477 research outputs found
Inference in particle tracking experiments by passing messages between images
Methods to extract information from the tracking of mobile objects/particles
have broad interest in biological and physical sciences. Techniques based on
simple criteria of proximity in time-consecutive snapshots are useful to
identify the trajectories of the particles. However, they become problematic as
the motility and/or the density of the particles increases due to uncertainties
on the trajectories that particles followed during the images' acquisition
time. Here, we report an efficient method for learning parameters of the
dynamics of the particles from their positions in time-consecutive images. Our
algorithm belongs to the class of message-passing algorithms, known in computer
science, information theory and statistical physics as Belief Propagation (BP).
The algorithm is distributed, thus allowing parallel implementation suitable
for computations on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle tracking in
turbulent flows, which is particularly challenging due to the strong transport
that those flows produce. Our numerical experiments show that the BP algorithm
compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is
far superior in speed. We also suggest and analyze a random-distance model that
provides theoretical justification for BP accuracy. Methods developed here
systematically formulate the problem of particle tracking and provide fast and
reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure
Simulation of colloidal suspension systems
The research work is focused on the development of a simulation platform for colloidal suspension. Based on discrete element method (DEM), the model developed takes into account the crucial interactions, i.e. the electrostatic repulsion, van der Waals attraction, Brownian force, hydration effects and hydrodynamic force. The mechanism of colloid particle diffusion in confined space and the combined influences of fluid flow field, geometrical confinement, and the interparticle interactions on the self-assembly process are investigated
Air-Fluidized Grains as a Model System: Self-Propelling and Jamming
This thesis examines two concepts -- self-propelling and jamming -- that have been employed to unify disparate non-equilibrium systems, in the context of a monolayer of grains fluidized by a temporally and spatially homogeneous upflow of air. The first experiment examines the single particle dynamics of air-fluidized rods. For Brownian rods, equipartition of energy holds and rotational motion sets a timescale after which directional memory is lost. Air-fluidized rods no longer obey equipartion; they self-propel, moving preferentially along their long axis. We show that self-propelling can be treated phenomenologically as an enhanced memory effect causing directional memory to persist for times longer than expected for thermal systems. The second experiment studies dense collections of self-propelling air-fluidized rods. We observe collective propagating modes that give rise to anomalously large fluctuations in the local number density. We quantify these compression waves by calculating the dynamic structure factor and show that the wavespeed is weakly linear with increasing density. It has been suggested that the observed behavior might be explained using the framework put forth by Baskaran et al. The third experiment seeks to determine whether a force analogous to the critical Casimir force in fluids exists for a large sphere fluidized in the presence of a background of smaller spheres. The behavior of such a large sphere is fully characterized showing that, rather than behaving like a sphere driven by turbulence, the large ball self-propels. We also show that the background is responsible for the purely attractive, intermediate-ranged interaction force between two simultaneously-fluidized large balls. The final experiment seeks to determine what parameters control the diverging relaxation timescale associated with the jamming transition. By tilting our apparatus, we quantify pressure, packing fraction, and temperature simultaneously with dynamics as we approach jamming. We obtain an equation of state that agrees well with simulation and free volume theory. We collapse the relaxation time by defining a time- and energy-scale using pressure, consistent with recent simulation. These experiments are further confirmation of the universality of the concepts of self-propelling and jamming
Dynamical models and machine learning for supervised segmentation
This thesis is concerned with the problem of how to outline regions of interest in medical images, when
the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning
and interactivity leads to a common theme of the need to balance conflicting requirements. First,
any machine learning method must strike a balance between how much it can learn and how well it
generalises. Second, interactive methods must balance minimal user demand with maximal user control.
To address the problem of weak boundaries,methods of supervised texture classification are investigated
that do not use explicit texture features. These methods enable prior knowledge about the image to
benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary
tracking, combines these image priors with efficient modes of interaction. We show the benefits of the
texture classifiers over intensity and gradient-based image models, in both classification and boundary
extraction.
To address the problem of irregular region shape, we devise a new type of statistical shape model
(SSM) that does not use explicit boundary features or assume high-level similarity between region
shapes. First, the models are used for shape discrimination, to constrain any segmentation framework
by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation
frameworks to draw shapes from a prior distribution. The generative models also include
novel methods to constrain shape generation according to information from both the image and user
interactions.
The shape models are first evaluated in terms of discrimination capability, and shown to out-perform
other shape descriptors. Experiments also show that the shape models can benefit a standard type of
segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape
models in supervised segmentation frameworks, and evaluate their benefits in user trials
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Advanced Bayesian Monte Carlo Methods for Inference and Control
Monte Carlo methods are are an ubiquitous tool in modern statistics. Under the Bayesian paradigm, they are used for estimating otherwise intractable integrals arising when integrating a function with respect to a posterior distribution . This thesis discusses several aspects of such Monte Carlo methods.
The first discussion evolves around the problem of sampling from only almost everywhere differentiable distributions, a class of distributions which includes all log-concave posteriors. A new sampling method based on a second-order diffusion process is proposed, new theoretical results are proved, and extensive numerical illustrations elucidate the benefits and weaknesses of various methods applicable in these settings.
In high-dimensional settings, one can exploit local structures of inverse problems to parallelise computations. This will be explored in both fully localisable problems, and problems where conditional independence of variables given some others holds only approximately. This thesis proposes two algorithms using parallelisation techniques, and shows their empirical performance on two localisable imaging problems.
Another problem arises when defining function space priors over high-dimensional domains. The commonly used Karhunen-Loève priors suffer from bad dimensional scaling: they require an orthogonal basis of the function space, which can often be obtained as a product of one-dimensional basis functions. This leads to the number of parameters growing exponentially in the dimension of the function domain. The trace-class neural network prior, proposed in this thesis, scales more favourably in the dimension of the function's domain. This prior is a Bayesian neural network prior, where each weight and bias has an independent Gaussian prior, but with a key difference to existing Bayesian neural network priors: the variances decrease in the width of the network, such that the variances form a summable sequence and the infinite width limit neural network is well defined. As is shown in this thesis, the resulting posterior of the unknown function is amenable to sampling using Hilbert space Markov chain Monte Carlo methods. These sampling methods are favoured because they are stable under mesh-refinement, in the sense that the acceptance probability does not shrink to 0 as more parameters are introduced to better approximate the well-defined infinite limit. Both numerical illustrations and theoretical results show that these priors are competitive and have distinct advantages over other function space priors.
These different function space priors are then used in stochastic control. To this end, a suitable likelihood for continuous value functions in a Bayesian approach to reinforcement learning is defined. This thesis proves that it can be used in conjunction with both the classical Karhunen-Loève prior and the proposed trace-class neural network prior. Numerical examples compare the resulting posteriors, and illustrate the new prior's performance and dimension robustness.Cantab Capital Institute for the Mathematics of Informatio
Structure and dynamics of the E. coli chemotaxis core signaling complex by cryo-electron tomography and molecular simulations
To enable the processing of chemical gradients, chemotactic bacteria possess large arrays of transmembrane chemoreceptors, the histidine kinase CheA, and the adaptor protein CheW, organized as coupled core-signaling units (CSU). Despite decades of study, important questions surrounding the molecular mechanisms of sensory signal transduction remain unresolved, owing especially to the lack of a high-resolution CSU structure. Here, we use cryo-electron tomography and sub-tomogram averaging to determine a structure of the Escherichia coli CSU at sub-nanometer resolution. Based on our experimental data, we use molecular simulations to construct an atomistic model of the CSU, enabling a detailed characterization of CheA conformational dynamics in its native structural context. We identify multiple, distinct conformations of the critical P4 domain as well as asymmetries in the localization of the P3 bundle, offering several novel insights into the CheA signaling mechanism
Pattern-theoretic foundations of automatic target recognition in clutter
Issued as final reportAir Force Office of Scientific Research (U.S.
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