Symmetric groups and conjugacy classes

Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial $\alpha,\beta\in S_n$, we prove that the product $\alpha^{S_n}\beta^{S_n}$ of the conjugacy classes $\alpha^{S_n}$ and $\beta^{S_n}$ is never a conjugacy class. Furthermore, if n is not even and $n$ is not a multiple of three, then $\alpha^{S_n}\beta^{S_n}$ is the union of at least three distinct conjugacy classes. We also describe the elements $\alpha,\beta\in S_n$ in the case when $\alpha^{S_n}\beta^{S_n}$ is the union of exactly two distinct conjugacy classes.Comment: 7 page

An investigation into the psychometric properties of the Hospital Anxiety and Depression Scale in patients with breast cancer

BACKGROUND: To determine the psychometric properties of the Hospital Anxiety and Depression Scale (HADS) in patients with breast cancer and determine the suitability of the instrument for use with this clinical group. METHODS: A cross-sectional design was used. The study used a pooled data set from three breast cancer clinical groups. The dependent variables were HADS anxiety and depression sub-scale scores. Exploratory and confirmatory factor analyses were conducted on the HADS to determine its psychometric properties in 110 patients with breast cancer. Seven models were tested to determine model fit to the data. RESULTS: Both factor analysis methods indicated that three-factor models provided a better fit to the data compared to two-factor (anxiety and depression) models for breast cancer patients. Clark and Watson's three factor tripartite and three factor hierarchical models provided the best fit. CONCLUSION: The underlying factor structure of the HADS in breast cancer patients comprises three distinct, but correlated factors, negative affectivity, autonomic anxiety and anhedonic depression. The clinical utility of the HADS in screening for anxiety and depression in breast cancer patients may be enhanced by using a modified scoring procedure based on a three-factor model of psychological distress. This proposed alternate scoring method involving regressing autonomic anxiety and anhedonic depression factors onto the third factor (negative affectivity) requires further investigation in order to establish its efficacy

Arithmetic Spacetime Geometry from String Theory

An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.Comment: 36 page

Evaluation of Bovine Myosin Heavy Chain Isoforms and Muscle Fiber Cross-Sectional Area on the Eating Quality of 11 Different Beef Muscles

Objective: The objective of this study was to investigate the contribution of muscle fiber type and size on the eating quality of 11 different beef muscles. Study Description: Eleven different beef muscles were utilized from two separate studies. In study 1, shoulder clod, flank, knuckle, mock tender, top sirloin butt, brisket, eye of round, and ribeye were collected from 10 U.S. Department of Agriculture choice carcasses (n = 80), and each muscle was fabricated into steaks at 2 days postmortem. In study 2, strip loin, tri-tip, and heel were collected from 10 USDA low choice carcasses (n = 30). Myofibrillar proteins were extracted and analyzed by immunoblot to determine muscle fiber type. Cross sectional area (CSA) and muscle fiber diameter were determined under the microscope. An average of 400 fibers per sample were analyzed to determine CSA and muscle fiber diameter. Pearson correlation analysis was conducted to determine the relationship between muscle fiber type, CSA, and diameter with the results for the eating quality of beef as determined by a trained panel that were reported in previous studies. Results: In study 1, there was a positive correlation between fiber type 1 and initial juiciness (r = 0.37; P \u3c 0.05), sustained juiciness (r = 0.39; P \u3c 0.05) and lipid flavor (r = 0.41; P \u3c 0.05). Conversely, there was a negative correlation between fiber type 2A and initial juiciness (r = -0.40; P \u3c 0.05) sustained juiciness (r = -0.42; P \u3c 0.05), and lipid flavor (r = -0.45; P \u3c 0.01). Both studies saw a negative correlation between muscle fiber CSA and diameter with connective tissue content (P \u3c 0.05), but positive correlations to overall tenderness (P \u3c 0.05). The Bottom Line: This study shows that muscles predominated by type 1 fibers will likely deliver a higher eating quality experience for consumers, while muscles with more glycolytic fibers 2A and 2X will deliver a less favorable eating experience for consumers. On the other hand, these data also demonstrated that larger muscle fiber CSA and diameter are not necessarily a negative eating quality marker as muscles with those characteristics had less connective tissue and had greater tenderness scores

A Graph Based Neural Network Approach to Immune Profiling of Multiplexed Tissue Samples

Multiplexed immunofluorescence provides an unprecedented opportunity for studying specific cell-to-cell and cell microenvironment interactions. We employ graph neural networks to combine features obtained from tissue morphology with measurements of protein expression to profile the tumour microenvironment associated with different tumour stages. Our framework presents a new approach to analysing and processing these complex multi-dimensional datasets that overcomes some of the key challenges in analysing these data and opens up the opportunity to abstract biologically meaningful interactions

High-solids black liquor firing in pulp and paper industry kraft recovery boilers: Phase 1 -- Final report. Volume 2: Project technical results

This project is a multiple-phase effort to develop technologies to improve high-solids black liquor firing in pulp mill recovery boilers. The principal means to this end is to construct and operate a pilot-scale recovery furnace simulator (RFS) in which these technologies can be tested. The Phase 1 objectives are to prepare a preliminary design for the RFS, delineate a project concept for evaluating candidate technologies, establish industrial partners, and report the results. Phase 1 addressed the objectives with seven tasks: Develop a preliminary design of the RFS; estimate the detailed design and construction costs of the RFS and the balance of the project; identify interested parties in the paper industry and key suppliers; plan the Phase 2 and Phase 3 tests to characterize the RFS; evaluate the economic justification for high-solids firing deployment in the industry; evaluate high-solids black liquor property data to support the RFS design; manage the project and reporting results, which included planning the future program direction

Preventing cardiotoxicity in patients with breast cancer and lymphoma: protocol for a multicentre randomised controlled trial (PROACT)

Introduction: Anthracyclines are included in chemotherapy regimens to treat several different types of cancer and are extremely effective. However, it is recognised that a significant side effect is cardiotoxicity; anthracyclines can cause irreversible damage to cardiac cells and ultimately impaired cardiac function and heart failure, which may only be evident years after exposure. The PROACT trial will establish the effectiveness of the ACE inhibitor enalapril maleate (enalapril) in preventing cardiotoxicity in patients with breast cancer and non-Hodgkin’s lymphoma (NHL) receiving anthracycline-based chemotherapy. Methods and analysis: PROACT is a prospective, randomised, open-label, blinded end-point, superiority trial which will recruit adult patients being treated for breast cancer and NHL at NHS hospitals throughout England. The trial aims to recruit 106 participants, who will be randomised to standard care (high-dose anthracycline-based chemotherapy) plus enalapril (intervention) or standard care alone (control). Patients randomised to the intervention arm will receive enalapril (starting at 2.5 mg two times per day and titrating up to a maximum dose of 10 mg two times per day), commencing treatment at least 2 days prior to starting chemotherapy and finishing 3 weeks after their last anthracycline dose. The primary outcome is the presence or absence of cardiac troponin T release at any time during anthracycline treatment, and 1 month after the last dose of anthracycline. Secondary outcomes will focus on cardiac function measured using echocardiogram assessment, adherence to enalapril and side effects. Ethics and dissemination: A favourable opinion was given following research ethics committee review by West Midlands—Edgbaston REC, Ref: 17/WM/0248. Trial findings will be disseminated through engagement with patients, the oncology and cardiology communities, NHS management and commissioning groups and through peer-reviewed publication

Safety and immunogenicity of novel 5T4 viral vectored vaccination regimens in early stage prostate cancer: a phase I clinical trial.

Prostate cancer (PCa) has been under investigation as a target for antigen-specific immunotherapies in metastatic disease settings for the last two decades leading to a licensure of the first therapeutic cancer vaccine, Sipuleucel-T, in 2010. However, neither Sipuleucel-T nor other experimental PCa vaccines that emerged later induce strong T-cell immunity. In this first-in-man study, VANCE, we evaluated a novel vaccination platform based on two replication-deficient viruses, chimpanzee adenovirus (ChAd) and MVA (Modified Vaccinia Ankara), targeting the oncofetal self-antigen 5T4 in early stage PCa. Forty patients, either newly diagnosed with early-stage PCa and scheduled for radical prostatectomy or patients with stable disease on an active surveillance protocol, were recruited to the study to assess the vaccine safety and T-cell immunogenicity. Secondary and exploratory endpoints included immune infiltration into the prostate, prostate-specific antigen (PSA) change, and assessment of phenotype and functionality of antigen-specific T cells. The vaccine had an excellent safety profile. Vaccination-induced 5T4-specific T-cell responses were measured in blood by ex vivo IFN-γ ELISpot and were detected in the majority of patients with a mean level in responders of 198 spot-forming cells per million peripheral blood mononuclear cells. Flow cytometry analysis demonstrated the presence of both CD8+ and CD4+ polyfunctional 5T4-specific T cells in the circulation. 5T4-reactive tumor-infiltrating lymphocytes were isolated from post-treatment prostate tissue. Some of the patients had a transient PSA rise 2-8 weeks following vaccination, possibly indicating an inflammatory response in the target organ. An excellent safety profile and T-cell responses elicited in the circulation and also detected in the prostate gland support the evaluation of the ChAdOx1-MVA 5T4 vaccine in efficacy trials. It remains to be seen if this vaccination strategy generates immune responses of sufficient magnitude to mediate clinical efficacy and whether it can be effective in late-stage PCa settings, as a monotherapy in advanced disease or as part of multi-modality PCa therapy. To address these questions, the phase I/II trial, ADVANCE, is currently recruiting patients with intermediate-risk PCa, and patients with advanced metastatic castration-resistant PCa, to receive this vaccine in combination with nivolumab. The trial was registered with the U.S. National Institutes of Health (NIH) Clinical Trials Registry (ClinicalTrials.gov identifier NCT02390063)

International Trade Under the Rule of Law Conference

The central focus of the conference was the dispute settlement system of the World Trade Organization (WTO), with a view toward exploring the need for a superstructure of international law governing trade and economic cooperation between countries