413 research outputs found
On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices
Wishart correlation matrices are the standard model for the statistical
analysis of time series. The ensemble averaged eigenvalue density is of
considerable practical and theoretical interest. For complex time series and
correlation matrices, the eigenvalue density is known exactly. In the real
case, however, a fundamental mathematical obstacle made it forbidingly
complicated to obtain exact results. We use the supersymmetry method to fully
circumvent this problem. We present an exact formula for the eigenvalue density
in the real case in terms of twofold integrals and finite sums.Comment: 4 pages, 2 figure
Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices
Motivated by its relation to an -hard problem, we analyze the
ground state properties of anti-ferromagnetic Ising-spin networks embedded on
planar cubic lattices, under the action of homogeneous transverse and
longitudinal magnetic fields. This model exhibits a quantum phase transition at
critical values of the magnetic field, which can be identified by the
entanglement behavior, as well as by a Majorization analysis. The scaling of
the entanglement in the critical region is in agreement with the area law,
indicating that even simple systems can support large amounts of quantum
correlations. We study the scaling behavior of low-lying energy gaps for a
restricted set of geometries, and find that even in this simplified case, it is
impossible to predict the asymptotic behavior, with the data allowing equally
good fits to exponential and power law decays. We can therefore, draw no
conclusion as to the algorithmic complexity of a quantum adiabatic ground-state
search for the system.Comment: 7 pages, 13 figures, final version (accepted for publication in PRA
Magnetic inflation and Stellar Mass. II. On the radii of wingle, rapidly rotating, fully convective M-dwarf stars
Main-sequence, fully convective M dwarfs in eclipsing binaries are observed to be larger than stellar evolutionary models predict by as much as 10%–15%. A proposed explanation for this discrepancy involves effects from strong magnetic fields, induced by rapid rotation via the dynamo process. Although, a handful of single, slowly rotating M dwarfs with radius measurements from interferometry also appear to be larger than models predict, suggesting that rotation or binarity specifically may not be the sole cause of the discrepancy. We test whether single, rapidly rotating, fully convective stars are also larger than expected by measuring their distribution. We combine photometric rotation periods from the literature with rotational broadening () measurements reported in this work for a sample of 88 rapidly rotating M dwarf stars. Using a Bayesian framework, we find that stellar evolutionary models underestimate the radii by 10 \% \mbox{--}15{ \% }_{-2.5}^{+3}, but that at higher masses (0.18 < M < 0.4 M Sun), the discrepancy is only about 6% and comparable to results from interferometry and eclipsing binaries. At the lowest masses (0.08 < M < 0.18 M Sun), we find that the discrepancy between observations and theory is 13%–18%, and we argue that the discrepancy is unlikely to be due to effects from age. Furthermore, we find no statistically significant radius discrepancy between our sample and the handful of M dwarfs with interferometric radii. We conclude that neither rotation nor binarity are responsible for the inflated radii of fully convective M dwarfs, and that all fully convective M dwarfs are larger than models predict.The authors would like to thank the referee for the thoughtful report, which greatly improved the manuscript. The authors would also like to thank Lisa Prato and Larissa Nofi for IGRINS training, and Heidi Larson, Jason Sanborn, and Andrew Hayslip for operating the DCT during our observations. We would also like to thank Jen Winters, Jonathan Irwin, Paul Dalba, Mark Veyette, Eunkyu Han, and Andrew Vanderburg for useful discussions and helpful comments on this work. Some of this work was supported by the NASA Exoplanet Research Program (XRP) under grant No. NNX15AG08G issued through the Science Mission Directorate.These results made use of the Lowell Observatory's Discovery Channel Telescope, supported by Discovery Communications, Inc., Boston University, the University of Maryland, the University of Toledo and Northern Arizona University; the Immersion Grating Infrared Spectrograph (IGRINS) that was developed under a collaboration between the University of Texas at Austin and the Korea Astronomy and Space Science Institute (KASI) with the financial support of the US National Science Foundation under grant AST-1229522, of the University of Texas at Austin, and of the Korean GMT Project of KASI; data taken at The McDonald Observatory of The University of Texas at Austin; and data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by NASA and the NSF. (NNX15AG08G - NASA Exoplanet Research Program (XRP); Discovery Communications, Inc.; Boston University; University of Maryland; University of Toledo; Northern Arizona University; AST-1229522 - US National Science Foundation; University of Texas at Austin; Korean GMT Project of KASI; NASA; NSF
Novel Technology for Door Handle Design
We note the recent article on ‘The potential of alcohol release doorplates to reduce surface contamination during hand contact’ in the Journal of Hospital Infection [1]. We agree that reducing microbial contamination of frequently touched door surfaces and bacterial transfer via hands could feasibly reduce the risk of healthcare-associated infections (HCAIs) [1–3]. We recently examined a novel prototype door handle with precisely the same intention. This door handle is steel-framed and vertically aligned with the hand-grip portion encased by a specially prepared surface material (Figure 1)
Energetics and Possible Formation and Decay Mechanisms of Vortices in Helium Nanodroplets
The energy and angular momentum of both straight and curved vortex states of
a helium nanodroplet are examined as a function of droplet size. For droplets
in the size range of many experiments, it is found that during the pickup of
heavy solutes, a significant fraction of events deposit sufficient energy and
angular momentum to form a straight vortex line. Curved vortex lines exist down
to nearly zero angular momentum and energy, and thus could in principle form in
almost any collision. Further, the coalescence of smaller droplets during the
cooling by expansion could also deposit sufficient angular momentum to form
vortex lines. Despite their high energy, most vortices are predicted to be
stable at the final temperature (0.38 K) of helium nanodroplets due to lack of
decay channels that conserve both energy and angular momentum.Comment: 10 pages, 8 figures, RevTex 4, submitted to Phys. Rev.
A real quaternion spherical ensemble of random matrices
One can identify a tripartite classification of random matrix ensembles into
geometrical universality classes corresponding to the plane, the sphere and the
anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the
anti-sphere with truncations of unitary matrices. This paper focusses on an
ensemble corresponding to the sphere: matrices of the form \bY= \bA^{-1} \bB,
where \bA and \bB are independent matrices with iid standard
Gaussian real quaternion entries. By applying techniques similar to those used
for the analogous complex and real spherical ensembles, the eigenvalue jpdf and
correlation functions are calculated. This completes the exploration of
spherical matrices using the traditional Dyson indices .
We find that the eigenvalue density (after stereographic projection onto the
sphere) has a depletion of eigenvalues along a ring corresponding to the real
axis, with reflective symmetry about this ring. However, in the limit of large
matrix dimension, this eigenvalue density approaches that of the corresponding
complex ensemble, a density which is uniform on the sphere. This result is in
keeping with the spherical law (analogous to the circular law for iid
matrices), which states that for matrices having the spherical structure \bY=
\bA^{-1} \bB, where \bA and \bB are independent, iid matrices the
(stereographically projected) eigenvalue density tends to uniformity on the
sphere.Comment: 25 pages, 3 figures. Added another citation in version
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the
maximum length of increasing subsequences in Poissonized ensembles of random
permutations, random fixed point free involutions and reversed random fixed
point free involutions. It is shown that these probabilities are equal to the
hard edge gap probability for matrix ensembles with unitary, orthogonal and
symplectic symmetry respectively. The gap probabilities can be written as a sum
over correlations for certain determinantal point processes. From these
expressions a proof can be given that the limiting form of Pr(L(t) \le l) in
the three cases is equal to the soft edge gap probability for matrix ensembles
with unitary, orthogonal and symplectic symmetry respectively, thereby
reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page
The Expanding Fireball of Nova Delphini 2013
A classical nova occurs when material accreting onto the surface of a white
dwarf in a close binary system ignites in a thermonuclear runaway. Complex
structures observed in the ejecta at late stages could result from interactions
with the companion during the common envelope phase. Alternatively, the
explosion could be intrinsically bipolar, resulting from a localized ignition
on the surface of the white dwarf or as a consequence of rotational distortion.
Studying the structure of novae during the earliest phases is challenging
because of the high spatial resolution needed to measure their small sizes.
Here we report near-infrared interferometric measurements of the angular size
of Nova Delphini 2013, starting from one day after the explosion and continuing
with extensive time coverage during the first 43 days. Changes in the apparent
expansion rate can be explained by an explosion model consisting of an
optically thick core surrounded by a diffuse envelope. The optical depth of the
ejected material changes as it expands. We detect an ellipticity in the light
distribution, suggesting a prolate or bipolar structure that develops as early
as the second day. Combining the angular expansion rate with radial velocity
measurements, we derive a geometric distance to the nova of 4.54 +/- 0.59 kpc
from the Sun.Comment: Published in Nature. 32 pages. Final version available at
http://www.nature.com/nature/journal/v515/n7526/full/nature13834.htm
Very Low-Mass Stellar and Substellar Companions to Solar-Like Stars from MARVELS I: A Low Mass Ratio Stellar Companion to TYC 4110-01037-1 in a 79-day Orbit
TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and
short orbital period are atypical amongst solar-like (Teff ~< 6000 K) binary
systems. Our analysis of TYC 4110-01037-1 reveals it to be a moderately aged
(~<5 Gyr) solar-like star having a mass of 1.07 +/- 0.08 MSun and radius of
0.99 +/- 0.18 RSun. We analyze 32 radial velocity measurements from the
SDSS-III MARVELS survey as well as 6 supporting radial velocity measurements
from the SARG spectrograph on the 3.6m TNG telescope obtained over a period of
~2 years. The best Keplerian orbital fit parameters were found to have a period
of 78.994 +/- 0.012 days, an eccentricity of 0.1095 +/- 0.0023, and a
semi-amplitude of 4199 +/- 11 m/s. We determine the minimum companion mass (if
sin i = 1) to be 97.7 +/- 5.8 MJup. The system's companion to host star mass
ratio, >0.087 +/- 0.003, places it at the lowest end of observed values for
short period stellar companions to solar-like (Teff ~< 6000 K) stars. One
possible way to create such a system would be if a triple-component stellar
multiple broke up into a short period, low q binary during the cluster
dispersal phase of its lifetime. A candidate tertiary body has been identified
in the system via single-epoch, high contrast imagery. If this object is
confirmed to be co-moving, we estimate it would be a dM4 star. We present these
results in the context of our larger-scale effort to constrain the statistics
of low mass stellar and brown dwarf companions to FGK-type stars via the
MARVELS survey.Comment: 22 pages; accepted in A
Anti-cancer effects and mechanism of actions of aspirin analogues in the treatment of glioma cancer
INTRODUCTION: In the past 25 years only modest advancements in glioma treatment have been made, with patient prognosis and median survival time following diagnosis only increasing from 3 to 7 months. A substantial body of clinical and preclinical evidence has suggested a role for aspirin in the treatment of cancer with multiple mechanisms of action proposed including COX 2 inhibition, down regulation of EGFR expression, and NF-κB signaling affecting Bcl-2 expression. However, with serious side effects such as stroke and gastrointestinal bleeding, aspirin analogues with improved potency and side effect profiles are being developed. METHOD: Effects on cell viability following 24 hr incubation of four aspirin derivatives (PN508, 517, 526 and 529) were compared to cisplatin, aspirin and di-aspirin in four glioma cell lines (U87 MG, SVG P12, GOS – 3, and 1321N1), using the PrestoBlue assay, establishing IC50 and examining the time course of drug effects. RESULTS: All compounds were found to decrease cell viability in a concentration and time dependant manner. Significantly, the analogue PN517 (IC50 2mM) showed approximately a twofold increase in potency when compared to aspirin (3.7mM) and cisplatin (4.3mM) in U87 cells, with similar increased potency in SVG P12 cells. Other analogues demonstrated similar potency to aspirin and cisplatin. CONCLUSION: These results support the further development and characterization of novel NSAID derivatives for the treatment of glioma
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