Model Order Selection Rules For Covariance Structure Classification

The adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper. This represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties. The considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of Model Order Selection (MOS) is exploited to devise suitable decision rules. Several MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed. At the analysis stage, illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

Direct and Indirect Searches for Axion Dark Matter

The majority of the matter in the Universe is non-luminous and unaccounted for by any known particle, making the unknown nature of dark matter one of the most urgent problems in fundamental physics. Amidst a broad landscape of particles proposed to explain the dark matter, axions have emerged as a particularly well-motivated candidate as they naturally arise in extensions of the Standard Model and can simultaneously reproduce the observed dark matter abundance while solving other outstanding mysteries in particle physics. Despite this, axions have remained largely unprobed, and new insights and innovative approaches are required to carefully test the axion dark matter hypothesis. This thesis aims to advance prospects for axion detection by identifying how axion signals may appear, developing optimized searches for these signals, and implementing robust analysis strategies. I will begin by showing how simulations of axion production in the early universe can direct search efforts toward the best-motivated mass range for axions that solve the Strong textit{CP} Problem related to the absence of a neutron electric dipole moment in quantum chromodynamics. I will then discuss the development of rigorous analysis frameworks for axion direct detection and their application to the search for axion dark matter with the ABRACADABRA detector. Lastly, I will show how astrophysical observations with textit{X}-ray and radio telescopes can be used in novel searches for axion dark matter. This thesis contributes to an increasingly comprehensive search program that will either discover or exclude axion dark matter in the coming years.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169679/1/fosterjw_1.pd

Hypothesis Testing Using Spatially Dependent Heavy-Tailed Multisensor Data

The detection of spatially dependent heavy-tailed signals is considered in this dissertation. While the central limit theorem, and its implication of asymptotic normality of interacting random processes, is generally useful for the theoretical characterization of a wide variety of natural and man-made signals, sensor data from many different applications, in fact, are characterized by non-Gaussian distributions. A common characteristic observed in non-Gaussian data is the presence of heavy-tails or fat tails. For such data, the probability density function (p.d.f.) of extreme values decay at a slower-than-exponential rate, implying that extreme events occur with greater probability. When these events are observed simultaneously by several sensors, their observations are also spatially dependent. In this dissertation, we develop the theory of detection for such data, obtained through heterogeneous sensors. In order to validate our theoretical results and proposed algorithms, we collect and analyze the behavior of indoor footstep data using a linear array of seismic sensors. We characterize the inter-sensor dependence using copula theory. Copulas are parametric functions which bind univariate p.d.f. s, to generate a valid joint p.d.f. We model the heavy-tailed data using the class of alpha-stable distributions. We consider a two-sided test in the Neyman-Pearson framework and present an asymptotic analysis of the generalized likelihood test (GLRT). Both, nested and non-nested models are considered in the analysis. We also use a likelihood maximization-based copula selection scheme as an integral part of the detection process. Since many types of copula functions are available in the literature, selecting the appropriate copula becomes an important component of the detection problem. The performance of the proposed scheme is evaluated numerically on simulated data, as well as using indoor seismic data. With appropriately selected models, our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of 10^-4. These results, using dependent alpha-stable signals, are presented for a two-sensor case. We identify the computational challenges associated with dependent alpha-stable modeling and propose alternative schemes to extend the detector design to a multisensor (multivariate) setting. We use a hierarchical tree based approach, called vines, to model the multivariate copulas, i.e., model the spatial dependence between multiple sensors. The performance of the proposed detectors under the vine-based scheme are evaluated on the indoor footstep data, and significant improvement is observed when compared against the case when only two sensors are deployed. Some open research issues are identified and discussed

Listening to the Universe through Indirect Detection

Indirect detection is the search for the particle nature of dark matter with astrophysical probes. Manifestly, it exists right at the intersection of particle physics and astrophysics, and the discovery potential for dark matter can be greatly extended using insights from both disciplines. This thesis provides an exploration of this philosophy. On the one hand, I will show how astrophysical observations of dark matter, through its gravitational interaction, can be exploited to determine the most promising locations on the sky to observe a particle dark matter signal. On the other, I demonstrate that refined theoretical calculations of the expected dark matter interactions can be used disentangle signals from astrophysical backgrounds. Both of these approaches will be discussed in the context of general searches, but also applied to the case of an excess of photons observed at the center of the Milky Way. This galactic center excess represents both the challenges and joys of indirect detection. Initially thought to be a signal of annihilating dark matter at the center of our own galaxy, it now appears more likely to be associated with a population of millisecond pulsars. Yet these pulsars were completely unanticipated, and highlight that indirect detection can lead to many new insights about the universe, hopefully one day including the particle nature of dark matter.Comment: Ph.D. thesis, MIT, April 2018; based on the work appearing in arXiv:1708.09385, arXiv:1612.05638, arXiv:1612.04814, arXiv:1511.08787, arXiv:1503.01773, and arXiv:1402.670

A Search For Nothing: Dark Matter And Invisible Decays Of The Higgs Boson At The Atlas Detector

This thesis presents a search for invisible decays of the Higgs boson using the vector boson fusion channel. This uses 36 fb^−1 of proton-proton collision data at √s = 13 TeV using the ATLAS detector at the Large Hadron Collider. The experimental methods for understanding the signal and background processes as well as detector effects are described in detail. The search is carried out in several regions defined by kinematic requirements on the final-state objects, and the observed event yields are used in a profile-likelihood fit in order to constrain the backgrounds. The results are interpreted using a modified frequentist method and are found to be consistent with the Standard Model expectations. An upper limit of 34% (28% expected) at 95% C.L. is placed on the invisible branching ratio of the Higgs boson. Re-interpretation of these results in terms of dark matter is also discussed, in the context of the Higgs portal and other simplified models

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays

This review is focused on tests of Einstein's theory of General Relativity with gravitational waves that are detectable by ground-based interferometers and pulsar timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and compactnesses can reach a half. This review begins with the theoretical basis and the predicted gravitational wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational wave interferometers and pulsar timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational wave tests for compact binary systems.Comment: 123 pages, 5 figures, replaced with version accepted for publication in the Living Reviews in Relativit