Statistical and Computational Tradeoffs in Stochastic Composite Likelihood

Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of the estimators resolve the computation-accuracy tradeoff differently, and taken together they span a continuous spectrum of computation-accuracy tradeoff resolutions. We prove the consistency of the estimators, provide formulas for their asymptotic variance, statistical robustness, and computational complexity. We discuss experimental results in the context of Boltzmann machines and conditional random fields. The theoretical and experimental studies demonstrate the effectiveness of the estimators when the computational resources are insufficient. They also demonstrate that in some cases reduced computational complexity is associated with robustness thereby increasing statistical accuracy.Comment: 30 pages, 97 figures, 2 author

Redundant Array Configurations for 21 cm Cosmology

Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays--in which the same mode on the sky is sampled by many antenna pairs--for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epoch of Reionization Array (HERA) as an interferometer with a dense, redundant core designed following these lessons to be optimized for 21 cm cosmology. We show how modestly supplementing or modifying a compact design like HERA's can still deliver high sensitivity while enhancing strategies for calibration and foreground mitigation. In particular, we compare the imaging capability of several array configurations, both instantaneously (to address instrumental and ionospheric effects) and with rotation synthesis (for foreground removal). We also examine the effects that configuration has on calibratability using instantaneous redundancy. We find that improved imaging with sub-aperture sampling via "off-grid" antennas and increased angular resolution via far-flung "outrigger" antennas is possible with a redundantly calibratable array configuration.Comment: 19 pages, 11 figures. Revised to match the accepted ApJ versio

Asymptotic Analysis of Generative Semi-Supervised Learning

Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP.Comment: 12 pages, 9 figure

Development of a Nucleus Pulposus Implant for Intervertebral Disc Repair

The intervertebral disc (IVD) is a fibrocartilaginous tissue connecting adjacent vertebrae in the spinal column. It comprises three distinct tissues: a gelatinous core known as the nucleus pulposus (NP), concentric fibrous rings encircling the NP known as the annulus fibrosus (AF), and the superior/inferior cartilaginous endplates (CEPs). The complex mechanical interplay of these tissues allows the IVD to withstand complex loading in the spine while maintaining trunk stability and flexibility. IVD pathologies, such as IVD degeneration (IDD) and herniation, are associated with cell-mediated inflammation in vivo. This inflammation creates a catabolic environment which degrades the extracellular matrix (ECM) of the IVD. Since ECM composition influences the mechanical properties of the tissue, this degradation compromises spine biomechanics, which may lead to low back pain, radiculopathy, and disability. Current treatment strategies for IVD pathologies are either palliative or are aggressive and only partly redress spine biomechanics. Furthermore, current interventions are not regenerative and may induce collateral pathologies in adjacent IVDs due to abnormal biomechanics post-repair. Mechanically robust scaffolds derived from decellularized tissues have the potential to re-establish spine biomechanics, alleviate the underlying pathology, and regenerate the native tissue. We have previously demonstrated the ability to decellularize bovine NP to form acellular bovine NP (ABNP), which exhibited a biomimetic ECM composition, supported cell seeding, and partially restored spine kinematics in an ex vivo model of IVD injury. Despite this, further refinement was necessary to improve its mechanical properties and characterize its regenerative potential. Furthermore, prior to translation, the ABNP must be evaluated using a well-characterized animal model that reproduces clinically relevant aspects of IDD. The goals of this research were to: i) fortify the mechanical properties of the ABNP, ii) determine the in vitro cytocompatibility and regenerative capacity of the ABNP, and iii) characterize a novel animal model of IVD degeneration for future in vivo testing of the implant

ELECTRO-MECHANICAL-THERMAL MODELING AND STABILITY OF PULSED POWER LOADS ON A DC NETWORK

Modern military aircraft are developing larger pulsed power loads varying from new weapon technologies to advanced avionics and other electrical equipment. Pulsing power loads emulate a pulse width modulated signal which have non-linear destabilizing effects on the electrical system. Additionally, these devices have thermal properties that can induce electrical stability issues at low and high temperatures and various pulsing load conditions. These non-linear electrical stability issues carry through to the mechanical and thermal systems of the aircraft and can damage components. The MATLAB/Simulink workspace is used to simulate a non-linear model of an aircraft’s electrical-mechanicalthermal (EMT) system. This system includes electrical generation with constant and pulsing power loads, mechanical fluid pumping, and thermal cooling systems. The goal of the EMT model is to demonstrate the destabilizing effects caused by both the thermal coupling of the pulsing load and the large signal analysis of the PWM signal. An operational boundary of the power pulsed device is found by varying the duty cycle for a given pulse period and power load based on bus voltage transients and voltage drop limits. The system is defined metastable for a given set of parameters if the system experiences periods of stability and instability based on varying operating points. Regions of complete stability, metastability, marginal metastability, and instability are determined based on bus voltage transient tolerances. Analyzing the marginally metastable boundary layer, thermal analysis is performed at different points of equivalent average power and varying pulse energy. Post processing the results determines the most efficient operational region of the system given thermal and electrical requirements

Detecting the 21 cm Forest in the 21 cm Power Spectrum

We describe a new technique for constraining the radio loud population of active galactic nuclei at high redshift by measuring the imprint of 21 cm spectral absorption features (the 21 cm forest) on the 21 cm power spectrum. Using semi-numerical simulations of the intergalactic medium and a semi-empirical source population we show that the 21 cm forest dominates a distinctive region of $k$-space, $k \gtrsim 0.5 \text{Mpc}^{-1}$. By simulating foregrounds and noise for current and potential radio arrays, we find that a next generation instrument with a collecting area on the order of $\sim 0.1\text{km}^2$ (such as the Hydrogen Epoch of Reionization Array) may separately constrain the X-ray heating history at large spatial scales and radio loud active galactic nuclei of the model we study at small ones. We extrapolate our detectability predictions for a single radio loud active galactic nuclei population to arbitrary source scenarios by analytically relating the 21 cm forest power spectrum to the optical depth power spectrum and an integral over the radio luminosity function.Comment: 20 pages, 17 figures, accepted for publication in MNRA