Statistical Treatment of Gravitational Clustering Algorithm

In neuroscience, simultaneously recorded spike trains from multiple neurons are increasingly common; however, the computational neuroscience problem of how to quantitatively analyze such data remains a challenge. Gerstein, et al. proposed a gravitational clustering algorithm (GCA) for multiple spike trains to qualitatively study interactions, in particular excitation, among multiple neurons. This thesis is mainly focused on a probabilistic treatment of GCA and a statistical treatment of Gerstein's interaction mode.For a formal probabilistic treatment, we adopt homogeneous Poisson processes to generate the spike trains; define an interaction mode based on Gerstein's formulation; analyze the asymptotic properties of its cluster index -- GCA distances (GCAD). Under this framework, we show how the expectation of GCAD is related to a particular interaction mode, i.e., we prove that a time-adjusted-GCAD is a reasonable cluster index for large samples. We also indicate possible stronger results, such as central limit theorems and convergence to a Gaussian process. In our statistical work, we construct a generalized mixture model to estimate Gerstein's interaction mode. We notice two key features of Gerstein's proposal: (1) each spike from each spike train was assumed to be triggered by either one previous spike from one other spike train or environment; (2) each spike train was transformed into a continuous longitudinal curve. Inspired by their work, we develop a Bayesian model to quantitatively estimate excitation effects in the network structure. Our approach generalizes the mixture model to accommodate the network structure through a matrix Dirichlet distribution. The network structure in our model could either approximate the directed acyclic graph of a Bayesian network or be the directed graph in a dynamic Bayesian network. This model can be generally applied on high-dimensional longitudinal data to model its dynamics. Finally, we assess the sampling properties of this model and its application to multiple spike trains by simulation

Bayesian analysis of multiple direct detection experiments

Bayesian methods offer a coherent and efficient framework for implementing uncertainties into induction problems. In this article, we review how this approach applies to the analysis of dark matter direct detection experiments. In particular we discuss the exclusion limit of XENON100 and the debated hints of detection under the hypothesis of a WIMP signal. Within parameter inference, marginalizing consistently over uncertainties to extract robust posterior probability distributions, we find that the claimed tension between XENON100 and the other experiments can be partially alleviated in isospin violating scenario, while elastic scattering model appears to be compatible with the frequentist statistical approach. We then move to model comparison, for which Bayesian methods are particularly well suited. Firstly, we investigate the annual modulation seen in CoGeNT data, finding that there is weak evidence for a modulation. Modulation models due to other physics compare unfavorably with the WIMP models, paying the price for their excessive complexity. Secondly, we confront several coherent scattering models to determine the current best physical scenario compatible with the experimental hints. We find that exothermic and inelastic dark matter are moderatly disfavored against the elastic scenario, while the isospin violating model has a similar evidence. Lastly the Bayes' factor gives inconclusive evidence for an incompatibility between the data sets of XENON100 and the hints of detection. The same question assessed with goodness of fit would indicate a 2 sigma discrepancy. This suggests that more data are therefore needed to settle this question.Comment: 29 pages, 8 figures; invited review for the special issue of the journal Physics of the Dark Universe; matches the published versio

Bayesian Inference in Processing Experimental Data: Principles and Basic Applications

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; Monte Carlo estimates of expectation, including a short introduction to Markov Chain Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic

Identifying Humans by the Shape of Their Heartbeats and Materials by Their X-Ray Scattering Profiles

Security needs at access control points presents itself in the form of human identification and/or material identification. The field of Biometrics deals with the problem of identifying individuals based on the signal measured from them. One approach to material identification involves matching their x-ray scattering profiles with a database of known materials. Classical biometric traits such as fingerprints, facial images, speech, iris and retinal scans are plagued by potential circumvention they could be copied and later used by an impostor. To address this problem, other bodily traits such as the electrical signal acquired from the brain (electroencephalogram) or the heart (electrocardiogram) and the mechanical signals acquired from the heart (heart sound, laser Doppler vibrometry measures of the carotid pulse) have been investigated. These signals depend on the physiology of the body, and require the individual to be alive and present during acquisition, potentially overcoming circumvention. We investigate the use of the electrocardiogram (ECG) and carotid laser Doppler vibrometry (LDV) signal, both individually and in unison, for biometric identity recognition. A parametric modeling approach to system design is employed, where the system parameters are estimated from training data. The estimated model is then validated using testing data. A typical identity recognition system can operate in either the authentication (verification) or identification mode. The performance of the biometric identity recognition systems is evaluated using receiver operating characteristic (ROC) or detection error tradeoff (DET) curves, in the authentication mode, and cumulative match characteristic (CMC) curves, in the identification mode. The performance of the ECG- and LDV-based identity recognition systems is comparable, but is worse than those of classical biometric systems. Authentication performance below 1% equal error rate (EER) can be attained when the training and testing data are obtained from a single measurement session. When the training and testing data are obtained from different measurement sessions, allowing for a potential short-term or long-term change in the physiology, the authentication EER performance degrades to about 6 to 7%. Leveraging both the electrical (ECG) and mechanical (LDV) aspects of the heart, we obtain a performance gain of over 50%, relative to each individual ECG-based or LDV-based identity recognition system, bringing us closer to the performance of classical biometrics, with the added advantage of anti-circumvention. We consider the problem of designing combined x-ray attenuation and scatter systems and the algorithms to reconstruct images from the systems. As is the case within a computational imaging framework, we tackle the problem by taking a joint system and algorithm design approach. Accurate modeling of the attenuation of incident and scattered photons within a scatter imaging setup will ultimately lead to more accurate estimates of the scatter densities of an illuminated object. Such scattering densities can then be used in material classification. In x-ray scatter imaging, tomographic measurements of the forward scatter distribution are used to infer scatter densities within a volume. A mask placed between the object and the detector array provides information about scatter angles. An efficient computational implementation of the forward and backward model facilitates iterative algorithms based upon a Poisson log-likelihood. The design of the scatter imaging system influences the algorithmic choices we make. In turn, the need for efficient algorithms guides the system design. We begin by analyzing an x-ray scatter system fitted with a fanbeam source distribution and flat-panel energy-integrating detectors. Efficient algorithms for reconstructing object scatter densities from scatter measurements made on this system are developed. Building on the fanbeam source, energy-integrating at-panel detection model, we develop a pencil beam model and an energy-sensitive detection model. The scatter forward models and reconstruction algorithms are validated on simulated, Monte Carlo, and real data. We describe a prototype x-ray attenuation scanner, co-registered with the scatter system, which was built to provide complementary attenuation information to the scatter reconstruction and present results of applying alternating minimization reconstruction algorithms on measurements from the scanner

Deep Learning for Decision Making and Autonomous Complex Systems

Deep learning consists of various machine learning algorithms that aim to learn multiple levels of abstraction from data in a hierarchical manner. It is a tool to construct models using the data that mimics a real world process without an exceedingly tedious modelling of the actual process. We show that deep learning is a viable solution to decision making in mechanical engineering problems and complex physical systems. In this work, we demonstrated the application of this data-driven method in the design of microfluidic devices to serve as a map between the user-defined cross-sectional shape of the flow and the corresponding arrangement of micropillars in the flow channel that contributed to the flow deformation. We also present how deep learning can be used in the early detection of combustion instability for prognostics and health monitoring of a combustion engine, such that appropriate measures can be taken to prevent detrimental effects as a result of unstable combustion. One of the applications in complex systems concerns robotic path planning via the systematic learning of policies and associated rewards. In this context, a deep architecture is implemented to infer the expected value of information gained by performing an action based on the states of the environment. We also applied deep learning-based methods to enhance natural low-light images in the context of a surveillance framework and autonomous robots. Further, we looked at how machine learning methods can be used to perform root-cause analysis in cyber-physical systems subjected to a wide variety of operation anomalies. In all studies, the proposed frameworks have been shown to demonstrate promising feasibility and provided credible results for large-scale implementation in the industry