a series of testings of various microplates with different boundary conditions and dimensions, both in air and immersed in water. This paper is the first that demonstrates the ability and performances of base excitation in the application of dynamic testing of microstructures that involves a natural fluid environment. Traditional modal analysis approaches are used to evaluate natural frequencies, modal damping and mode shapes from the experimental data. The obtained experimental results are discussed and compared with theoretical predictions. This research experimentally determines the dynamic characteristics of the fluid-loaded silicon microplates, which can contribute to the design of plate-based microsystems. The experimental system and testing approaches presented in this paper can be widely applied to the investigation of the dynamics of microstructures and nanostructures.

FemtoNewton force sensing with optically trapped nanotubes

We extract the distribution of both center-of-mass and angular fluctuations from three-dimensional tracking of optically trapped nanotubes. We measure the optical force and torque constants from autocorrelation and cross-correlation of the tracking signals. This allows us to isolate the angular Brownian motion. We demonstrate that nanotubes enable nanometer spatial and femtonewton force resolution in photonic force microscopy, the smallest to date. This has wide implications in nanotechnology, biotechnology, nanofluidics, and material science.

Handwritten and machine-printed text discrimination using a template matching approach

We propose a novel template matching approach for the discrimination of handwritten and machine-printed text. We first pre-process the scanned document images by performing denoising, circles/lines exclusion and word-block level segmentation. We then align and match characters in a flexible sized gallery with the segmented regions, using parallelised normalised cross-correlation. The experimental results over the Pattern Recognition & Image Analysis Research Lab-Natural History Museum (PRImA-NHM) dataset show remarkably high robustness of the algorithm in classifying cluttered, occluded and noisy samples, in addition to those with significant high missing data. The algorithm, which gives 84.0% classification rate with false positive rate 0.16 over the dataset, does not require training samples and generates compelling results as opposed to the training-based approaches, which have used the same benchmark.