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

Utility of commonly used commercial human chorionic gonadotropin immunoassays in the diagnosis and management of trophoblastic diseases.

A multi-centre study involving worldwide collaboration highlighted the between-method variation in hCG quantification and estimation and the resultant potential misdiagnosis of GTD

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

The Hypolipidemic Activity of Metal Complexes of Amine Carboxyboranes in Rodents

The metal complexes of amine-carboxyborane including copper, chromium, zinc, calcium amd cobalt were effective hypolipidemic agents lowering both serum cholesterol and triglyceride levels significantly in mice at 8 mg/kg/day, I.P. after 16 days. The agents reduced acetyl CoA synthetase, ATP-dependent citrate lyase, acyl CoA cholesterol acyl transferase, sn-glycerol-3-phosphate acyl transferase activities of rat liver and small intestinal mucosa after 14 days treatment. The neutral cholesterol ester hydrolase activity was elevated by the agents in both tissues. The metal complexes altered lipid levels in the bile of rats after treatment as well as the bile acid composition after 14 days administration, orally. The agents blocked enterohepatic absorption of cholesterol from rat isolated intestinal loops

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

No. 5 - International Trade under the Rule of Law: An American Society of International Law Centennial Regional Meeting

Organized and sponsored by the Dean Rusk Center and designated an American Society of International Law Centennial Regional Meeting, this conference focused on the Dispute Settlement System (DSS) of the World Trade Organization (WTO) with a view toward discussing the need for a superstructure of international law governing trade and economic cooperation between states

Increased EZH2 expression in prostate cancer is associated with metastatic recurrence following external beam radiotherapy

Background Enhancer of zeste 2 (EZH2) promotes prostate cancer progression. We hypothesized that increased EZH2 expression is associated with postradiotherapy metastatic disease recurrence, and may promote radioresistance. Methods EZH2 expression was investigated using immunohistochemistry in diagnostic prostate biopsies of 113 prostate cancer patients treated with radiotherapy with curative intent. Associations between EZH2 expression in malignant and benign tissue in prostate biopsy cores and outcomes were investigated using univariate and multivariate Cox regression analyses. LNCaP and PC3 cell radiosensitivity was investigated using colony formation and γH2AX assays following UNC1999 chemical probe‐mediated EZH2 inhibition. Results While there was no significant association between EZH2 expression and biochemical recurrence following radiotherapy, univariate analysis revealed that prostate cancer cytoplasmic and total EZH2 expression were significantly associated with metastasis development postradiotherapy (P = 0.034 and P = 0.003, respectively). On multivariate analysis, the prostate cancer total EZH2 expression score remained statistically significant (P = 0.003), while cytoplasmic EZH2 expression did not reach statistical significance (P = 0.053). No association was observed between normal adjacent prostate EZH2 expression and biochemical recurrence or metastasis. LNCaP and PC3 cell treatment with UNC1999 reduced histone H3 lysine 27 tri‐methylation levels. Irradiation of LNCaP or PC3 cells with a single 2 Gy fraction with UNC1999‐mediated EZH2 inhibition resulted in a statistically significant, though modest, reduction in cell colony number for both cell lines. Increased γH2AX foci were observed 24 hours after ionizing irradiation in LNCaP cells, but not in PC3, following UNC1999‐mediated EZH2 inhibition vs controls. Conclusions Taken together, these results reveal that high pretreatment EZH2 expression in prostate cancer in diagnostic biopsies is associated with an increased risk of postradiotherapy metastatic disease recurrence, but EZH2 function may only at most play a modest role in promoting prostate cancer cell radioresistance

Image-based consensus molecular subtype (imCMS) classification of colorectal cancer using deep learning

OBJECTIVE Complex phenotypes captured on histological slides represent the biological processes at play in individual cancers, but the link to underlying molecular classification has not been clarified or systematised. In colorectal cancer (CRC), histological grading is a poor predictor of disease progression, and consensus molecular subtypes (CMSs) cannot be distinguished without gene expression profiling. We hypothesise that image analysis is a cost-effective tool to associate complex features of tissue organisation with molecular and outcome data and to resolve unclassifiable or heterogeneous cases. In this study, we present an image-based approach to predict CRC CMS from standard H&E sections using deep learning. DESIGN Training and evaluation of a neural network were performed using a total of n=1206 tissue sections with comprehensive multi-omic data from three independent datasets (training on FOCUS trial, n=278 patients; test on rectal cancer biopsies, GRAMPIAN cohort, n=144 patients; and The Cancer Genome Atlas (TCGA), n=430 patients). Ground truth CMS calls were ascertained by matching random forest and single sample predictions from CMS classifier. RESULTS Image-based CMS (imCMS) accurately classified slides in unseen datasets from TCGA (n=431 slides, AUC)=0.84) and rectal cancer biopsies (n=265 slides, AUC=0.85). imCMS spatially resolved intratumoural heterogeneity and provided secondary calls correlating with bioinformatic prediction from molecular data. imCMS classified samples previously unclassifiable by RNA expression profiling, reproduced the expected correlations with genomic and epigenetic alterations and showed similar prognostic associations as transcriptomic CMS. CONCLUSION This study shows that a prediction of RNA expression classifiers can be made from H&E images, opening the door to simple, cheap and reliable biological stratification within routine workflows