Fingerprint databases for theorems

We discuss the advantages of searchable, collaborative, language-independent databases of mathematical results, indexed by "fingerprints" of small and canonical data. Our motivating example is Neil Sloane's massively influential On-Line Encyclopedia of Integer Sequences. We hope to encourage the greater mathematical community to search for the appropriate fingerprints within each discipline, and to compile fingerprint databases of results wherever possible. The benefits of these databases are broad - advancing the state of knowledge, enhancing experimental mathematics, enabling researchers to discover unexpected connections between areas, and even improving the refereeing process for journal publication.Comment: to appear in Notices of the AM

First Dark Matter Limits from a Large-Mass, Low-Background Superheated Droplet Detector

We report on the fabrication aspects and calibration of the first large active mass ($\sim15$ g) modules of SIMPLE, a search for particle dark matter using Superheated Droplet Detectors (SDDs). While still limited by the statistical uncertainty of the small data sample on hand, the first weeks of operation in the new underground laboratory of Rustrel-Pays d'Apt already provide a sensitivity to axially-coupled Weakly Interacting Massive Particles (WIMPs) competitive with leading experiments, confirming SDDs as a convenient, low-cost alternative for WIMP detection.Comment: Final version, Phys. Rev. Lett. (in press

The vulnerability of public spaces: challenges for UK hospitals under the 'new' terrorist threat

This article considers the challenges for hospitals in the United Kingdom that arise from the threats of mass-casualty terrorism. Whilst much has been written about the role of health care as a rescuer in terrorist attacks and other mass-casualty crises, little has been written about health care as a victim within a mass-emergency setting. Yet, health care is a key component of any nation's contingency planning and an erosion of its capabilities would have a significant impact on the generation of a wider crisis following a mass-casualty event. This article seeks to highlight the nature of the challenges facing elements of UK health care, with a focus on hospitals both as essential contingency responders under the United Kingdom's civil contingencies legislation and as potential victims of terrorism. It seeks to explore the potential gaps that exist between the task demands facing hospitals and the vulnerabilities that exist within them

Pinnacle sets of signed permutations

Pinnacle sets record the values of the local maxima for a given family of permutations. They were introduced by Davis-Nelson-Petersen-Tenner as a dual concept to that of peaks, previously defined by Billey-Burdzy-Sagan. In recent years pinnacles and admissible pinnacles sets for the type $A$ symmetric group have been widely studied. In this article we define the pinnacle set of signed permutations of types $B$ and $D$. We give a closed formula for the number of type $B$/$D$ admissible pinnacle sets and answer several other related enumerative questions.Comment: 15 pages, 3 figures, to appear in Discrete Mathematic

Differential Indicators of Diabetes-Induced Oxidative Stress in New Zealand White Rabbits: Role of Dietary Vitamin E Supplementation

Determination of reliable bioindicators of diabetes-induced oxidative stress and the role of dietary vitamin E supplementation were investigated. Blood (plasma) chemistries, lipid peroxidation (LPO), and antioxidant enzyme activities were measured over 12 weeks in New Zealand White rabbits (control, diabetic, and diabetic + vitamin E). Cholesterol and triglyceride levels did not correlate with diabetic state. PlasmaLPOwas influenced by diabetes and positively correlated with glucose concentration only, not cholesterol or triglycerides. Liver glutathione peroxidase (GPX) activity negatively correlated with glucose and triglyceride levels. Plasma and erythrocyte GPX activities positively correlated with glucose, cholesterol, and triglyceride concentrations. Liver superoxide dismutase activity positively correlated with glucose and cholesterol concentration. Vitamin E reduced plasma LPO, but did not affect the diabetic state. Thus, plasmaLPOwas the most reliable indicator of diabetes-induced oxidative stress. Antioxidant enzyme activities and types of reactive oxygen species generated were tissue dependent. Diabetes-induced oxidative stress is diminished by vitamin E supplementation

Sorting Permutations: Games, Genomes, and Cycles

Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, abbreviated cds, and context directed reversal, abbreviated cdr. These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates. This paper investigates mathematical aspects of these two sorting operations. The main result of this paper is a generalization of previously discovered characterizations of cds-sortability of a permutation. The combinatorial structure underlying this generalization suggests natural combinatorial two-player games. These games are the main mathematical innovation of this paper.Comment: to appear in Discrete Mathematics, Algorithms and Application

On the Lucky and Displacement Statistics of Stirling Permutations

Stirling permutations are parking functions, and we investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we consider two extreme cases: extremely lucky Stirling permutations (those with maximally many lucky cars) and extremely unlucky Stirling permutations (those with exactly one lucky car). We show that the number of extremely lucky Stirling permutations of order $n$ is the Catalan number $C_n$, and the number of extremely unlucky Stirling permutations is $(n-1)!$. We also give some results for luck that lies between these two extremes. Further, we establish that the displacement of any Stirling permutation of order $n$ is $n^2$, and we prove several results about displacement composition vectors. We conclude with directions for further study.Comment: 17 pages, 3 table

Association of Stromal Tumor-Infiltrating Lymphocytes With Recurrence-Free Survival in the N9831 Adjuvant Trial in Patients With Early-Stage HER2-Positive Breast Cancer

Importance The presence of tumor-infiltrating lymphocytes at diagnosis is reported to be prognostic in triple-negative breast cancer. Objective To evaluate the association of stromal tumor-infiltrating lymphocytes (STILs) with recurrence-free survival (RFS) in women with human epidermal growth factor receptor 2 (HER2)–positive breast cancer treated with chemotherapy or chemotherapy plus trastuzumab in the N9831 trial. Design, Setting, and Participants Hematoxylin-eosin–stained tumor slides from patients with early-stage HER2-positive breast cancer in 2 of the 3 arms of the N9831 trial were assessed for STILs at an academic medical center. The amounts of STILs were quantitated in deciles, and a level of at least 60% STILs was used for the prespecified categorical cutoff. The association between STILs and RFS was evaluated with Cox models. Exposure Standard chemotherapy consisting of doxorubicin-cyclophosphamide followed by weekly paclitaxel (arm A) or doxorubicin-cyclophosphamide followed by weekly paclitaxel plus trastuzumab followed by trastuzumab alone (arm C). Main Outcomes and Measures Stromal tumor-infiltrating lymphocytes and their association with RFS. Results A total of 489 patients from arm A and 456 patients from arm C were assessed with a median (range) follow-up of 4.4 (0-13.6) years. The 10-year Kaplan-Meier estimates for RFS in arm A were 90.9% and 64.5% for patients with high and low levels of STILs, respectively (hazard ratio [HR], 0.23 [95% CI, 0.07-0.73]; P = .01). The 10-year estimates for RFS in arm C were 80.0% and 80.1% for patients with high and low levels of STILs, respectively (HR, 1.26 [95% CI, 0.50-3.17]; P = .63). The test for interaction between trastuzumab treatment and STIL status was statistically significant (P = .03). In a multivariable analysis, STIL status remained significantly associated with RFS in arm A and not significantly associated in arm C (HR, 1.01 [95% CI, 0.89-1.15]; interaction P = .04). Conclusions and Relevance This analysis of participants in the N9831 trial found that the presence of STILs was prognostically associated with RFS in patients treated with chemotherapy alone but not in patients treated with chemotherapy plus trastuzumab. High levels of STILs were associated with lack of trastuzumab therapy benefit, in contrast to a previously reported association between increased levels of STILs and increased trastuzumab benefit in HER2-positive patients

Contribution of complement activation pathways to neuropathology differs among mouse models of Alzheimer's disease

<p>Abstract</p> <p>Background</p> <p>Complement proteins and activation products have been found associated with neuropathology in Alzheimer's disease (AD). Recently, a C5a receptor antagonist was shown to suppress neuropathology in two murine models of AD, Tg2576 and 3xTg. Previously, a genetic deficiency of C1q in the Tg2576 mouse model showed an accumulation of fibrillar plaques similar to the complement sufficient Tg2576, but reactive glia were significantly decreased and neuronal integrity was improved suggesting detrimental consequences for complement activation in AD. The goal of this study was to define the role of the classical complement activation pathway in the progression of pathology in the 3xTg mouse that develops tangles in addition to fibrillar plaques (more closely reflecting human AD pathology) and to assess the influence of complement in a model of AD with a higher level of complement hemolytic activity.</p> <p>Methods</p> <p>3xTg mice deficient in C1q (3xTgQ-/-) were generated, and both 3xTg and 3xTgQ-/- were backcrossed to the BUB mouse strain which has higher in vitro hemolytic complement activity. Mice were aged and perfused, and brain sections stained for pathological markers or analyzed for proinflammatory marker expression.</p> <p>Results</p> <p>3xTgQ-/- mice showed similar amounts of fibrillar amyloid, reactive glia and hyperphosphorylated tau as the C1q-sufficient 3xTg at the ages analyzed. However, 3xTg and 3xTgQ-/- on the BUB background developed pathology earlier than on the original 3xTg background, although the presence of C1q had no effect on neuropathological and pro-inflammatory markers. In contrast to that seen in other transgenic models of AD, C1q, C4 and C3 immunoreactivity was undetectable on the plaques of 3xTg in any background, although C3 was associated with reactive astrocytes surrounding the plaques. Importantly, properdin a component of the alternative complement pathway was associated with plaques in all models.</p> <p>Conclusions</p> <p>In contrast to previously investigated transgenic models of AD, development of neuropathology in 3xTg mice, which progresses much slower than other murine models, may not be influenced by fibrillar amyloid mediated activation of the classical complement pathway, suggesting that the alternative complement pathway activation or a C3-independent cleavage of C5 could account for the detrimental effects in these mice that are prevented by the C5a receptor antagonist. Furthermore, the paucity of complement activation may be a factor in the slower kinetics of progression of pathology in the 3xTg model of this disease.</p