Homomorphisms of matrix algebras and constructions of Butson–Hadamard matrices

An $n\times n$ matrix $H$ is Butson–Hadamard if its entries are $k$th roots of unity and it satisfies $H{H}^1=n{I}_n$. Write $\mathrm{BH}(n,k)$ for the set of such matrices.Suppose that $k=p^{\alpha }{q}^{\beta }$ where $p$ and $q$ are primes and $\alpha \ge 1$. A recent result of Östergård and Paavola uses a matrix $H\in \mathrm{BH}(n,pk)$ to construct $H^{\prime }\in \mathrm{BH}(pn,k)$. We simplify the proof of this result and remove the restriction on the number of prime divisors of $k$. More precisely, we prove that if $k=mt$, and each prime divisor of $k$ divides $t$, then we can construct a matrix $H^{\prime }\in \mathrm{BH}(mn,t)$ from any $H\in \mathrm{BH}(n,k)$.     

Intersection forms of toric hyperkähler varieties

This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of harmonic forms on complete hyperkähler manifolds of linear growth.

     

Student Perceptions of a Summer Ventures in Science and Mathematics Camp Experience

“As the world becomes increasingly technological, the value of (the ideas and skills of its population) will be determined in no small measure by the effectiveness of science, technology, engineering, and mathematics (STEM) education in the United States” and “STEM education will determine whether the United States will remain a leader among nations and whether we will be able to solve immense challenges in such areas as energy, health, environmental protection, and national security” (President's Council of Advisors on Science and Technology, 2010, p. vii). Research on the effectiveness of STEM‐focused school and other learning experiences (e.g., short‐term camps) on student attitudes and performance outcomes is sparse. In this study, we documented the influence of an intensive STEM summer program on high school students’ attitudes toward STEM concepts and interests in STEM careers. Attending the summer program was associated with gains on students’ attitudes toward some aspects of STEM as well as specific career interests. Notably, students reported statistically significant views of important aspects of STEM and their attitudes toward science and mathematics were more positive than their attitudes about engineering and technology.     

Random Variable Generation Using Concavity Properties of Transformed Densities

Abstract

Algorithms are developed for constructing random variable generators for families of densities. The generators depend on the concavity structure of a transformation of the density. The resulting algorithms are rejection algorithms and the methods of this article are concerned with constructing good rejection algorithms for general densities.     

Proliferative reactive gliosis is compatible with glial metabolic support and neuronal function

Background

Trail-making tests, such as the Concept Shifting Task (CST), can be used to test the effects of treatment on cognitive performance over time in various neuropsychological disorders. However, cognitive performance in such experimental designs might improve as a result of the practice obtained during repeated testing rather than the treatment itself. The current study investigated if practice affects the accuracy and duration of performance on the repeatedly administered Concept Shifting Task modified to make it resistant to practice (mCST). The mCST was administered to 54 healthy participants twice a day, before and after a short break, for eight days. Results. The ANOVA and meta-analysis showed that there was no improvement in the mCST accuracy on the last vs. the first trial (Hedges' g = .14, p = .221) or within the session (after vs. before the break on all days; g = .01, p = .922). However, the participants performed the task faster on the last vs. the first trial (g = -.75, p < .001) and after vs. before the break on all days (g = -.12, p = .002). Conclusions. Repeated administration of the mCST does not affect the accuracy of performance on the test. However, practice might contribute to faster performance on the mCST over time and within each session.     

Direct evidence for an intrinsic square vortex lattice in the overdoped high- T(c) superconductor La(1.83)Sr(0.17)CuO(4+delta)

We report here the first direct observations of a well ordered vortex lattice in the bulk of a La(2-x)Sr(x)CuO(4+delta) single crystal (slightly overdoped, x = 0.17). Our small angle neutron scattering investigation of the mixed phase reveals a crossover from triangular to square coordination with increasing magnetic field. The existence of an intrinsic square vortex lattice has never been observed in high-temperature superconductors and is indicative of the coupling of the vortex lattice to a source of anisotropy, such as those provided by a d-wave order parameter or the presence of stripes.     

Average speaking fundamental frequency in soprano singers with and without symptoms of vocal attrition

Nineteen trained soprano singers aged 18–30 years vocalized tasks designed to assess average speaking fundamental frequency (SFF) during spontaneous speaking and reading. Vocal range and perceptual characteristics while singing with low intensity and high frequency were also assessed, and subjects completed a survey of vocal habits/symptoms. Recorded signals were digitized prior to being analyzed for SFF using the Kay Computerized Speech Lab program. Subjects were assigned to a normal voice or impaired voice group based on ratings of perceptual tasks and survey results. Data analysis showed group differences in mean SFF, no differences in vocal range, higher mean SFF values for reading than speaking, and 58% ability to perceive speaking in low pitch. The role of speaking in too low pitch as causal for vocal symptoms and need for voice classification differentiation in vocal performance studies are discussed.     

Electronically tunable surface-coil-type resonator for L-band EPR spectroscopy

The automatic frequency control (AFC) circuit in conventional electron paramagnetic resonance (EPR) spectrometers automatically tunes the microwave source to the resonance frequency of the resonator. The circuit works satisfactorily for samples stable enough that the geometric relations in the resonance structure do not change in a significant way. When EPR signals are measured during in vivo experiments with small rodents, however, the distance between the signal source and the surface-coil detector can change rapidly. When a conventional AFC circuit keeps the oscillator tuned to the resonator under those conditions, the resultant frequency change may exceed +/-5 MHz and markedly shift the position of the EPR signal. Such a shift results in unacceptable effects on the spectra, especially when the experimenter is dealing with narrow EPR lines. The animal movement also causes a mismatching of the resonator and the 50-ohm transmission line. Direct results of this mismatching are increased noise; shifts in the position of the baseline; and a high probability of overdriving the signal preamplifier with consequent loss of the EPR signal. We therefore designed, built, and tested a new surface-coil resonator using varactor diodes for tuning the resonance frequency to the fixed frequency oscillator and for capacitive matching of the resonator to the 50-ohm transmission line. The performance of the automatic matching system was tested in vivo by measuring EPR spectra of lithium phthalocyanine implanted in rats. Stability and sensitivity of the spectrometer were evaluated by measuring EPR spectra with and without the use of the automatic matching system. The overall experimental performance of the spectrometer was found to significantly improve during in vivo experiments using the automatic matching system. Excellent matching between the 50-ohm transmission line and the resonator was maintained under all experimental circumstances that were tested. This should allow us now to carry out experiments that previously were not possible.     

beta-Sheet mediated self-assembly of dipeptides of omega-amino acids and remarkable fibrillation in the solid state

Single crystal X-ray diffraction studies show that the extended structure of dipeptide Boc-beta-Ala-m-ABA-OMe (m-ABA: meta-aminobenzoic acid) self-assembles in the solid state by intermolecular hydrogen bonding to create an infinite parallel beta-sheet structure. In dipeptide Boc-gamma-Abu-m-ABA-OMe (gamma-Abu: gamma-aminobutyric acid), two such parallel beta-sheets are further cross-linked by intermolecular hydrogen bonding through m-aminobenzoic acid moieties. SEM (scanning electron microscopy) studies reveal that both the peptides and form amyloid-like fibrils in the solid state. The fibrils are also found to be stained readily by Congo red, a characteristic feature of the amyloid fiber whose accumulation causes several fatal diseases such as Alzheimer's, prion-protein etc.