Universality laws for randomized dimension reduction, with applications

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain geometric features of the set. The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability. This paper studies a natural family of randomized dimension reduction maps and a large class of data sets. It proves that there is a phase transition in the success probability of the dimension reduction map as the embedding dimension increases. For a given data set, the location of the phase transition is the same for all maps in this family. Furthermore, each map has the same stability properties, as quantified through the restricted minimum singular value. These results can be viewed as new universality laws in high-dimensional stochastic geometry. Universality laws for randomized dimension reduction have many applications in applied mathematics, signal processing, and statistics. They yield design principles for numerical linear algebra algorithms, for compressed sensing measurement ensembles, and for random linear codes. Furthermore, these results have implications for the performance of statistical estimation methods under a large class of random experimental designs

Treating Homeless Opioid Dependent Patients with Buprenorphine in an Office-Based Setting

CONTEXT Although office-based opioid treatment with buprenorphine (OBOT-B) has been successfully implemented in primary care settings in the US, its use has not been reported in homeless patients. OBJECTIVE To characterize the feasibility of OBOT-B in homeless relative to housed patients. DESIGN A retrospective record review examining treatment failure, drug use, utilization of substance abuse treatment services, and intensity of clinical support by a nurse care manager (NCM) among homeless and housed patients in an OBOT-B program between August 2003 and October 2004. Treatment failure was defined as elopement before completing medication induction, discharge after medication induction due to ongoing drug use with concurrent nonadherence with intensified treatment, or discharge due to disruptive behavior. RESULTS Of 44 homeless and 41 housed patients enrolled over 12 months, homeless patients were more likely to be older, nonwhite, unemployed, infected with HIV and hepatitis C, and report a psychiatric illness. Homeless patients had fewer social supports and more chronic substance abuse histories with a 3- to 6-fold greater number of years of drug use, number of detoxification attempts and percentage with a history of methadone maintenance treatment. The proportion of subjects with treatment failure for the homeless (21%) and housed (22%) did not differ (P=.94). At 12 months, both groups had similar proportions with illicit opioid use [Odds ratio (OR), 0.9 (95% CI, 0.5–1.7) P=.8], utilization of counseling (homeless, 46%; housed, 49%; P=.95), and participation in mutual-help groups (homeless, 25%; housed, 29%; P=.96). At 12 months, 36% of the homeless group was no longer homeless. During the first month of treatment, homeless patients required more clinical support from the NCM than housed patients. CONCLUSIONS Despite homeless opioid dependent patients' social instability, greater comorbidities, and more chronic drug use, office-based opioid treatment with buprenorphine was effectively implemented in this population comparable to outcomes in housed patients with respect to treatment failure, illicit opioid use, and utilization of substance abuse treatment

A well-separated pairs decomposition algorithm for k-d trees implemented on multi-core architectures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Variations of k-d trees represent a fundamental data structure used in Computational Geometry with numerous applications in science. For example particle track tting in the software of the LHC experiments, and in simulations of N-body systems in the study of dynamics of interacting galaxies, particle beam physics, and molecular dynamics in biochemistry. The many-body tree methods devised by Barnes and Hutt in the 1980s and the Fast Multipole Method introduced in 1987 by Greengard and Rokhlin use variants of k-d trees to reduce the computation time upper bounds to O(n log n) and even O(n) from O(n2). We present an algorithm that uses the principle of well-separated pairs decomposition to always produce compressed trees in O(n log n) work. We present and evaluate parallel implementations for the algorithm that can take advantage of multi-core architectures.The Science and Technology Facilities Council, UK

Sampling-based Algorithms for Optimal Motion Planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics Researc

HIV Prevention in Care and Treatment Settings: Baseline Risk Behaviors among HIV Patients in Kenya, Namibia, and Tanzania.

HIV care and treatment settings provide an opportunity to reach people living with HIV/AIDS (PLHIV) with prevention messages and services. Population-based surveys in sub-Saharan Africa have identified HIV risk behaviors among PLHIV, yet data are limited regarding HIV risk behaviors of PLHIV in clinical care. This paper describes the baseline sociodemographic, HIV transmission risk behaviors, and clinical data of a study evaluating an HIV prevention intervention package for HIV care and treatment clinics in Africa. The study was a longitudinal group-randomized trial in 9 intervention clinics and 9 comparison clinics in Kenya, Namibia, and Tanzania (N = 3538). Baseline participants were mostly female, married, had less than a primary education, and were relatively recently diagnosed with HIV. Fifty-two percent of participants had a partner of negative or unknown status, 24% were not using condoms consistently, and 11% reported STI symptoms in the last 6 months. There were differences in demographic and HIV transmission risk variables by country, indicating the need to consider local context in designing studies and using caution when generalizing findings across African countries. Baseline data from this study indicate that participants were often engaging in HIV transmission risk behaviors, which supports the need for prevention with PLHIV (PwP). TRIAL REGISTRATION: ClinicalTrials.gov NCT01256463

A distance for partially labeled trees

In a number of practical situations, data have structure and the relations among its component parts need to be coded with suitable data models. Trees are usually utilized for representing data for which hierarchical relations can be defined. This is the case in a number of fields like image analysis, natural language processing, protein structure, or music retrieval, to name a few. In those cases, procedures for comparing trees are very relevant. An approximate tree edit distance algorithm has been introduced for working with trees labeled only at the leaves. In this paper, it has been applied to handwritten character recognition, providing accuracies comparable to those by the most comprehensive search method, being as efficient as the fastest.This work is supported by the Spanish Ministry projects DRIMS (TIN2009-14247-C02), and Consolider Ingenio 2010 (MIPRCV, CSD2007-00018), partially supported by EU ERDF and the Pascal Network of Excellence