Set partitions, tableaux, and subspace profiles under regular split semisimple matrices

We introduce a family of univariate polynomials indexed by integer partitions. At prime powers, they count the number of subspaces in a finite vector space that transform under a regular diagonal matrix in a specified manner. At 1, they count set partitions with specified block sizes. At 0, they count standard tableaux of specified shape. At -1, they count standard shifted tableaux of a specified shape. These polynomials are generated by a new statistic on set partitions (called the interlacing number) as well as a polynomial statistic on standard tableaux. They allow us to express q-Stirling numbers of the second kind as sums over standard tableaux and as sums over set partitions. For partitions whose parts are at most two, these polynomials are the non-zero entries of the Catalan triangle associated to the q-Hermite orthogonal polynomial sequence. In particular, when all parts are equal to two, they coincide with the polynomials defined by Touchard that enumerate chord diagrams by number of crossings.Comment: 28 pages, minor change

Splitting subspaces and a finite field interpretation of the Touchard-Riordan Formula

We enumerate the number of $T$-splitting subspaces of dimension $m$ for an arbitrary operator $T$ on a $2m$-dimensional vector space over a finite field. When $T$ is regular split semisimple, comparison with an alternate method of enumeration leads to a new proof of the Touchard-Riordan formula for enumerating chord diagrams by their number of crossings.Comment: 15 page

Effect of holistic yoga program on anxiety symptoms in adolescent girls with polycystic ovarian syndrome: A randomized control trial

Context: Yoga techniques practiced for varying durations have been shown to reduce state anxiety. This was never assessed in adolescents with polycystic ovarian syndrome (PCOS). Aims: To compare the effect of a holistic yoga program with the conventional exercise program on anxiety level in adolescents with PCOS. Settings and Design: Ninety adolescent (15-18 years) girls from a residential college in Andhra Pradesh, who satisfied the Rotterdam criteria, were randomized into two groups. Materials and Methods: Anxiety levels were assessed at inclusion and after 12 weeks of intervention wherein yoga group practiced a holistic yoga module while the control group practiced a matching set of physical exercises (1 h/day, for 12 weeks). Statistical Analysis Used: Mann-Whitney U test was used to compare difference scores (delta change) between the two groups Results: Changes in state anxiety after the intervention were nonsignificantly different between the two groups (P=0.243), while changes after the intervention were significantly different between the two groups (P=0.002) for trait anxiety. Conclusions: Twelve weeks of a holistic yoga program in adolescents with PCOS is significantly better than physical exercise program in reducing anxiety symptoms

Comparison of lymphocyte apoptotic index and qualitative DNA damage in yoga practitioners and breast cancer patients: A pilot study

Background: Yoga is found to be effective in reducing stress levels and radiation-induced DNA damage, and improving the quality of life, in breast cancer patients. The present study was aimed at comparing the apoptotic index (AI) and DNA damage of advanced yoga practitioners with those of breast cancer patients. Materials and Methods: This cross-sectional pilot study compared three groups (n = 9 each) of age-matched subjects viz. (1) Carcinoma breast patients in stage II or III undergoing radiation therapy after completing three cycles of chemotherapy; (2) Senior yoga practitioners who were practicing asanas, pranayama and meditation daily for more than 10 years; and (3) Normal healthy volunteers. Peripheral blood lymphocytes were isolated, and qualitative DNA damage (QDD) and AI were evaluated by single-cell gel electrophoresis assay. Approximately 500 cells were counted in each case. Number of cells that were normal, undergoing apoptosis, and with DNA damage were categorized and percentages were calculated. Results: Data being normally distributed, one-way analysis of variance (ANOVA) showed significant interaction between groups in AI (P = 0.016) and QDD (P = 0.045). On post-hoc analysis using Scheffe test, AI was significantly lower in non-yoga volunteers as compared with the breast cancer group (P = 0.019) and QDD was significantly lower in yoga practitioners when compared with non-yoga volunteers (P = 0.047). Conclusion: Cellular dysfunction (QDD) requires restorative mechanisms (AI) to restore the system to a balance. The results of this pilot study show trends, which indicate that in ill-health, there is inadequate restorative mechanisms (AI) although dysfunction (QDD) is high. Through regular practice of yoga, cellular dysfunction can be lowered, thus necessitating reduced restorative mechanisms. AI and QDD could also be useful indicators for predicting the three zones of health viz. disease, health, and positive health

Prospective Analysis of Patients with Metastatic Breast Cancer receiving Eribulin Mesylate as Second or More Lines of Chemotherapy: An Indian Experience

Background: Eribulin mesylate is a non-taxane microtubule inhibitor which can be used after anthracycline and taxane treatment in patients with metastatic breast cancer (MBC). The purpose of this study was to investigate the efficacy and safety of eribulin monotherapy in heavily pretreated patients with MBC. Methods: In this study, a total of 45 eligible patients with MBC who received eribulin in HCG Cancer Speciality Center from November 2014 to March 2016 were prospectively analyzed. Breslow (generalized Wilcoxon) survival analysis was carried out for progression-free survival and for overall survival. Patients were excluded if they had not taken treatment for 3 cycles and defaulted/expired during the treatment. Results: In this study, median age of patients was 52 years. A total of 27 (60%) patients had estrogen receptor and progesterone receptor (PR) positive primary tumors, whereas HER2 was overexpressed or amplified in 7 (15.6%); a triple negative subtype was recorded in 13 patients (28.9%). Regarding toxicity, 30 patients (66.67%) tolerated treatment well and 3 patients (6.67%) got anemia, 6 patients (13.3%) experienced neutropenia, and 7 (15.62%) patients had neurological toxicity. About 14 (31.1%) patients showed PR, 12 (26.7%) patients had stable disease (SD), whereas 19 (42.25%) patients showed progression disease (PD). Response evaluation at 6 cycles was possible in 18 patients and revealed that 4 (22.5%) patients showed PR, 10 (55.5%) patients had SD, whereas 4 (22.2%) patients had PD. Progression-free survival of the overall study population was 3.95 months. Conclusions: Eribulin mesylate is efficacious and tolerable chemotherapy as second- and third-line treatment options for MBC

Effects of an integrated yoga program in modulating psychological stress and radiation-induced genotoxic stress in breast cancer patients undergoing radiotherapy

10.1177/1534735407306214Integrative Cancer Therapies63242-25

Alirocumab and cardiovascular outcomes after acute coronary syndrome

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