On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fr\'echet Lie algebra, and find all inequivalent integrable $\mathbb Z$-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.Comment: 26 page

Specific heat and magnetic measurements in Nd0.5Sr0.5MnO3, Nd0.5Ca0.5MnO3 and Ho0.5Ca0.5MnO3 samples

We studied the magnetization as a function of temperature and magnetic field in the compounds Nd0.5Sr0.5MnO3, Nd0.5Ca0.5MnO3 and Ho0.5Ca0.5MnO3. It allowed us to identify the ferromagnetic, antiferromagnetic and charge ordering phases in each case. The intrinsic magnetic moments of Nd3+ and Ho3+ ions experienced a short range order at low temperatures. We also did specific heat measurements with applied magnetic fields between 0 and 9 T and temperatures between 2 and 300 K in all three samples. Close to the charge ordering and ferromagnetic transition temperatures the specific heat curves showed peaks superposed to the characteristic response of the lattice oscillations. Below 10 K the specific heat measurements evidenced a Schottky-like anomaly for all samples. However, we could not successfully fit the curves to either a two level nor a distribution of two-level Schottky anomaly. Our results indicated that the peak temperature of the Schottky anomaly was higher in the compounds with narrower conduction band.Comment: submitted to PR

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation due to propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801$-$2304 of approximately 160 \rad at an elongation of 0.95$^\circ$ from the centre of the solar disk. This corresponds to a lower limit of the magnetic field strength along this line of sight of $> 393\mu\mathrm{G}$. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 20mG, along a path passing 2.5 solar radii from the solar limb. Which is consistent with predictions obtained using extensions to the Source Surface models published by Wilcox Solar ObservatoryComment: 16 pages, 4 figures (1 colour): Submitted to Solar Physic

Reproducibility and intratumoral heterogeneity of the PAM50 breast cancer assay

Background: The PAM50 assay is used routinely in clinical practice to determine breast cancer prognosis and management; however, research assessing how technical variation and intratumoral heterogeneity contribute to misclassification and reproducibility of these tests is limited. Methods: We evaluated the impact of intratumoral heterogeneity on the reproducibility of results for the PAM50 assay by testing RNA extracted from formalin-fixed paraffin embedded breast cancer blocks sampled at distinct spatial locations. Samples were classified according to intrinsic subtype (Luminal A, Luminal B, HER2-enriched, Basal-like, or Normal-like) and risk of recurrence with proliferation score (ROR-P, high, medium, or low). Intratumoral heterogeneity and technical reproducibility (replicate assays on the same RNA) were assessed as percent categorical agreement between paired intratumoral and replicate samples. Euclidean distances between samples, calculated across the PAM50 genes and the ROR-P score, were compared for concordant vs. discordant samples. Results: Technical replicates (N = 144) achieved 93% agreement for ROR-P group and 90% agreement on PAM50 subtype. For spatially distinct biological replicates (N = 40 intratumoral replicates), agreement was lower (81% for ROR-P and 76% for PAM50 subtype). The Euclidean distances between discordant technical replicates were bimodal, with discordant samples showing higher Euclidian distance and biologic heterogeneity. Conclusion: The PAM50 assay achieved very high technical reproducibility for breast cancer subtyping and ROR-P, but intratumoral heterogeneity is revealed by the assay in a small proportion of cases

Coherent information analysis of quantum channels in simple quantum systems

The coherent information concept is used to analyze a variety of simple quantum systems. Coherent information was calculated for the information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled two-level atoms, and for the information transfer from a two-level atom to another atom and to a photon field. The coherent information is shown to be equal to zero for all full-measurement procedures, but it completely retains its original value for quantum duplication. Transmission of information from one open subsystem to another one in the entire closed system is analyzed to learn quantum information about the forbidden atomic transition via a dipole active transition of the same atom. It is argued that coherent information can be used effectively to quantify the information channels in physical systems where quantum coherence plays an important role.Comment: 24 pages, 7 figs; Final versiob after minor changes, title changed; to be published in Phys. Rev. A, September 200

Electric current circuits in astrophysics

Cosmic magnetic structures have in common that they are anchored in a dynamo, that an external driver converts kinetic energy into internal magnetic energy, that this magnetic energy is transported as Poynting fl ux across the magnetically dominated structure, and that the magnetic energy is released in the form of particle acceleration, heating, bulk motion, MHD waves, and radiation. The investigation of the electric current system is particularly illuminating as to the course of events and the physics involved. We demonstrate this for the radio pulsar wind, the solar flare, and terrestrial magnetic storms

TP53 Pathway Function, Estrogen Receptor Status, and Breast Cancer Risk Factors in the Carolina Breast Cancer Study

Background: TP53 and estrogen receptor (ER) both play essential roles in breast cancer development and progression, with recent research revealing cross-talk between TP53 and ER signaling pathways. Although many studies have demonstrated heterogeneity of risk factor associations across ER subtypes, associations by TP53 status have been inconsistent. Methods: This case-case analysis included incident breast cancer cases (47% Black) from the Carolina Breast Cancer Study (1993- 2013). Formalin-fixed paraffin-embedded tumor samples were classified for TP53 functional status (mutant-like/wild-type-like) using a validated RNA signature. For IHC-based TP53 status, mutant-like was classified as at least 10% positivity. We used two-stage polytomous logistic regression to evaluate risk factor heterogeneity due to RNA-based TP53 and/or ER, adjusting for each other and for PR, HER2, and grade. We then compared this with the results when using IHC-based TP53 classification. Results: The RNA-based classifier identified 55% of tumors as TP53 wild-type-like and 45% as mutant-like. Several hormonerelated factors (oral contraceptive use, menopausal status, age at menopause, and pre- and postmenopausal body mass index) were associated with TP53 mutant-like status, whereas reproductive factors (age at first birth and parity) and smoking were associated with ER status. Multiparity was associated with both TP53 and ER. When classifying TP53 status using IHC methods, no associations were observed with TP53. Associations observed with RNA-based TP53 remained after accounting for basal-like subtype. Conclusions: This case-case study found breast cancer risk factors associated with RNA-based TP53 and ER

Prognostic significance of RNA-based TP53 pathway function among estrogen receptor positive and negative breast cancer cases

TP53 and estrogen receptor (ER) are essential in breast cancer development and progression, but TP53 status (by DNA sequencing or protein expression) has been inconsistently associated with survival. We evaluated whether RNA-based TP53 classifiers are related to survival. Participants included 3213 women in the Carolina Breast Cancer Study (CBCS) with invasive breast cancer (stages I–III). Tumors were classified for TP53 status (mutant-like/wildtype-like) using an RNA signature. We used Cox proportional hazards models to estimate covariate-adjusted hazard ratios (HRs) and 95% confidence intervals (CIs) for breast cancer-specific survival (BCSS) among ER- and TP53-defined subtypes. RNA-based results were compared to DNA- and IHC-based TP53 classification, as well as Basal-like versus non-Basal-like subtype. Findings from the diverse (50% Black), population-based CBCS were compared to those from the largely white METABRIC study. RNA-based TP53 mutant-like was associated with BCSS among both ER-negatives and ER-positives (HR (95% CI) = 5.38 (1.84–15.78) and 4.66 (1.79–12.15), respectively). Associations were attenuated when using DNA- or IHC-based TP53 classification. In METABRIC, few ER-negative tumors were TP53-wildtype-like, but TP53 status was a strong predictor of BCSS among ER-positives. In both populations, the effect of TP53 mutant-like status was similar to that for Basal-like subtype. RNA-based measures of TP53 status are strongly associated with BCSS and may have value among ER-negative cancers where few prognostic markers have been robustly validated. Given the role of TP53 in chemotherapeutic response, RNA-based TP53 as a prognostic biomarker could address an unmet need in breast cancer

The Landscape of Immune Microenvironments in Racially Diverse Breast Cancer Patients

Background: Immunotherapy is a rapidly evolving treatment option in breast cancer; However, the breast cancer immune microenvironment is understudied in Black and younger (<50 years) patients. Methods: We used histologic and RNA-based immunoprofiling methods to characterize the breast cancer immune landscape in 1,952 tumors from the Carolina Breast Cancer Study (CBCS), a population-based study that oversampled Black (n ¼ 1,030) and young women (n ¼ 1,039). We evaluated immune response leveraging markers for 10 immune cell populations, compared profiles to those in The Cancer Genome Atlas (TCGA) Project [n ¼ 1,095 tumors, Black (n ¼ 183), and young women (n ¼ 295)], and evaluated in association with clinical and demographic variables, including recurrence. Results: Consensus clustering identified three immune clusters in CBCS (adaptive-enriched, innate-enriched, or immune-quiet) that varied in frequency by race, age, tumor grade and subtype; however, only two clusters were identified in TCGA, which were predominantly comprised of adaptive-enriched and innate-enriched tumors. In CBCS, the strongest adaptive immune response was observed for basal-like, HER2-positive (HER2þ), triple-negative breast cancer (TNBC), and high-grade tumors. Younger patients had higher proportions of adaptive-enriched tumors, particularly among estrogen receptor (ER)-negative (ER-) cases. Black patients had higher frequencies of both adaptive-enriched and innate-enriched tumors. Immune clusters were associated with recurrence among ER- tumors, with adaptive-enriched showing the best and innate-enriched showing the poorest 5-year recurrence-free survival. Conclusions: These data suggest that immune microenvironments are intricately related to race, age, tumor subtype, and grade. Impact: Given higher mortality among Black and young women, more defined immune classification using cell-type–specific panels could help explain higher recurrence and ultimately lead to target-able interventions