Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique global equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards global equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a global inequality with respect to the "lower bound metric" from [CHLZ]

Digital Image Processing

Newspapers and the popular scientific press today publish many examples of highly impressive images. These images range, for example, from those showing regions of star birth in the distant Universe to the extent of the stratospheric ozone depletion over Antarctica in springtime, and to those regions of the human brain affected by Alzheimer’s disease. Processed digitally to generate spectacular images, often in false colour, they all make an immediate and deep impact on the viewer’s imagination and understanding. Professor Jonathan Blackledge’s erudite but very useful new treatise Digital Image Processing: Mathematical and Computational Methods explains both the underlying theory and the techniques used to produce such images in considerable detail. It also provides many valuable example problems - and their solutions - so that the reader can test his/her grasp of the physical, mathematical and numerical aspects of the particular topics and methods discussed. As such, this magnum opus complements the author’s earlier work Digital Signal Processing. Both books are a wonderful resource for students who wish to make their careers in this fascinating and rapidly developing field which has an ever increasing number of areas of application. The strengths of this large book lie in: • excellent explanatory introduction to the subject; • thorough treatment of the theoretical foundations, dealing with both electromagnetic and acoustic wave scattering and allied techniques; • comprehensive discussion of all the basic principles, the mathematical transforms (e.g. the Fourier and Radon transforms), their interrelationships and, in particular, Born scattering theory and its application to imaging systems modelling; discussion in detail - including the assumptions and limitations - of optical imaging, seismic imaging, medical imaging (using ultrasound), X-ray computer aided tomography, tomography when the wavelength of the probing radiation is of the same order as the dimensions of the scatterer, Synthetic Aperture Radar (airborne or spaceborne), digital watermarking and holography; detail devoted to the methods of implementation of the analytical schemes in various case studies and also as numerical packages (especially in C/C++); • coverage of deconvolution, de-blurring (or sharpening) an image, maximum entropy techniques, Bayesian estimators, techniques for enhancing the dynamic range of an image, methods of filtering images and techniques for noise reduction; • discussion of thresholding, techniques for detecting edges in an image and for contrast stretching, stochastic scattering (random walk models) and models for characterizing an image statistically; • investigation of fractal images, fractal dimension segmentation, image texture, the coding and storing of large quantities of data, and image compression such as JPEG; • valuable summary of the important results obtained in each Chapter given at its end; • suggestions for further reading at the end of each Chapter. I warmly commend this text to all readers, and trust that they will find it to be invaluable. Professor Michael J Rycroft Visiting Professor at the International Space University, Strasbourg, France, and at Cranfield University, England

Identification of an appropriate data assimilation approach in seismic history matching and its effect on prediction uncertainty

Reservoir management may be improved if the present state of the field is known and if changes can be predicted. The former requires information about current fluid sweep and pressure change, while the latter requires accurate reservoir description and a predictive tool such as a simulation model. With this information, important decisions can then be made, including facility maintenance and well optimisation. We apply an automated history matching method which updates a parameter such as permeability, barrier transmissibilities and NTG (Net:Gross) by matching 4D seismic predictions from the simulations to observed data. Firstly, we look at the choice of starting model in the history matching process by testing our parameterisation and updating scheme to see whether it can convert a realisation into a better representation resembling reality. We set up some synthetic test cases to validate the history matching and parameterisation scheme. We find that, if we use a pilot point separation that is equivalent to the range of the variogram used in a generation of permeability distributions, we can obtain a good representation of the model. Secondly, we investigate the impact of successively updating barriers by adding new data to our observed dataset and comparing this to a single history match where all data is used. We demonstrate the method by applying it to the UKCS Schiehallion reservoir. We update an upscaled version of the operator’s model for increased speed. We consider a number of parameters to be uncertain, including barrier transmissibilities. Our results show a good match to the observed seismic and dynamic well data with significant improvement to the base case. The best result occurs when early data is used in short simulations first as we learn about optimum parameter values. Later data may be added for fine tuning or to explore new parameters. We investigate the value of seismic data in reducing forecasting uncertainty. The aim here is to look at the reduced uncertainty that we obtain in Schiehallion when we add 4D seismic to the history matching procedure. We look at the change to parameters and then take some of the best models and predict the behaviour of an in-fill well. We quantify the accuracy of history match predictions and the impact of time-lapse seismic data.Akakus Oil Operation

Unconstrained Face Recognition

Although face recognition has been actively studied over the past decade, the state-of-the-art recognition systems yield satisfactory performance only under controlled scenarios and recognition accuracy degrades significantly when confronted with unconstrained situations due to variations such as illumintion, pose, etc. In this dissertation, we propose novel approaches that are able to recognize human faces under unconstrained situations. Part I presents algorithms for face recognition under illumination/pose variations. For face recognition across illuminations, we present a generalized photometric stereo approach by modeling all face appearances belonging to all humans under all lighting conditions. Using a linear generalization, we achieve a factorization of the observation matrix consisting of face appearances of different individuals, each under a different illumination. We resolve ambiguities in factorization using surface integrability and symmetry constraints. In addition, an illumination-invariant identity descriptor is provided to perform face recognition across illuminations. We further extend the generalized photometric stereo approach to an illuminating light field approach, which is able to recognize faces under pose and illumination variations. Face appearance lies in a high-dimensional nonlinear manifold. In Part II, we introduce machine learning approaches based on reproducing kernel Hilbert space (RKHS) to capture higher-order statistical characteristics of the nonlinear appearance manifold. In particular, we analyze principal components of the RKHS in a probabilistic manner and compute distances such as the Chernoff distance, the Kullback-Leibler divergence between two Gaussian densities in RKHS. Part III is on face tracking and recognition from video. We first present an enhanced tracking algorithm that models online appearance changes in a video sequence using a mixture model and produces good tracking results in various challenging scenarios. For video-based face recognition, while conventional approaches treat tracking and recognition separately, we present a simultaneous tracking-and-recognition approach. This simultaneous approach solved using the sequential importance sampling algorithm improves accuracy in both tracking and recognition. Finally, we propose a unifying framework called probabilistic identity characterization able to perform face recognition under registration/illumination/pose variation and from a still image, a group of still images, or a video sequence

Contemporary Robotics

This book book is a collection of 18 chapters written by internationally recognized experts and well-known professionals of the field. Chapters contribute to diverse facets of contemporary robotics and autonomous systems. The volume is organized in four thematic parts according to the main subjects, regarding the recent advances in the contemporary robotics. The first thematic topics of the book are devoted to the theoretical issues. This includes development of algorithms for automatic trajectory generation using redudancy resolution scheme, intelligent algorithms for robotic grasping, modelling approach for reactive mode handling of flexible manufacturing and design of an advanced controller for robot manipulators. The second part of the book deals with different aspects of robot calibration and sensing. This includes a geometric and treshold calibration of a multiple robotic line-vision system, robot-based inline 2D/3D quality monitoring using picture-giving and laser triangulation, and a study on prospective polymer composite materials for flexible tactile sensors. The third part addresses issues of mobile robots and multi-agent systems, including SLAM of mobile robots based on fusion of odometry and visual data, configuration of a localization system by a team of mobile robots, development of generic real-time motion controller for differential mobile robots, control of fuel cells of mobile robots, modelling of omni-directional wheeled-based robots, building of hunter- hybrid tracking environment, as well as design of a cooperative control in distributed population-based multi-agent approach. The fourth part presents recent approaches and results in humanoid and bioinspirative robotics. It deals with design of adaptive control of anthropomorphic biped gait, building of dynamic-based simulation for humanoid robot walking, building controller for perceptual motor control dynamics of humans and biomimetic approach to control mechatronic structure using smart materials

An investigation into the association between qualitatively different perceptions of the learning context and students' approaches to studying

Includes bibliography.A number of distinct paradigms exist in the field of research into student learning in higher education. It is inevitable that new research initiatives will adopt one of these paradigms as the primary focus of the investigation. However, the relationship that exists between paradigms is not one of mutual exclusivity; rather it is synergetic in nature with developments in one informing advances in another. The perspective adopted in this thesis research is grounded in the naturalistic investigations into student learning in higher education undertaken by Noel Entwistle and his fellow researchers. When reference is made to this distinctive paradigm it is not to suggest that other researchers, adopting fundamentally different paradigms, have not informed the development of the concepts and ideas that are distinctive to this perspective. Indeed, parallel work undertaken by John Biggs into student motivation and its relation to approaches to studying made a significant contribution to the development of specific aspects of the paradigm, a contribution which may not be explicitly clear to readers unfamiliar with the early development of the Approaches to Studying Inventory. Similarly, the pioneering work on the intellectual development of students in higher education undertaken by William Perry provided an important basis for the refinement of concepts within the paradigm that this thesis research has adopted. Because the work of these researchers is implicitly acknowledged, it is important to stress that their role was at least as important as the role of those whose contributions are more explicitly evident, and who subsequently took their ideas and developed them further within the specific paradigm

Molecular Imaging

The present book gives an exceptional overview of molecular imaging. Practical approach represents the red thread through the whole book, covering at the same time detailed background information that goes very deep into molecular as well as cellular level. Ideas how molecular imaging will develop in the near future present a special delicacy. This should be of special interest as the contributors are members of leading research groups from all over the world