5,440 research outputs found
Hyperelliptic Theta-Functions and Spectral Methods
A code for the numerical evaluation of hyperelliptic theta-functions is
presented. Characteristic quantities of the underlying Riemann surface such as
its periods are determined with the help of spectral methods. The code is
optimized for solutions of the Ernst equation where the branch points of the
Riemann surface are parameterized by the physical coordinates. An exploration
of the whole parameter space of the solution is thus only possible with an
efficient code. The use of spectral approximations allows for an efficient
calculation of all quantities in the solution with high precision. The case of
almost degenerate Riemann surfaces is addressed. Tests of the numerics using
identities for periods on the Riemann surface and integral identities for the
Ernst potential and its derivatives are performed. It is shown that an accuracy
of the order of machine precision can be achieved. These accurate solutions are
used to provide boundary conditions for a code which solves the axisymmetric
stationary Einstein equations. The resulting solution agrees with the
theta-functional solution to very high precision.Comment: 25 pages, 12 figure
Correlations and functional connections in a population of grid cells
We study the statistics of spike trains of simultaneously recorded grid cells
in freely behaving rats. We evaluate pairwise correlations between these cells
and, using a generalized linear model (kinetic Ising model), study their
functional connectivity. Even when we account for the covariations in firing
rates due to overlapping fields, both the pairwise correlations and functional
connections decay as a function of the shortest distance between the vertices
of the spatial firing pattern of pairs of grid cells, i.e. their phase
difference. The functional connectivity takes positive values between cells
with nearby phases and approaches zero or negative values for larger phase
differences. We also find similar results when, in addition to correlations due
to overlapping fields, we account for correlations due to theta oscillations
and head directional inputs. The inferred connections between neurons can be
both negative and positive regardless of whether the cells share common spatial
firing characteristics, that is, whether they belong to the same modules, or
not. The mean strength of these inferred connections is close to zero, but the
strongest inferred connections are found between cells of the same module.
Taken together, our results suggest that grid cells in the same module do
indeed form a local network of interconnected neurons with a functional
connectivity that supports a role for attractor dynamics in the generation of
the grid pattern.Comment: Accepted for publication in PLoS Computational Biolog
STARRY: Analytic Occultation Light Curves
We derive analytic, closed form, numerically stable solutions for the total
flux received from a spherical planet, moon or star during an occultation if
the specific intensity map of the body is expressed as a sum of spherical
harmonics. Our expressions are valid to arbitrary degree and may be computed
recursively for speed. The formalism we develop here applies to the computation
of stellar transit light curves, planetary secondary eclipse light curves, and
planet-planet/planet-moon occultation light curves, as well as thermal
(rotational) phase curves. In this paper we also introduce STARRY, an
open-source package written in C++ and wrapped in Python that computes these
light curves. The algorithm in STARRY is six orders of magnitude faster than
direct numerical integration and several orders of magnitude more precise.
STARRY also computes analytic derivatives of the light curves with respect to
all input parameters for use in gradient-based optimization and inference, such
as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit
observed light curves to infer properties of a celestial body's surface map.Comment: 55 pages, 20 figures. Accepted to the Astronomical Journal. Check out
the code at https://github.com/rodluger/starr
On the Transit Potential of the Planet Orbiting iota Draconis
Most of the known transiting exoplanets are in short-period orbits, largely
due to the bias inherent in detecting planets through the transit technique.
However, the eccentricity distribution of the known radial velocity planets
results in many of those planets having a non-negligible transit probability.
One such case is the massive planet orbiting the giant star iota Draconis, a
situation where both the orientation of the planet's eccentric orbit and the
size of the host star inflate the transit probability to a much higher value
than for a typical hot Jupiter. Here we present a revised fit of the radial
velocity data with new measurements and a photometric analysis of the stellar
variability. We provide a revised transit probability, an improved transit
ephemeris, and discuss the prospects for observing a transit of this planet
from both the ground and space.Comment: 6 pages, 7 figures, accepted for publication in ApJ. Radial
velocities will be made available in the on-line version and through the NASA
Star and Exoplanet Database (NStED). Minor corrections from ApJ proof have
been applie
A statistical model for brain networks inferred from large-scale electrophysiological signals
Network science has been extensively developed to characterize structural
properties of complex systems, including brain networks inferred from
neuroimaging data. As a result of the inference process, networks estimated
from experimentally obtained biological data, represent one instance of a
larger number of realizations with similar intrinsic topology. A modeling
approach is therefore needed to support statistical inference on the bottom-up
local connectivity mechanisms influencing the formation of the estimated brain
networks. We adopted a statistical model based on exponential random graphs
(ERGM) to reproduce brain networks, or connectomes, estimated by spectral
coherence between high-density electroencephalographic (EEG) signals. We
validated this approach in a dataset of 108 healthy subjects during eyes-open
(EO) and eyes-closed (EC) resting-state conditions. Results showed that the
tendency to form triangles and stars, reflecting clustering and node
centrality, better explained the global properties of the EEG connectomes as
compared to other combinations of graph metrics. Synthetic networks generated
by this model configuration replicated the characteristic differences found in
brain networks, with EO eliciting significantly higher segregation in the alpha
frequency band (8-13 Hz) as compared to EC. Furthermore, the fitted ERGM
parameter values provided complementary information showing that clustering
connections are significantly more represented from EC to EO in the alpha
range, but also in the beta band (14-29 Hz), which is known to play a crucial
role in cortical processing of visual input and externally oriented attention.
These findings support the current view of the brain functional segregation and
integration in terms of modules and hubs, and provide a statistical approach to
extract new information on the (re)organizational mechanisms in healthy and
diseased brains.Comment: Due to the limitation "The abstract field cannot be longer than 1,920
characters", the abstract appearing here is slightly shorter than that in the
PDF fil
Thermodynamic Description of Inelastic Collisions in General Relativity
We discuss head-on collisions of neutron stars and disks of dust ("galaxies")
following the ideas of equilibrium thermodynamics, which compares equilibrium
states and avoids the description of the dynamical transition processes between
them. As an always present damping mechanism, gravitational emission results in
final equilibrium states after the collision. In this paper we calculate
selected final configurations from initial data of colliding stars and disks by
making use of conservation laws and solving the Einstein equations. Comparing
initial and final states, we can decide for which initial parameters two
colliding neutron stars (non-rotating Fermi gas models) merge into a single
neutron star and two rigidly rotating disks form again a final (differentially
rotating) disk of dust. For the neutron star collision we find a maximal energy
loss due to outgoing gravitational radiation of 2.3% of the initial mass while
the corresponding efficiency for colliding disks has the much larger limit of
23.8%.Comment: 25 pages, 9 figure
Direct imaging of extra-solar planets in star forming regions: Lessons learned from a false positive around IM Lup
Most exoplanet imagers consist of ground-based adaptive optics coronagraphic
cameras which are currently limited in contrast, sensitivity and astrometric
precision, but advantageously observe in the near-IR (1- 5{\mu}m). Because of
these practical limitations, our current observational aim at detecting and
characterizing planets puts heavy constraints on target selection, observing
strategies, data reduction, and follow-up. Most surveys so far have thus
targeted young systems (1-100Myr) to catch the putative remnant thermal
radiation of giant planets, which peaks in the near-IR. They also favor systems
in the solar neighborhood (d<80pc), which eases angular resolution requirements
but also ensures a good knowledge of the distance and proper motion, which are
critical to secure the planet status, and enable subsequent characterization.
Because of their youth, it is very tempting to target the nearby star forming
regions, which are typically twice as far as the bulk of objects usually combed
for planets by direct imaging. Probing these interesting reservoirs sets
additional constraints that we review in this paper by presenting the planet
search that we initiated in 2008 around the disk-bearing T Tauri star IM Lup
(Lupus star forming region, 140-190pc). We show and discuss why age
determination, the choice of evolutionary model for the central star and the
planet, precise knowledge of the host star proper motion, relative or absolute
astrometric accuracy, and patience are the key ingredients for exoplanet
searches around more distant young stars. Unfortunately, most of the time,
precision and perseverance are not paying off: we discovered a candidate
companion around IM Lup in 2008, which we report here to be an unbound
background object. We nevertheless review in details the lessons learned from
our endeavor, and additionally present the best detection limits ever
calculated for IM Lup.Comment: 8 pages, 3 figures, 3 tables, accepted to A&
The Period-Luminosity Relation of Red Supergiant Stars in the Small Magellanic Cloud
The characteristics of light variation of RSGs in SMC are analyzed based on
the nearly 8-10 year long data collected by the ASAS and MACHO projects. The
identified 126 RSGs are classified into five categories accordingly: 20 with
poor photometry, 55 with no reliable period, 6 with semi-regular variation, 15
with Long Secondary Period (LSP) and distinguishable short period and 30 with
only LSP. For the semi-regular variables and the LSP variables with
distinguishable short period, the Ks band period-luminosity (P-L) relation is
analyzed and compared with that of the Galaxy, LMC and M33. It is found that
the RSGs in these galaxies obey similar P-L relation except the Galaxy. In
addition, the P-L relations in the infrared bands, namely the 2MASS JHKs,
Spitzer/IRAC and Spitzer/MIPS 24 {\mu}m bands, are derived with high
reliability. The best P-L relation occurs in the Spitzer/IRAC [3.6] and [4.5]
bands. Based on the comparison with the theoretical calculation of the P-L
relation, the mode of pulsation of RSGs in SMC is suggested to be the first
overtone radial mode.Comment: 82 pages, 31 figures, 6 tables, accepted for publication in Ap
Magnetism in Dense Quark Matter
We review the mechanisms via which an external magnetic field can affect the
ground state of cold and dense quark matter. In the absence of a magnetic
field, at asymptotically high densities, cold quark matter is in the
Color-Flavor-Locked (CFL) phase of color superconductivity characterized by
three scales: the superconducting gap, the gluon Meissner mass, and the
baryonic chemical potential. When an applied magnetic field becomes comparable
with each of these scales, new phases and/or condensates may emerge. They
include the magnetic CFL (MCFL) phase that becomes relevant for fields of the
order of the gap scale; the paramagnetic CFL, important when the field is of
the order of the Meissner mass, and a spin-one condensate associated to the
magnetic moment of the Cooper pairs, significant at fields of the order of the
chemical potential. We discuss the equation of state (EoS) of MCFL matter for a
large range of field values and consider possible applications of the magnetic
effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in
magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A.
Schmitt, H.-U. Ye
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