Completely contractive projections on operator algebras

The main goal of this paper is to find operator algebra variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others, concerning projections on C*-algebras and their ranges. (See papers of these authors referenced in the bibliography.) In particular we investigate the `bicontractive projection problem' and related questions in the category of operator algebras. To do this, we will add the ingredient of `real positivity' from recent papers of the first author with Read.Comment: To appear Pacific J Math; several corrections and small improvements. Keywords Operator algebra, completely contractive map, projection, conditional expectation, bicontractive projection, real positive, noncommutative Banach-Stone theore

Instance-Based Clustering for Databases

We present a method for automatically clustering similar attribute values in a database system spanning multiple domains. The method constructs a value abstraction hierarchy for each attribute using rules that are derived from the database instance. The rules have a confidence and popularity that combine to express the "usefulness" of the rule. Attribute values are clustered if they are used as the premise for rules with the same consequence. By iteratively applying the algorithm, a hierarchy of clusters can be found. The algorithm can be improved by allowing domain expen direction during the clustering process

High-throughput, Efficient, and Unbiased Capture of Small RNAs from Low-input Samples for Sequencing.

MicroRNAs hold great promise as biomarkers of disease. However, there are few efficient and robust methods for measuring microRNAs from low input samples. Here, we develop a high-throughput sequencing protocol that efficiently captures small RNAs while minimizing inherent biases associated with library production. The protocol is based on early barcoding such that all downstream manipulations can be performed on a pool of many samples thereby reducing reagent usage and workload. We show that the optimization of adapter concentrations along with the addition of nucleotide modifications and random nucleotides increases the efficiency of small RNA capture. We further show, using unique molecular identifiers, that stochastic capture of low input RNA rather than PCR amplification influences the biased quantitation of intermediately and lowly expressed microRNAs. Our improved method allows the processing of tens to hundreds of samples simultaneously while retaining high efficiency quantitation of microRNAs in low input samples from tissues or bodily fluids

Measuring the Justice Gap: Flaws in the Interstate Allocation of Civil Legal Services Funding and a Proposed Remedy

With the supply of legal services not particularly responsive to demand, we conclude that the justice gap could be narrowed simply by reforming the way in which policymakers distribute legal services funds while holding constant the total amount of funds distributed. In reaching this conclusion, we proceed in two parts. First, drawing largely from Access Across America and LSC data, we analyze the supply of legal services funding across states. Since eligibility for Legal Services Corporation (LSC) funds is principally determined by income (only individuals in households with income at or below 125% of the federal poverty level are LSC eligible),8 variations in legal services funding among states are strongly correlated with LSC eligibility levels. However, LSC funding likely accounts for well under forty-three percent (43%) of overall legal services funding, with the remainder (“non-LSC funding”) generated by, inter alia, state and local grants, filing fees, interest on lawyer trust accounts (“IOLTA”), and private grants. Because the precise magnitude of non-LSC funding is unclear, we estimate it with three different measures. Using each of these measures, we then analyze its disparity among states. In every case, after explaining Access Across America’s finding that non-LSC funding is not proportional to population, we conclude that it also has no statistically significant relationship to key economic indicators, such as LSC eligibility, median household income, or unemployment. In fact, of the variables we tested, only the number of lawyers in a state relates significantly to any of our measures of non-LSC funding, and of these three measures, the only one for which the number of lawyers has statistical significance is non-LSC funding received by organizations that also receive LSC funding. After examining how legal services funds are supplied across states, we then analyze how they are demanded. Measuring demand is quite challenging, particularly on the state level, because it requires assessing not the amount of legal services that low-income individuals do use, but rather the amount that they want to use, which is an unobservable variable. The LSC has attempted to measure such demand through a survey of individuals seeking assistance from LSC-funded programs, but, as the LSC concedes, this approach comes with inherent limitations that likely under-represent unmet needs. We therefore take a different approach: after assuming that the overall frequency with which civil legal services are delivered reflects the relative demand for these services across states, we estimate demand within each state through proxies for the most significant categories of services. Because, according to LSC data, nearly eighty-five percent (85%) of LSC-eligible cases arise from just four types of disputes (consumer finance, family, housing, and income), we can reasonably project state-level demand for legal services by estimating the frequency of these disputes within each state. Upon doing so, we find that there is no clear connection between state-level demand and supply, particularly with respect to LSC funding. In other words, states with the greatest need for LSC funding (because their residents encounter legal problems the most based on our estimates) do not necessarily have more funding than states with lower funding needs. Though we recognize that fixing this imbalance will not be easy, we conclude by offering a proposal that attempts to do so. In this regard, we recommend that the LSC move away from complete reliance on an income-based test toward a needs-based test. Such a framework would allow the LSC to more effectively serve unmet demand for civil legal services and thus, help realize Justice Powell’s ideal