Single Particle Tracking: Analysis Techniques for Live Cell Nanoscopy.

Single molecule experiments are a set of experiments designed specifically to study the properties of individual molecules. It has only been in the last three decades where single molecule experiments have been applied to the life sciences; where they have been successfully implemented in systems biology for probing the behaviors of sub-cellular mechanisms. The advent and growth of super-resolution techniques in single molecule experiments has made the fundamental behaviors of light and the associated nano-probes a necessary concern among life scientists wishing to advance the state of human knowledge in biology. This dissertation disseminates some of the practices learned in experimental live cell microscopy. The topic of single particle tracking is addressed here in a format that is designed for the physicist who embarks upon single molecule studies. Specifically, the focus is on the necessary procedures to generate single particle tracking analysis techniques that can be implemented to answer biological questions. These analysis techniques range from designing and testing a particle tracking algorithm to inferring model parameters once an image has been processed. The intellectual contributions of the author include the techniques in diffusion estimation, localization filtering, and trajectory associations for tracking which will all be discussed in detail in later chapters. The author of this thesis has also contributed to the software development of automated gain calibration, live cell particle simulations, and various single particle tracking packages. Future work includes further evaluation of this laboratory\u27s single particle tracking software, entropy based approaches towards hypothesis validations, and the uncertainty quantification of gain calibration

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

Inverse problem theory in shape and action modeling

In this thesis we consider shape and action modeling problems under the perspective of inverse problem theory. Inverse problem theory proposes a mathematical framework for solving model parameter estimation problems. Inverse problems are typically ill-posed, which makes their solution challenging. Regularization theory and Bayesian statistical methods, which are proposed in the context of inverse problem theory, provide suitable methods for dealing with ill-posed problems. Regarding the application of inverse problem theory in shape and action modeling, we first discuss the problem of saliency prediction, considering a model proposed by the coherence theory of attention. According to coherence theory, salience regions emerge via proto-objects which we model using harmonic functions (thin-membranes). We also discuss the modeling of the 3D scene, as it is fundamental for extracting suitable scene features, which guide the generation of proto-objects. The next application we consider is the problem of image fusion. In this context, we propose a variational image fusion framework, based on confidence driven total variation regularization, and we consider its application to the problem of depth image fusion, which is an important step in the dense 3D scene reconstruction pipeline. The third problem we encounter regards action modeling, and in particular the recognition of human actions based on 3D data. Here, we employ a Bayesian nonparametric model to capture the idiosyncratic motions of the different body parts. Recognition is achieved by comparing the motion behaviors of the subject to a dictionary of behaviors for each action, learned by examples collected from other subjects. Next, we consider the 3D modeling of articulated objects from images taken from the web, with application to the 3D modeling of animals. By decomposing the full object in rigid components and by considering different aspects of these components, we model the object up this hierarchy, in order to obtain a 3D model of the entire object. Single view 3D modeling as well as model registration is performed, based on regularization methods. The last problem we consider, is the modeling of 3D specular (non-Lambertian) surfaces from a single image. To solve this challenging problem we propose a Bayesian non-parametric model for estimating the normal field of the surface from its appearance, by identifying the material of the surface. After computing an initial model of the surface, we apply regularization of its normal field considering also a photo-consistency constraint, in order to estimate the final shape of the surface. Finally, we conclude this thesis by summarizing the most significant results and by suggesting future directions regarding the application of inverse problem theory to challenging computer vision problems, as the ones encountered in this work

Recent Advances in Single-Particle Tracking: Experiment and Analysis

This Special Issue of Entropy, titled “Recent Advances in Single-Particle Tracking: Experiment and Analysis”, contains a collection of 13 papers concerning different aspects of single-particle tracking, a popular experimental technique that has deeply penetrated molecular biology and statistical and chemical physics. Presenting original research, yet written in an accessible style, this collection will be useful for both newcomers to the field and more experienced researchers looking for some reference. Several papers are written by authorities in the field, and the topics cover aspects of experimental setups, analytical methods of tracking data analysis, a machine learning approach to data and, finally, some more general issues related to diffusion

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

Bayesian Inference Approaches for Particle Trajectory Analysis in Cell Biology

Despite the importance of single particle motion in biological systems, systematic inference approaches to analyze particle trajectories and evaluate competing motion models are lacking. An automated approach for robust evaluation of motion models that does not require manual intervention is highly desirable to enable analysis of datasets from high-throughput imaging technologies that contain hundreds or thousands of trajectories of biological particles, such as membrane receptors, vesicles, chromosomes or kinetochores, mRNA particles, or whole cells in developing embryos. Bayesian inference is a general theoretical framework for performing such model comparisons that has proven successful in handling noise and experimental limitations in other biological applications. The inherent Bayesian penalty on model complexity, which avoids overfitting, is particularly important for particle trajectory analysis given the highly stochastic nature of particle diffusion. This thesis presents two complementary approaches for analyzing particle motion using Bayesian inference. The first method, MSD-Bayes, discriminates a wide range of motion models--including diffusion, directed motion, anomalous and confined diffusion--based on mean- square displacement analysis of a set of particle trajectories, while the second method, HMM-Bayes, identifies dynamic switching between diffusive and directed motion along individual trajectories using hidden Markov models. These approaches are validated on biological particle trajectory datasets from a wide range of experimental systems, demonstrating their broad applicability to research in cell biology

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas

Modelling and inference of spatio-temporal processes in Single Molecule Localisation Microscopy

Recent advancements in super-resolution microscopy have enabled cellular structures to be imaged beyond sub-diffraction limits. In order to do so, a widely used class of super resolution methods called single molecule localisation microscopy (SMLM) exploit the stochastic nature of fluorescent probes, or fluorophores, that move between bright and dark states until they permanently cease to transition. When observing a large number of fluorophores, this behaviour enables only a sparse subset of them to be detected at any one time, resulting in the ability to accurately record and accumulate their spatial measurements to produce a super-resolved image. While this stochastic behaviour has been heavily exploited, it induces multiple localisations per molecule which gives rise to misleading representations of the true structures of interest. Accurate quantification of the underlying photo-kinetic behaviour is therefore required before any spatial analysis can be conducted. In this thesis, we model the photo-kinetic behaviour of a molecule as a continuous time Markov process that can transition between a photo-emitting On state, several (unknown) non-photon emitting dark states and an permanently dark state. From this, we develop the Photo-Switching Hidden Markov Model (PSHMM) which relates this underlying behaviour to an observed signal indicating whether or not a molecule is detected in a given frame. Under this model, we derive a maximum likelihood estimator which is used to estimate the unknown transition rates and photo-kinetic model. Under different experimental conditions, the statistical properties of this estimator are also investigated. When an unknown number of fluorescing molecules is filmed, the PSHMM set-up subsequently allows us to derive the distribution of the total number of observed localisations in an experiment, from which an accurate molecular counting tool can be constructed. Finally, we formulate true molecular positions as a spatio-temporal hidden point process and describe the observation process it generates at each time step. The full Bayes filter is then derived, from which the point process and static parameters of the model can be inferred using Markov Chain Monte Carlo (MCMC).Open Acces