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

Linear time distance transforms for quadtrees

Linear time algorithms are given for computing the chessboard distance transform for both pointer-based and linear quadtree representations. Comparisons between algorithmic styles for the two representations are made. Both versions of the algorithm consist of a pair of tree traversals.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29144/1/0000186.pd

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

The hidden benefits of control: The effect of peer competition on employee responses to restrictive controls

Managers must decide whether to grant their employees the freedom to make their own choices or to restrict their employees’ decision rights by proscribing specific actions, behaviors and decisions. Prior research finds that employees perceive restrictive controls as a signal that their manager does not trust them to behave appropriately. While this might be true sometimes, I argue that an employee’s belief as to why a restriction was imposed could depend on contextual factors, such as how competitive the workplace is. Specifically, I predict that, compared settings where there is little peer competition or the competition is not salient, experiencing stronger peer competition will push employees to view a restrictive control through a lens of how it affects their performance relative to their peers, increasing the likelihood that employees will view a restrictive control as improving fairness. If so, employees might respond positively to the imposition of a restrictive control rather than negatively, as suggested by prior research. The results of a laboratory experiment suggest that employee reactions to a control decision depends not only on the presence of peer competition, but also on the perceived cost incurred by management to impose the control.Ph.D

A spatial analysis and game theoretical approach over the disputed islands in the Aegean Sea

Throughout history, the Aegean Sea has been a sea of crisis. Today, Turkey and Greece--the two countries surrounding the Aegean Sea--continue to dispute several issues regarding the Aegean. The most significant dispute is over the sovereignty of several islands. This research presents a method to produce an arbitration solution to allocate these disputed islands between the two countries. We identify 39 disputed islands and six important attributes for each island, including perimeter, area, population, distance to Greece, distance to Turkey, and territorial water area. After applying spatial analysis to two open-source maps, we apply utility theory, the Analytical Hierarchy Process, and the Nash arbitration scheme to propose an arbitration solution. The arbitration solution tends to allocate to Turkey those islands with larger areas of territorial waters and greater proximity to the Turkish mainland, and allocate to Greece those islands with larger population and greater proximity to the Greek mainland.http://archive.org/details/aspatialnalysisn1094549378Lieutenant Junior Grade, Turkish Naval ForcesApproved for public release; distribution is unlimited