A Combinatorial Formula for Macdonald Polynomials

We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi's combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients K_{lambda,mu}(q,t) in the case that mu is a partition with parts less than or equal to 2.Comment: 29 page

Trapezoidal lattice paths and multivariate analogues

AbstractIn 1996, Garsia and Haiman introduced a bivariate analogue of the Catalan numbers that counts multiplicities of the sign character in a certain doubly graded Sn-module. Haglund conjectured a combinatorial interpretation for this sequence by defining two statistics on the set of lattice paths staying inside the triangle bounded by x=0, y=x, and y=n. This conjecture was eventually proved by Garsia and Haglund. Later, the present author introduced similar statistics for lattice paths staying inside other triangles, whose generating function is conjectured to give the higher q,t-Catalan sequences of Garsia and Haiman. This article generalizes these combinatorial statistics to lattice paths within certain trapezoidal regions. We introduce a five-variable generating function for these paths and prove formulas, bijections, and recursions involving this generating function. An open question is to find representation-theoretical interpretations for these statistics analogous to those previously conjectured for the paths staying inside triangular regions

Effective constructions in plethysms and Weintraub's conjecture

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power

Generation of spin currents via Raman scattering

We show theoretically that stimulated spin flip Raman scattering can be used to inject spin currents in doped semiconductors with spin split bands. A pure spin current, where oppositely oriented spins move in opposite directions, can be injected in zincblende crystals and structures. The calculated spin current should be detectable by pump-probe optical spectroscopy and anomalous Hall effect measurement

Theory of band gap bowing of disordered substitutional II-VI and III-V semiconductor alloys

For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A(x)B(1-x)C can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A(x)B(1-x)C semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight binding models for the pure AC and BC systems. The electronic properties of the A(x)B(1-x)C system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1-x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA). We apply this treatment to the II-VI system Cd(x)Zn(1-x)Se, to the III-V system In(x)Ga(1-x)As and to the III-nitride system Ga(x)Al(1-x)N.Comment: 14 pages, 10 figure

Targeting DNA repair in Metastatic Castration-Resistant Prostate Cancer (mCRPC): Genomic Screening for a Clinical Trial of Rucaparib

Objectives: The high prevalence of men with mCRPC carrying pathogenic mutations in DNA damage repair (DDR) genes may have implications for clinical treatment, as poly(ADP-ribose) polymerase (PARP) inhibitors, such as rucaparib, have shown preliminary evidence of activity in these patients. The ongoing phase 2 TRITON2 study (NCT02952534) is evaluating rucaparib in mCRPC patients harboring a deleterious germline or somatic mutation in BRCA1, BRCA2, ATM, or other DDR gene. Here we present results from genomic screening of tissue and plasma samples from mCRPC patients. Methods: Comprehensive genomic profiling was performed by Foundation Medicine, Inc., using FFPE tumor tissue and plasma circulating cell-free DNA (cfDNA) samples. These next-generation sequencing (NGS) assays detect germline and somatic genomic alterations (GAs), but do not distinguish between them. Results: By Jan 15, 2019, prostate or metastatic tumor tissue samples from 1050 mCRPC patients were processed. Sequencing was successful for 68% of prostate samples, 82% of soft-tissue metastatic samples, and 57% of bone metastatic samples. In total, tissue sequencing results were obtained for 774 (74%) patients. GAs in BRCA1, BRCA2, or ATM were observed in 16.7% of patients’ tissue. In parallel, plasma from 654 mCRPC patients was collected and sequenced: 96% of plasma samples had sufficient cfDNA to obtain sequencing results, and sequencing success was independent of the location of metastases (visceral, nodal, or bone). GAs in BRCA1, BRCA2, or ATM were observed in 21.4% of patients’ plasma. There was high concordance between the alterations detected by the tissue and plasma assays. For example, in 86% of patients the plasma assay detected the same BRCA2 alteration present in tissue. Conclusions: Genomic profiling may help guide clinical decision-making for mCRPC patients. Tumor and plasma testing successfully identified patients with eligible somatic or germline GAs for enrollment into TRITON2. These data continue to support the utilization of plasma genomic testing, particularly in patients without a lesion that can be biopsied. Source of Funding: Clovis Oncology, Inc

American Heart Association's Life Simple 7 and risk of atrial fibrillation in a population without known cardiovascular disease: The ARIC (Atherosclerosis risk in communities) study

Background-The American Heart Association has defined metrics of ideal cardiovascular health known as Life's Simple 7 (LS7) to prevent cardiovascular disease. We examined the association between LS7 and incident atrial fibrillation (AF) in a biracial cohort of middle- and older-aged adults without known cardiovascular disease. Methods and Results-This analysis included 13 182 ARIC (Atherosclerosis Risk in Communities) study participants (mean baseline age=54±5.7 years; 56% women; 25% black) free of AF and cardiovascular disease. An overall LS7 score was calculated as the sum of the LS7 component scores and classified as inadequate (0-4), average (5-9), or optimal (10-14) cardiovascular health. The primary outcome was incident AF, identified primarily by ECG and hospital discharge coding of AF through December 31, 2014. A total of 2266 (17%) incident AF cases were detected over a median follow-up of 25.1 years. Compared with the inadequate category (n=1057), participants in the average (n=8629) and optimal (n=3496) categories each had a lower risk of developing AF in a multivariable Cox proportional hazards model (hazard ratio 0.59, 95% confidence interval 0.51, 0.67 for average; and hazard ratio 0.38, 95% confidence interval 0.32, 0.44 for optimal). In a similar model, a 1-point-higher LS7 score was associated with a 12% lower risk of incident AF (hazard ratio 0.88, 95% confidence interval 0.86, 0.89). Conclusions-A higher LS7 score is strongly associated with a lower risk of AF in individuals without baseline cardiovascular disease. Determining whether interventions that improve the population's cardiovascular health also reduce AF incidence is needed

The Moderating Effect of Mental Toughness: Perception of Risk and Belief in the Paranormal

This research demonstrates that higher levels of mental toughness provide cognitive-perceptual processing advantages when evaluating risk. No previous research, however, has examined mental toughness in relation to perception of risk and paranormal belief (a variable associated with distorted perception of causality and elevated levels of perceived risk). Accordingly, the present paper investigated relationships between these factors. A sample of 174 participants completed self-report measures assessing mental toughness, general perception of risk, and paranormal belief. Responses were analyzed via correlations and moderation analyses. Results revealed that mental toughness correlated negatively with perception of risk and paranormal belief, whereas paranormal belief correlated positively with perception of risk. For the moderation effects, simple slopes analyses indicated that high levels of MT and subfactors of commitment and confidence reduced the strength of association between paranormal belief and perceived risk. Therefore, MT potentially acts as a protective factor among individuals who believe in the paranormal, reducing the tendency to perceive elevated levels of risk