23,879 research outputs found
Malmheden's theorem revisited
In 1934 H. Malmheden discovered an elegant geometric algorithm for solving
the Dirichlet problem in a ball. Although his result was rediscovered
independently by Duffin 23 years later, it still does not seem to be widely
known. In this paper we return to Malmheden's theorem, give an alternative
proof of the result that allows generalization to polyharmonic functions and,
also, discuss applications of his theorem to geometric properties of harmonic
measures in balls in Euclidean spaces
Two-dimensional shapes and lemniscates
A shape in the plane is an equivalence class of sufficiently smooth Jordan
curves, where two curves are equivalent if one can be obtained from the other
by a translation and a scaling. The fingerprint of a shape is an equivalence of
orientation preserving diffeomorphisms of the unit circle, where two
diffeomorphisms are equivalent if they differ by right composition with an
automorphism of the unit disk. The fingerprint is obtained by composing Riemann
maps onto the interior and exterior of a representative of a shape in a
suitable way. In this paper, we show that there is a one-to-one correspondence
between shapes defined by polynomial lemniscates of degree n and nth roots of
Blaschke products of degree n. The facts that lemniscates approximate all
Jordan curves in the Hausdorff metric and roots of Blaschke products
approximate all orientation preserving diffeomorphisms of the circle in the
C^1-norm suggest that lemniscates and roots of Blaschke products are natural
objects to study in the theory of shapes and their fingerprints
Reflective Ghost Imaging through Turbulence
Recent work has indicated that ghost imaging may have applications in
standoff sensing. However, most theoretical work has addressed
transmission-based ghost imaging. To be a viable remote-sensing system, the
ghost imager needs to image rough-surfaced targets in reflection through long,
turbulent optical paths. We develop, within a Gaussian-state framework,
expressions for the spatial resolution, image contrast, and signal-to-noise
ratio of such a system. We consider rough-surfaced targets that create fully
developed speckle in their returns, and Kolmogorov-spectrum turbulence that is
uniformly distributed along all propagation paths. We address both classical
and nonclassical optical sources, as well as a computational ghost imager.Comment: 13 pages, 3 figure
Phase-conjugate optical coherence tomography
Quantum optical coherence tomography (Q-OCT) offers a factor-of-two
improvement in axial resolution and the advantage of even-order dispersion
cancellation when it is compared to conventional OCT (C-OCT). These features
have been ascribed to the non-classical nature of the biphoton state employed
in the former, as opposed to the classical state used in the latter.
Phase-conjugate OCT (PC-OCT), introduced here, shows that non-classical light
is not necessary to reap Q-OCT's advantages. PC-OCT uses classical-state signal
and reference beams, which have a phase-sensitive cross-correlation, together
with phase conjugation to achieve the axial resolution and even-order
dispersion cancellation of Q-OCT with a signal-to-noise ratio that can be
comparable to that of C-OCT.Comment: 4 pages, 3 figure
Neutrino emissivity under neutral kaon condensation
Neutrino emissivity from neutron star matter with neutral kaon condensate is
considered. It is shown that a new cooling channel is opened, and what is more,
all previously known channels acquire the greater emissivity reaching the level
of the direct URCA cycle in normal matter.Comment: 7 pages, 1 figure, to be published in Phys.Rev.C, revised version:
the sectioning changed and more discussion adde
Recruitment Market Trend Analysis with Sequential Latent Variable Models
Recruitment market analysis provides valuable understanding of
industry-specific economic growth and plays an important role for both
employers and job seekers. With the rapid development of online recruitment
services, massive recruitment data have been accumulated and enable a new
paradigm for recruitment market analysis. However, traditional methods for
recruitment market analysis largely rely on the knowledge of domain experts and
classic statistical models, which are usually too general to model large-scale
dynamic recruitment data, and have difficulties to capture the fine-grained
market trends. To this end, in this paper, we propose a new research paradigm
for recruitment market analysis by leveraging unsupervised learning techniques
for automatically discovering recruitment market trends based on large-scale
recruitment data. Specifically, we develop a novel sequential latent variable
model, named MTLVM, which is designed for capturing the sequential dependencies
of corporate recruitment states and is able to automatically learn the latent
recruitment topics within a Bayesian generative framework. In particular, to
capture the variability of recruitment topics over time, we design hierarchical
dirichlet processes for MTLVM. These processes allow to dynamically generate
the evolving recruitment topics. Finally, we implement a prototype system to
empirically evaluate our approach based on real-world recruitment data in
China. Indeed, by visualizing the results from MTLVM, we can successfully
reveal many interesting findings, such as the popularity of LBS related jobs
reached the peak in the 2nd half of 2014, and decreased in 2015.Comment: 11 pages, 30 figure, SIGKDD 201
Is There a Relationship between the Density of Primordial Black Holes in a Galaxy and the Rate of Cosmological Gamma-Ray Bursts?
The rate of accretion of matter from a solar-type star onto a primordial
black hole (PBH) that passes through it is calculated. The probability that a
PBH is captured into an orbit around a star in a galaxy is found. The mean
lifetime of the PBH in such an orbit and the rate of orbital captures of PBHs
in the galaxy are calculated. It is shown that this rate does not depend on the
mass of the PBH. This mechanism cannot make an appreciable contribution to the
rate of observed gamma-ray bursts. The density of PBHs in the galaxy can reach
a critical value - the density of the mass of dark matter in the galaxy.Comment: 7 page
Adaptive phase estimation is more accurate than non-adaptive phase estimation for continuous beams of light
We consider the task of estimating the randomly fluctuating phase of a
continuous-wave beam of light. Using the theory of quantum parameter
estimation, we show that this can be done more accurately when feedback is used
(adaptive phase estimation) than by any scheme not involving feedback
(non-adaptive phase estimation) in which the beam is measured as it arrives at
the detector. Such schemes not involving feedback include all those based on
heterodyne detection or instantaneous canonical phase measurements. We also
demonstrate that the superior accuracy adaptive phase estimation is present in
a regime conducive to observing it experimentally.Comment: 15 pages, 9 figures, submitted to PR
Effects of Differential Rotation on the Maximum Mass of Neutron Stars
The merger of binary neutron stars is likely to lead to differentially
rotating remnants. In this paper we numerically construct models of
differentially rotating neutron stars in general relativity and determine their
maximum allowed mass. We model the stars adopting a polytropic equation of
state and tabulate maximum allowed masses as a function of differential
rotation and stiffness of the equation of state. We also provide a crude
argument that yields a qualitative estimate of the effect of stiffness and
differential rotation on the maximum allowed mass.Comment: 6 pages, to appear in Ap
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