Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center acts by characters on the deformed standard modules, providing a "localization map." We construct a universal graded deformation, and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming the Koszul dual algebra. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category $\mathcal{O}$ for $\mathfrak{gl}_n$ is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the "category $\mathcal{O}$" of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.Comment: 39 pages; v3: final versio

Training Complex Models with Multi-Task Weak Supervision

As machine learning models continue to increase in complexity, collecting large hand-labeled training sets has become one of the biggest roadblocks in practice. Instead, weaker forms of supervision that provide noisier but cheaper labels are often used. However, these weak supervision sources have diverse and unknown accuracies, may output correlated labels, and may label different tasks or apply at different levels of granularity. We propose a framework for integrating and modeling such weak supervision sources by viewing them as labeling different related sub-tasks of a problem, which we refer to as the multi-task weak supervision setting. We show that by solving a matrix completion-style problem, we can recover the accuracies of these multi-task sources given their dependency structure, but without any labeled data, leading to higher-quality supervision for training an end model. Theoretically, we show that the generalization error of models trained with this approach improves with the number of unlabeled data points, and characterize the scaling with respect to the task and dependency structures. On three fine-grained classification problems, we show that our approach leads to average gains of 20.2 points in accuracy over a traditional supervised approach, 6.8 points over a majority vote baseline, and 4.1 points over a previously proposed weak supervision method that models tasks separately

Invasive Enterobacter sakazakii Disease in Infants

Enterobacter sakazakii kills 40%–80% of infected infants and has been associated with powdered formula. We analyzed 46 cases of invasive infant E. sakazakii infection to define risk factors and guide prevention and treatment. Twelve infants had bacteremia, 33 had meningitis, and 1 had a urinary tract infection. Compared with infants with isolated bacteremia, infants with meningitis had greater birthweight (2,454 g vs. 850 g, p = 0.002) and gestational age (37 weeks vs. 27.8 weeks, p = 0.02), and infection developed at a younger age (6 days vs. 35 days, p<0.001). Among meningitis patients, 11 (33%) had seizures, 7 (21%) had brain abscess, and 14 (42%) died. Twenty-four (92%) of 26 infants with feeding patterns specified were fed powdered formula. Formula samples associated with 15 (68%) of 22 cases yielded E. sakazakii; in 13 cases, clinical and formula strains were indistinguishable. Further clarification of clinical risk factors and improved powdered formula safety is needed

DNA Fingerprinting of Mycobacterium tuberculosis: Lessons Learned and Implications for the Future

DNA fingerprinting of Mycobacterium tuberculosis—a relatively new laboratory technique—offers promise as a powerful aid in the prevention and control of tuberculosis (TB). Established in 1996 by the Centers for Disease Control and Prevention (CDC), the National Tuberculosis Genotyping Surveillance Network was a 5-year prospective, population-based study of DNA fingerprinting conducted from 1996 to 2000. The data from this study suggest multiple molecular epidemiologic and program management uses for DNA fingerprinting in TB public health practice. From these data, we also gain a clearer understanding of the overall diversity of M. tuberculosis strains as well as the presence of endemic strains in the United States. We summarize the key findings and the impact that DNA fingerprinting may have on future approaches to TB control. Although challenges and limitations to the use of DNA fingerprinting exist, the widespread implementation of the technique into routine TB prevention and control practices appears scientifically justified

SUD inclined settling bioreactor for gentle expansion, concentration and harvest of gene and cell therapies

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Quality Assessment of Mycobacterium tuberculosis Genotyping in a Large Laboratory Network

Quality assessment exercises were conducted to evaluate the reproducibility of IS6110 DNA fingerprinting performed by eight laboratories in the National Tuberculosis Genotyping and Surveillance Network. Three panels, each with 8 to 16 isolates, were typed at all laboratories, resulting in 280 images. When the pattern obtained by the majority for each isolate was used as the standard, exact matches were obtained for 73% of patterns; 90% and 97% of patterns matched within one- and two-band differences, respectively. A second approach involved retyping of randomly selected isolates at the Centers for Disease Control and Prevention. Retyping was done for 8–19 isolates per laboratory (76 total). Paired images matched exactly for 54% of isolates and within one and two band differences, 78% and 93%, respectively. We evaluated reasons for mismatching. We also evaluated the reproducibility of spoligotyping using a test panel of 13 isolates; a discrepancy of 1 in 91 results was noted

National Tuberculosis Genotyping and Surveillance Network: Design and Methods

The National Tuberculosis Genotyping and Surveillance Network was established in 1996 to perform a 5-year, prospective study of the usefulness of genotyping Mycobacterium tuberculosis isolates to tuberculosis control programs. Seven sentinel sites identified all new cases of tuberculosis, collected information on patients and contacts, and obtained patient isolates. Seven genotyping laboratories performed DNA fingerprinting analysis by the international standard IS6110 method. BioImage Whole Band Analyzer software was used to analyze patterns, and distinct patterns were assigned unique designations. Isolates with six or fewer bands on IS6110 patterns were also spoligotyped. Patient data and genotyping designations were entered in a relational database and merged with selected variables from the national surveillance database. In two related databases, we compiled the results of routine contact investigations and the results of investigations of the relationships of patients who had isolates with matching genotypes. We describe the methods used in the study