Computing Approximate Statistical Discrepancy

Consider a geometric range space (X,A) where X is comprised of the union of a red set R and blue set B. Let Phi(A) define the absolute difference between the fraction of red and fraction of blue points which fall in the range A. The maximum discrepancy range A^* = arg max_{A in (X,A)} Phi(A). Our goal is to find some A^ in (X,A) such that Phi(A^*) - Phi(A^) <= epsilon. We develop general algorithms for this approximation problem for range spaces with bounded VC-dimension, as well as significant improvements for specific geometric range spaces defined by balls, halfspaces, and axis-aligned rectangles. This problem has direct applications in discrepancy evaluation and classification, and we also show an improved reduction to a class of problems in spatial scan statistics

Approximate Maximum Halfspace Discrepancy

Consider the geometric range space (X, H_d) where X ? ?^d and H_d is the set of ranges defined by d-dimensional halfspaces. In this setting we consider that X is the disjoint union of a red and blue set. For each halfspace h ? H_d define a function ?(h) that measures the "difference" between the fraction of red and fraction of blue points which fall in the range h. In this context the maximum discrepancy problem is to find the h^* = arg max_{h ? (X, H_d)} ?(h). We aim to instead find an h? such that ?(h^*) - ?(h?) ? ?. This is the central problem in linear classification for machine learning, in spatial scan statistics for spatial anomaly detection, and shows up in many other areas. We provide a solution for this problem in O(|X| + (1/?^d) log? (1/?)) time, for constant d, which improves polynomially over the previous best solutions. For d = 2 we show that this is nearly tight through conditional lower bounds. For different classes of ? we can either provide a ?(|X|^{3/2 - o(1)}) time lower bound for the exact solution with a reduction to APSP, or an ?(|X| + 1/?^{2-o(1)}) lower bound for the approximate solution with a reduction to 3Sum. A key technical result is a ?-approximate halfspace range counting data structure of size O(1/?^d) with O(log (1/?)) query time, which we can build in O(|X| + (1/?^d) log? (1/?)) time

Practical Low-Dimensional Halfspace Range Space Sampling

We develop, analyze, implement, and compare new algorithms for creating epsilon-samples of range spaces defined by halfspaces which have size sub-quadratic in 1/epsilon, and have runtime linear in the input size and near-quadratic in 1/epsilon. The key to our solution is an efficient construction of partition trees. Despite not requiring any techniques developed after the early 1990s, apparently such a result was never explicitly described. We demonstrate that our implementations, including new implementations of several variants of partition trees, do indeed run in time linear in the input, appear to run linear in output size, and observe smaller error for the same size sample compared to the ubiquitous random sample (which requires size quadratic in 1/epsilon). This result has direct applications in speeding up discrepancy evaluation, approximate range counting, and spatial anomaly detection

A Nanoscale Parametric Feedback Oscillator

We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry and system-size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in this size regime

THE FORGOTTEN ALLY: U.S./SOUTH KOREAN RELATIONS DURING THE VIETNAM WAR

South Korea participated in the Vietnam War as America’s ally on a tremendous scale involving over 300,000 soldiers from 1964-1973. Despite this massive commitment, South Korea’s involvement has attracted little scholarly interest or public attention. The prevailing explanation in relevant historiography often dismisses South Korea’s role as a mercenary exchange taken under U.S. pressure or in pursuit of economic incentives. Alternatively, I argue that the South Korean government had a legitimate national interest in participating in the Vietnam War in pursuit of political, national defense, and economic advancements that were uniquely motivated by concurrent hostilities with North Korea. South Korea’s national interests aligned with the U.S. such that they willingly and effectively contributed to the Vietnam War. By the war’s end, U.S. and South Korean national interests diverged sharply as relations declined, which left South Korea’s wartime role as an embattled and largely forgotten memory in the U.S

Development of statistical methodologies and risk models to perform real-time safety monitoring in interventional cardiology

Thesis (S.M.)--Harvard-MIT Division of Health Sciences and Technology, 2006.Vita.Includes bibliographical references (p. 52-56).Post-marketing surveillance of medical pharmaceuticals and devices has received a great deal of media, legislative, and academic attention in the last decade. Among medical devices, these have largely been due to a small number of highly publicized adverse events, some of them in the domain of cardiac surgery and interventional cardiology. Phase three clinical trials for these devices are generally underpowered to detect rare adverse event rates, are performed in near-optimal environments, and regulators face significant pressure to deliver important medical devices to the public in a timely fashion. All of these factors emphasize the importance of systematic monitoring of these devices after being released to the public, and the FDA and other regulatory agencies continue to struggle to perform this duty using a variety of voluntary and mandatory adverse event rate reporting policies. Data quality and comprehensiveness have generally suffered in this environment, and delayed awareness of potential problems. However, a number of mandatory reporting policies combined with improved standardization of data collection and definitions in the field of interventional cardiology and other clinical domains have provided recent opportunities for nearly "real-time" safety monitoring of medical device data.(cont.) Existing safety monitoring methodologies are non-medical in nature, and not well adapted to the relatively heterogeneous and noisy data common in medical applications. A web-based database-driven computer application was designed, and a number of experimental statistical methodologies were adapted from non-medical monitoring techniques as a proof of concept for the utility of an automated safety monitoring application. This application was successfully evaluated by comparing a local institution's drug-eluting stent in-hospital mortality rates to University of Michigan's bare-metal stent event rates. Sensitivity analyses of the experimental methodologies were performed, and a number of notable performance parameters were discovered. In addition, an evaluation of a number of well-validated external logistic regression models, and found that while population level estimation was well-preserved, individual estimation was compromised by application to external data. Subsequently, exploration of an alternative modeling technique, support vector machines, was performed in an effort to find a method with superior calibration performance for use in the safety monitoring application.by Michael E. Matheny.S.M

Hospital Mortality in the United States following Acute Kidney Injury

Acute kidney injury (AKI) is a common reason for hospital admission and complication of many inpatient procedures. The temporal incidence of AKI and the association of AKI admissions with in-hospital mortality are a growing problem in the world today. In this review, we discuss the epidemiology of AKI and its association with in-hospital mortality in the United States. AKI has been growing at a rate of 14% per year since 2001. However, the in-hospital mortality associated with AKI has been on the decline starting with 21.9% in 2001 to 9.1 in 2011, even though the number of AKI-related in-hospital deaths increased almost twofold from 147,943 to 285,768 deaths. We discuss the importance of the 71% reduction in AKI-related mortality among hospitalized patients in the United States and draw on the discussion of whether or not this is a phenomenon of hospital billing (coding) or improvements to the management of AKI