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Recent gravitational wave detections from black hole mergers have underscored
the critical role black hole perturbation theory and the Teukolsky equation
play in understanding the behaviour of black holes. The separable nature of the
Teukolsky equation has long been leveraged to study the vacuum linear Teukolsky
equation; however, as theory and measurements advance, solving the sourced
Teukolsky equation is becoming a frontier of research. In particular,
second-order calculations, such as in quasi-normal mode and self-force
problems, have extended sources. This paper presents a novel method for
analytically separating the Teukolsky equation's source, aimed to improve
efficiency. Separating the source is a non-trivial problem due to the angular
and radial mixing of generic quantities in Kerr spacetime. We provide a
proof-of-concept demonstration of our method and show that it is accurate,
separating the Teukolsky source produced by the stress-energy tensor of an
ideal gas cloud surrounding a Kerr black hole. The detailed application of our
method is provided in an accompanying \textit{Mathematica} notebook. Our
approach opens up a new avenue for accurate black hole perturbation theory
calculations with sources in both the time and frequency domain.
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In the present treatise, a stability analysis of the bottom boundary layer
under solitary waves based on energy bounds and nonmodal theory is performed.
The instability mechanism of this flow consists of a competition between
streamwise streaks and two- dimensional perturbations. For lower Reynolds
numbers and early times, streamwise streaks display larger amplification due to
their quadratic dependence on the Reynolds number, whereas two-dimensional
perturbations become dominant for larger Reynolds numbers and later times in
the deceleration region of this flow, as the maximum amplification of
two-dimensional perturbations grows exponentially with the Reynolds number. By
means of the present findings, we can give some indications on the physical
mecha- nism and on the interpretation of the results by direct numerical
simulation in (Vittori & Blondeaux 2008; Ozdemir et al. 2013) and by
experiments in (Sumer et al. 2010). In addition, three critical Reynolds
numbers can be defined for which the stability prop- erties of the flow change.
In particular, it is shown that this boundary layer changes from a
monotonically stable to a non-monotonically stable flow at a Reynolds number of
18.
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We improve proofs in "The Floyd-Warshall Algorithm, the AP and the TSP (III).
We also simplify the method for obtaining a good upper bound for an optimal
solution.
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Background: In our recent experiment, $^9$Be+p at 5.67A MeV, the breakup
decay rates to the 3 configurations, $\alpha$+$\alpha$+n, $^8$Be$^*$+n and
$^5$He+$^4$He of $^9$Be, were observed and quantified, in a full kinematics
approach. Unfolding step by step the accessibility to the above configurations,
it will require similar studies at lower and higher energies as well as the
interpretation of the data in a theoretical framework. Purpose: Investigate the
breakup decay rate of $^9$Be+p at 2.72A MeV, where the $\alpha$+$\alpha$+n
configuration is mainly accessible. Compare and interpret data at 2.72A MeV and
5.67A MeV into a 4-body CDCC formalism; Point out and discuss couplings to
continuum. Methods: Our experimental method includes an exclusive breakup
measurement in a full kinematic approach of $^9$Be incident on a proton target
at 2.72A MeV, together with elastic scattering and other reaction channels
measurements under the same experimental conditions. The interpretation of the
data at 2.72A MeV and 5.67A MeV is considered in a 4-body CDCC approach, using
the Transformed Harmonic Oscillator method for the 3-body projectile. Results:
An elastic scattering angular distribution at 2.72A MeV is measured, which
compares very well with CDCC calculations, indicating a strong coupling to
continuum. At the same energy, the measured breakup and total reaction cross
sections present good agreement with the calculated values. Further on, the
elastic scattering and breakup cross section data at 5.67A MeV are found in
very good agreement with the CDCC calculations. The present results support
further our 3-body model for the structure of $^9$Be, validating relevant
radiative reaction rates obtained previously.
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For an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$.
Following a recent work of Z. W. Sun, we show that every natural number can be
written in any of the following forms with $x,y,z\in\Z$: $$x^2+3y^2+t_z,
x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$$ This confirms a
conjecture of Sun.
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We prove non-asymptotic stretched exponential tail bounds on the height of a
randomly sampled node in a random combinatorial tree, which we use to prove
bounds on the heights and widths of random trees from a variety of models. Our
results allow us to prove a conjecture and settle an open problem of Janson
(https://doi.org/10.1214/11-PS188), and nearly prove another conjecture and
settle another open problem from the same work (up to a polylogarithmic
factor).
The key tool for our work is an equivalence in law between the degrees along
the path to a random node in a random tree with given degree statistics, and a
random truncation of a size-biased ordering of the degrees of such a tree. We
also exploit a Poissonization trick introduced by Camarri and Pitman
(https://doi.org/10.1214/EJP.v5-58) in the context of inhomogeneous continuum
random trees, which we adapt to the setting of random trees with fixed degrees.
Finally, we propose and justify a change to the conventions of branching
process nomenclature: the name "Galton-Watson trees" should be permanently
retired by the community, and replaced with the name "Bienaym\'e trees".
|
We derive a closed-form, analytical expression for the spectrum of
long-wavelength density perturbations in inflationary models with two (or more)
inflaton degrees of freedom that is valid in the slow-roll approximation. We
illustrate several classes of potentials for which this expression reduces to a
simple, algebraic expression.
|
The advent and fast development of neural networks have revolutionized the
research on dialogue systems and subsequently have triggered various challenges
regarding their automatic evaluation. Automatic evaluation of open-domain
dialogue systems as an open challenge has been the center of the attention of
many researchers. Despite the consistent efforts to improve automatic metrics'
correlations with human evaluation, there have been very few attempts to assess
their robustness over multiple domains and dimensions. Also, their focus is
mainly on the English language. All of these challenges prompt the development
of automatic evaluation metrics that are reliable in various domains,
dimensions, and languages. This track in the 11th Dialogue System Technology
Challenge (DSTC11) is part of the ongoing effort to promote robust and
multilingual automatic evaluation metrics. This article describes the datasets
and baselines provided to participants and discusses the submission and result
details of the two proposed subtasks.
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The dielectric constant of a sheath, whether ionic or electronic, formed
around the cylindrical limbs of a hairpin probe, is often considered the same
as that of a vacuum. However, this assumption does not hold true for electron
sheaths and electron-permeating ionic sheaths, resulting in a deviation of the
sheath dielectric constant from that of a vacuum. This deviation significantly
influences the effective dielectric between the cylindrical limbs. As a result,
it impacts the theoretically estimated resonance frequency characteristic curve
of a DC-biased hairpin probe. In this study, we investigate the influence of
electron temperature on the sheath dielectric and, consequently, on the
resonance frequency characteristic curve. The findings shows that electron
temperature primarily determines the resonance frequency characteristic curve.
With increasing electron temperature, the peak in the resonance frequency
characteristic curve shifts towards higher positive probe bias values and
exhibits a broadening near the maxima instead of a sharp peak. This broadening
near the maxima has also been validated with an experimentally measured
resonance frequency characteristic curve in a capacitively coupled argon
discharge.
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Referring to quantum mechanics, Einstein used to say "The old one does not
play dice." And this is true since the probability of quantum mechanics is not
the classical probability of games such as dice. Historically this was the
first example of a non-classical probability theory, which we introduce in this
expository article using undergraduate linear algebra. There is a short
appendix on qubits. Knowledge of quantum mechanics is not required.
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Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G
and an integral domain R, the group ring R[G] does not contain non-trivial zero
divisors. We define the length of an element a in R[G] as the minimal
non-negative integer k for which there are ring elements r_1,...,r_k in R and
group elements g_1,...,g_k in G such that a = r_1 g_1+...+r_k g_k. We
investigate the conjecture when R is the field of rational numbers. By a
reduction to the finite field with two elements, we show that if ab = 0 for
non-trivial elements in the group ring of a torsion-free group over the
rationals, then the lengths of a and b cannot be among certain combinations.
More precisely, we show for various pairs of integers (i,j) that if one of the
lengths is at most i then the other length must exceed j. Using combinatorial
arguments we show this for the pairs (3,6) and (4,4). With a computer-assisted
approach we strengthen this to show the statement holds for the pairs (3,16)
and (4,7). As part of our method, we describe a combinatorial structure, which
we call matched rectangles, and show that for these a canonical labeling can be
computed in quadratic time. Each matched rectangle gives rise to a presentation
of a group. These associated groups are universal in the sense that there is no
counterexample to the conjecture among them if and only if the conjecture is
true over the rationals.
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In this short note we observe that the Hilali conjecture holds for two-stage
spaces, i.e. we argue that the dimension of the rational cohomology is at least
as large as the dimension of the rational homotopy groups for these spaces. We
also prove the Hilali conjecture for a class of spaces which puts it into the
context of fibrations.
|
We discuss whether homogeneous Cauchy stress implies homogeneous strain in
isotropic nonlinear elasticity. While for linear elasticity the positive answer
is clear, we exhibit, through detailed calculations, an example with
inhomogeneous continuous deformation but constant Cauchy stress. The example is
derived from a non rank-one convex elastic energy.
|
Using modified Arrhenius approximations, the activation energies of water,
alcohols, and hexane structure rearrangement reactions responsible for
temperature dependences of their dynamic and dielectric characteristics were
determined. The interactions of van der Waals and charged centers of water and
alcohol molecules regulate translational and rotational motion of molecules,
ensuring coordination and balance of thermal effects of exothermic and
endothermic reactions of changes in local structure of liquid. The long range
action of fluctuating dipoles of hydrogen bonds and their resonant excitation
by thermal energy underlies the anomalies in temperature dependences of water
properties and initiates its phase transitions at points 273 K and 298 K. The
deviation of the molecular dynamics of water from Arrhenius and Stokes Einstein
equations in range from 273 to 298 K was associated with a high contribution of
collective dynamics of ice like phase of water consisting of a network of
hydrogen bonds structured by hexagonal clusters of Ih ice.
|
We describe how some problems (interpretability,lack of object-orientedness)
of modern deep networks potentiallycould be solved by adapting a biologically
plausible saccadicmechanism of perception. A sketch of such a saccadic
visionmodel is proposed. Proof of concept experimental results areprovided to
support the proposed approach.
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It was shown that quantum mechanical qubit states as elements of two
dimensional complex space can be generalized to elements of even subalgebra of
geometric (Clifford) algebra over Euclidian space. The construction critically
depends on generalization of formal, unspecified, complex plane to arbitrary
variable, but explicitly defined, planes in 3D, and of usual Hopf fibration to
maps generated by arbitrary unit value bivectors. Analysis of the new structure
demonstrates that quantum state evolution in terms of two dimensional complex
space gives only restricted information compared to that in even geometric
algebra.
|
Using the Geant4 toolkit, a Monte-Carlo code to simulate the detector
background of the Simbol-X focal plane instrument has been developed with the
aim to optimize the design of the instrument. Structural design models of the
mirror and detector satellites have been built and used as baseline for our
simulations, to evaluate the different background contributions that must be
taken into account to determine the sensitivity of the Simbol-X detectors. We
work towards a simulation based background and mass model which can be used
before and during the mission.
For different material compositions, material thicknesses, locations etc. the
response of the instrument to the diffuse cosmic hard X-ray background and to
the cosmic proton induced background have been calculated. As a result we
present estimates of the background count rate expected in the low and high
energy detector, and anti-coincidence rates. The effect of induced
radioactivity in the detector and shielding materials and soft proton
scattering in the mirror shells are also under study.
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Context: Many current and future surveys aim to detect the highest redshift
(z >~ 7) sources through their Lyman-alpha (Ly-alpha) emission, using the
narrow-band imaging method. However, to date the surveys have only yielded
non-detections and upper limits as no survey has reached the necessary
combination of depth and area to detect these very young star forming galaxies.
Aims: We aim to calculate model luminosity functions and mock surveys of
Ly-alpha emitters at z >~ 7 based on a variety of approaches.
Methods: We calculate model luminosity functions at different redshifts based
on three different approaches: a semi-analytical model based on CDM, a simple
phenomenological model, and an extrapolation of observed Schechter functions at
lower redshifts. The results of the first two models are compared with
observations made at redshifts z ~ 5.7 and z ~ 6.5, and they are then
extrapolated to higher redshift.
Results: We present model luminosity functions for redshifts between z = 7 -
12.5 and give specific number predictions for future planned or possible
narrow-band surveys for Ly-alpha emitters. We also investigate what constraints
future observations will be able to place on the Ly-alpha luminosity function
at very high redshift.
Conclusion: It should be possible to observe z = 7 - 10 Ly-alpha emitters
with present or near-future instruments if enough observing time is allocated.
In particular, large area surveys such as ELVIS (Emission Line galaxies with
VISTA Survey) will be useful in collecting a large sample. However, to get a
large enough sample to constrain well the z >= 10 Ly-alpha luminosity function,
instruments further in the future, such as an ELT, will be necessary.
|
Unifying seemingly disparate algorithmic ideas to produce better performing
algorithms has been a longstanding goal in reinforcement learning. As a primary
example, TD($\lambda$) elegantly unifies one-step TD prediction with Monte
Carlo methods through the use of eligibility traces and the trace-decay
parameter $\lambda$. Currently, there are a multitude of algorithms that can be
used to perform TD control, including Sarsa, $Q$-learning, and Expected Sarsa.
These methods are often studied in the one-step case, but they can be extended
across multiple time steps to achieve better performance. Each of these
algorithms is seemingly distinct, and no one dominates the others for all
problems. In this paper, we study a new multi-step action-value algorithm
called $Q(\sigma)$ which unifies and generalizes these existing algorithms,
while subsuming them as special cases. A new parameter, $\sigma$, is introduced
to allow the degree of sampling performed by the algorithm at each step during
its backup to be continuously varied, with Sarsa existing at one extreme (full
sampling), and Expected Sarsa existing at the other (pure expectation).
$Q(\sigma)$ is generally applicable to both on- and off-policy learning, but in
this work we focus on experiments in the on-policy case. Our results show that
an intermediate value of $\sigma$, which results in a mixture of the existing
algorithms, performs better than either extreme. The mixture can also be varied
dynamically which can result in even greater performance.
|
The notion of asymptotic Fekete arrays, arrays of points in a compact set
$K\subset {\bf C}^d$ which behave asymptotically like Fekete arrays, has been
well-studied, albeit much more recently in dimensions $d>1$. Here we show that
one can allow a more flexible definition where the points in the array need not
lie in $K$. Our results, which work in the general setting of weighted
pluripotential theory, rely heavily, in the multidimensional setting, on the
ground-breaking work of Berman, Boucksom and Nystrom.
|
We construct a class of non-weight modules over the twisted $N=2$
superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the
Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan
subalgebra of even part $\T_{\bar 0}$. These modules over $\T$ when restricted
to the $\mathfrak{h}$ are free of rank $1$ or when restricted to the
$\mathfrak{t}$ are free of rank $2$. We provide the sufficient and necessary
conditions for those modules being simple, as well as giving the sufficient and
necessary conditions for two $\T$-modules being isomorphic. We also compute the
action of an automorphism on them. Moreover, based on the weighting functor
introduced in \cite{N2}, a class of intermediate series modules $A_\sigma$ are
obtained. As a byproduct, we give a sufficient condition for two $\T$-modules
are not isomorphic.
|
There is increasing evidence that the highly ionized multiphase components of
AGN disk winds may be due to thermal instability. The ions responsible for
forming the observed X-ray absorption lines may only exist in relatively cold
clumps that can be identified with the so-called 'warm absorbers'. Here we
calculate synthetic absorption lines for such warm absorbers from first
principles by combining 2D hydrodynamic solutions of a two-phase medium with a
dense grid of photoionization models to determine the detailed ionization
structure of the gas. Our calculations reveal that cloud disruption, which
leads to a highly complicated velocity field (i.e. a clumpy flow), will only
mildly affect line shapes and strengths when the cold gas becomes highly mixed
but not depleted. Prior to complete disruption, clouds which are optically thin
to the driving UV resonance lines will cause absorption at an increasingly
blueshifted line of sight velocity as they are accelerated. This behavior will
imprint an identifiable signature on the line profile if warm absorbers are
enshrouded in an even broader absorption line produced by a high column of
intercloud gas. Interestingly, we show that it is possible to develop a
spectral diagnostic for cloud acceleration by differencing the absorption
components of a doublet line, a result which can be qualitatively understood
using a simple partial covering model. Our calculations also permit us to
comment on the spectral differences between cloud disruption and ionization
changes driven by flux variability. Notably, cloud disruption offers another
possibility for explaining absorption line variability.
|
Large scale analysis and statistics of socio-technical systems that just a
few short years ago would have required the use of consistent economic and
human resources can nowadays be conveniently performed by mining the enormous
amount of digital data produced by human activities. Although a
characterization of several aspects of our societies is emerging from the data
revolution, a number of questions concerning the reliability and the biases
inherent to the big data "proxies" of social life are still open. Here, we
survey worldwide linguistic indicators and trends through the analysis of a
large-scale dataset of microblogging posts. We show that available data allow
for the study of language geography at scales ranging from country-level
aggregation to specific city neighborhoods. The high resolution and coverage of
the data allows us to investigate different indicators such as the linguistic
homogeneity of different countries, the touristic seasonal patterns within
countries and the geographical distribution of different languages in
multilingual regions. This work highlights the potential of geolocalized
studies of open data sources to improve current analysis and develop indicators
for major social phenomena in specific communities.
|
We study the structure of finite quandles in terms of subquandles. Every
finite quandle $Q$ decomposes in a natural way as a union of disjoint
$Q$-complemented subquandles; this decomposition coincides with the usual orbit
decomposition of $Q$. Conversely, the structure of a finite quandle with a
given orbit decomposition is determined by its structure maps. We describe a
procedure for finding all non-connected quandle structures on a disjoint union
of subquandles.
|
This study employed grain dynamic models to examine the density distribution
of debris discs, and discussed the effects of the collisional time-intervals of
asteroidal bodies, the maximum grain sizes, and the chemical compositions of
the dust grains of the models, in order to find out whether a steady out-moving
flow with an 1/R profile could be formed. The results showed that a model with
new grains every 100 years, a smaller maximum grain size, and a composition
C400 has the best fit to the 1/R profile because: (1) the grains have larger
values of beta on average,therefore, they can be blown out easily; (2) the new
grains are generated frequently enough to replace those have been blown out.
With the above two conditions, some other models can have a steady out-moving
flow with an approximate 1/R profile. However, those models in which new grains
are generated every 1000 years have density distributions far from the profile
of a continuous out-moving flow. Moreover, the analysis on the signatures of
planets in debris discs showed that there are no indications when a planet is
in a continuous out-moving flow, however, the signatures are obvious in a
debris disc with long-lived grains.
|
A new proposal is given for designing a non-volatile, completely spin logic
device, that can be reprogrammed for different functional classical logical
operations. We use the concept of bias driven spin dependent circular current
and current induced magnetic field in a quantum ring under asymmetric
ring-to-electrode interface configuration to implement all the Boolean
operations. We extend our idea to build two kinds of parallel computing
architectures for getting parallelized operations, all at a particular time.
For one case, different kinds of parallel operations are performed in a single
device, whereas in the other type all the possible inputs of a logic gate are
processed in parallel and all the outputs are read simultaneously. The
performance and reliability are investigated in terms of power, delay and
power-delay-product and finally the system temperature. We find that both the
individual and simultaneous logic operations studied here are much superior
compared to the operations performed in different conventional logic families
like complementary metal oxide semiconductor logic, transistor-transistor
logic, etc. The key advantage is that we can perform several logic operations,
as many as we wish, repeating the same or different logic gates using a single
setup, which indeed reduces wiring in the circuits and hence consumes much less
power. Our analysis can be utilized to design optimized logic circuits at
nano-scale level.
|
Response functions to perturbations in the temperature, pressure,
microturbulent velocity, and magnetic intensity were calculated for the Stokes
parameter profiles of the lines Fe I 525.06, 525.02 and Fe II 614.92 nm. The
procedure proposed by Grossmann-Doerth, Larsson, and Solanki (1988) was used.
We show that the depression response functions may be used not only to
determine the depths at which changes in the physical conditions affect most
effectively the absorption and emission in the continuum and in lines, but to
estimate the response of Stokes profiles as well. The response was estimated
using sensitivity indicators calculated as an integral of the response function
over all photospheric layers. An anomalous temperature sensitivity was found
for the Stokes profiles in lines with high excitation and ionization potentials
such as the lines of O I, C I, Fe II. The depression of such lines increases
rather than decreases with growing temperature. The magnetic sensitivity of
Stokes profiles depends primarily on the magnetic field conditions. The
response of V profiles is the greatest under the weak-field and
intermediate-field conditions for photospheric lines with large values of the
Lande factor, wavelength, and equivalent width. The results of calculations of
sensitivity indicators are presented for magnetic lines together with the
indices of magnetic and temperature enhancement.
|
We estimate the contributions by double-parton interactions to the cross
sections for pp->pi^0 pi^0 X and dA->pi^0 pi^0 X at RHIC. We find that such
contributions become important at large forward rapidities of the produced
pions. This is in particular the case for dA scattering, where they strongly
enhance the azimuthal-angular independent "pedestal" component of the cross
section, providing a natural explanation of this feature of the RHIC dA data.
We argue that the discussed processes open a window to studies of double quark
distributions in nucleons. We also briefly address the roles of shadowing and
energy loss in dA scattering, which we show to affect the double-inclusive pion
cross section much more strongly than the single-inclusive one. We discuss the
implications of our results for the interpretation of pion azimuthal
correlations.
|
By considering a Gaussian truncation of ${\cal N}=4$ super Yang-Mills, we
derive a set of Dyson equations that account for the ladder diagram
contribution to connected correlators of circular Wilson loops. We consider
different numbers of loops, with different relative orientations. We show that
the Dyson equations admit a spectral representation in terms of eigenfunctions
of a Schr\"odinger problem, whose classical limit describes the strong coupling
limit of the ladder resummation. We also verify that in supersymmetric cases
the exact solution to the Dyson equations reproduces known matrix model
results.
|
We show, by analyzing its characteristics, that the ghost-free, 5 degree of
freedom, Wess--Zumino massive gravity model admits superluminal shock wave
solutions and thus is acausal. Ironically, this pathology arises from the very
constraint that removes the (sixth) Boulware-Deser ghost mode.
|
The Astropy Project (http://astropy.org) is, in its own words, "a community
effort to develop a single core package for Astronomy in Python and foster
interoperability between Python astronomy packages." For five years this
project has been managed, written, and operated as a grassroots,
self-organized, almost entirely volunteer effort while the software is used by
the majority of the astronomical community. Despite this, the project has
always been and remains to this day effectively unfunded. Further, contributors
receive little or no formal recognition for creating and supporting what is now
critical software. This paper explores the problem in detail, outlines possible
solutions to correct this, and presents a few suggestions on how to address the
sustainability of general purpose astronomical software.
|
Recent major milestones have successfully decoded non-invasive brain signals
(e.g. functional Magnetic Resonance Imaging (fMRI) and electroencephalogram
(EEG)) into natural language. Despite the progress in model design, how to
split the datasets for training, validating, and testing still remains a matter
of debate. Most of the prior researches applied subject-specific data
splitting, where the decoding model is trained and evaluated per subject. Such
splitting method poses challenges to the utilization efficiency of dataset as
well as the generalization of models. In this study, we propose a cross-subject
data splitting criterion for brain-to-text decoding on various types of
cognitive dataset (fMRI, EEG), aiming to maximize dataset utilization and
improve model generalization. We undertake a comprehensive analysis on existing
cross-subject data splitting strategies and prove that all these methods suffer
from data leakage, namely the leakage of test data to training set, which
significantly leads to overfitting and overestimation of decoding models. The
proposed cross-subject splitting method successfully addresses the data leakage
problem and we re-evaluate some SOTA brain-to-text decoding models as baselines
for further research.
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We consider the problem of the depinning of a weakly driven ($F\ll F_{c}$)
pancake vortex from a columnar defect in a Josephson-coupled superconductor,
where $F$ denotes the force acting on the vortex ($F_{c}$ is the critical
force).
The dynamics of the vortex is supposed to be of the Hall type. The Euclidean
action $S_{Eucl}(T)$ is calculated in the entire temperature range; the result
is universal and does not depend on the detailed form of the pinning potential.
We show that the transition from quantum to classical behavior is second-order
like with the temperature $T_{c}$ of the transition scaling like $F^{{4}/{3}}.$
Special attention is paid to the regime of applicability of our results, in
particular, the influence of the large vortex mass appearing in the superclean
limit is discussed.
|
We present here the first work to propose different mechanisms for hiding
data in the Extensible Messaging and Presence Protocol (XMPP). This is a very
popular instant messaging protocol used by many messaging platforms such as
Google Talk, Cisco, LiveJournal and many others. Our paper describes how to
send a secret message from one XMPP client to another, without raising the
suspicion of any intermediaries. The methods described primarily focus on using
the underlying protocol as a means for steganography, unlike other related
works that try to hide data in the content of instant messages. In doing so, we
provide a more robust means of data hiding and additionally offer some
preliminary analysis of its general security, in particular against
entropic-based steganalysis.
|
We show that the ordinates of the nontrivial zeros of certain $L-$functions
attached to half-integral weight cusp forms are uniformly distributed modulo
one.
|
Generating images from natural language instructions is an intriguing yet
highly challenging task. We approach text-to-image generation by combining the
power of the retrained CLIP representation with an off-the-shelf image
generator (GANs), optimizing in the latent space of GAN to find images that
achieve maximum CLIP score with the given input text. Compared to traditional
methods that train generative models from text to image starting from scratch,
the CLIP+GAN approach is training-free, zero shot and can be easily customized
with different generators.
However, optimizing CLIP score in the GAN space casts a highly challenging
optimization problem and off-the-shelf optimizers such as Adam fail to yield
satisfying results. In this work, we propose a FuseDream pipeline, which
improves the CLIP+GAN approach with three key techniques: 1) an AugCLIP score
which robustifies the CLIP objective by introducing random augmentation on
image. 2) a novel initialization and over-parameterization strategy for
optimization which allows us to efficiently navigate the non-convex landscape
in GAN space. 3) a composed generation technique which, by leveraging a novel
bi-level optimization formulation, can compose multiple images to extend the
GAN space and overcome the data-bias.
When promoted by different input text, FuseDream can generate high-quality
images with varying objects, backgrounds, artistic styles, even novel
counterfactual concepts that do not appear in the training data of the GAN we
use. Quantitatively, the images generated by FuseDream yield top-level
Inception score and FID score on MS COCO dataset, without additional
architecture design or training. Our code is publicly available at
\url{https://github.com/gnobitab/FuseDream}.
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Robot learning has emerged as a promising tool for taming the complexity and
diversity of the real world. Methods based on high-capacity models, such as
deep networks, hold the promise of providing effective generalization to a wide
range of open-world environments. However, these same methods typically require
large amounts of diverse training data to generalize effectively. In contrast,
most robotic learning experiments are small-scale, single-domain, and
single-robot. This leads to a frequent tension in robotic learning: how can we
learn generalizable robotic controllers without having to collect impractically
large amounts of data for each separate experiment? In this paper, we propose
RoboNet, an open database for sharing robotic experience, which provides an
initial pool of 15 million video frames, from 7 different robot platforms, and
study how it can be used to learn generalizable models for vision-based robotic
manipulation. We combine the dataset with two different learning algorithms:
visual foresight, which uses forward video prediction models, and supervised
inverse models. Our experiments test the learned algorithms' ability to work
across new objects, new tasks, new scenes, new camera viewpoints, new grippers,
or even entirely new robots. In our final experiment, we find that by
pre-training on RoboNet and fine-tuning on data from a held-out Franka or Kuka
robot, we can exceed the performance of a robot-specific training approach that
uses 4x-20x more data. For videos and data, see the project webpage:
https://www.robonet.wiki/
|
The magnetic ordering of La$_{1/3}$Sr$_{2/3}$FeO$_3$ perovskite has been
studied by neutron powder diffraction and $^{57}$Fe M\"ossbauer spectroscopy
down to 2 K. From symmetry analysis, a chiral helical model and a collinear
model are proposed to describe the magnetic structure. Both are commensurate,
with propagation vector k = (0,0,1) in R-3c space group. In the former model,
the magnetic moments of Fe adopt the magnetic space group P3$_{2}$21 and have
helical and antiferromagnetic ordering propagating along the c axis. The model
allows only one Fe site, with a magnetic moment of 3.46(2) $\mu_{\rm{B}}$ at 2
K. In the latter model, the magnetic moments of iron ions adopt the magnetic
space group C2/c or C2'/c' and are aligned collinearly. The model allows the
presence of two inequivalent Fe sites with magnetic moments of amplitude
3.26(3) $\mu_{\rm{B}}$ and 3.67(2) $\mu_{\rm{B}}$, respectively. The neutron
diffraction pattern is equally well fitted by either model. The M\"ossbauer
spectroscopy study suggests a single charge state Fe$^{3.66+}$ above the
magnetic transition and a charge disproportionation into Fe$^{(3.66-\zeta)+}$
and Fe$^{(3.66+2\zeta)+}$ below the magnetic transition. The compatibility of
the magnetic structure models with the M\"ossbauer spectroscopy results is
discussed.
|
The nature of current sheet formation in the vicinity of three-dimensional
(3D) magnetic null points is investigated. The particular focus is upon the
effect of the compressibility of the plasma on the qualitative and quantitative
properties of the current sheet. An initially potential 3D null is subjected to
shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas,
in press (2007)]. It is found that as the incompressible limit is approached,
the collapse of the null point is suppressed, and an approximately planar
current sheet aligned to the fan plane is present instead. This is the case
regardless of whether the spine or fan of the null is sheared. Both the peak
current and peak reconnection rate are reduced. The results have a bearing on
previous analytical solutions for steady-state reconnection in incompressible
plasmas, implying that fan current sheet solutions are dynamically accessible,
while spine current sheet solutions are not.
|
We revisit on rational solution of Sasa-Satsuma equation, which can be used
to describe evolution of optical field in a nonlinear fiber with some
high-order effects. We find a striking dynamical process which involves both
modulational instability and modulational stability regimes, in contrast to the
rogue waves and W-shaped soliton reported before which involves modulational
instability and stability respectively. It is demonstrated that stable W-shaped
solitons can be generated from a weak modulation signal on continuous wave
background. This provides a possible way to obtain stable high-intensity pulse
from low-intensity continuous wave background.
|
We consider a gravitational plane wave passing through a galactic dark matter
halo composed of weakly self-interacting, self-gravitating, Bose-Einstein
condensate of ultralight particles. Treating the gravitational wave as a time
dependent perturbation, we study energy transfer between the gravitational wave
and the Bose-Einstein condensate by applying linear response theory to a
non-uniform condensate described by the Bogoliubov-de Gennes theory, and
compute the fractional loss in gravitational wave energy. We apply our results
to investigate the extent to which this loss effects the estimation of the
distance between the gravitational wave source and the earth. We show that the
effect is negligible.
|
Model rockets have been employed in student projects, but very few papers in
aerospace education offer concise summaries of activities at university-course
levels. This paper aims to address this gap in the literature. The rockets used
by our students reached some 500 m (~1,640 feet) in altitude, deployed a
parachute, and spent 2-3 minutes descending to the ground. We present a series
of analyses and experiments that students performed in order to predict the
flight time, the maximum altitude, and the landing location of these rockets.
They wrote computer programs to numerically integrate equations of motion, and
experimentally measured input parameters (e.g., the thrust profile and drag
coefficients). Once launched, these rockets could not be controlled; targeting
the landing location would thus mean tilting the launch rail to a required
angle. The largest source of error in landing location came from the difficulty
in modeling wind velocities. Also discussed in this paper are the infrared
spectroscopy and the extraction experiment as novel additions to model rocket
projects.
|
We consider a smooth interface between a topological nodal-line semimetal and
a topologically trivial insulator (e.g., the vacuum) or another semimetal with
a nodal ring of different radius. Using a low-energy effective Hamiltonian
including only the two crossing bands, we show that these junctions accommodate
a two-dimensional zero-energy level and a set of two-dimensional dispersive
bands, corresponding to states localized at the interface. We characterize the
spectrum, identifying the parameter ranges in which these states are present,
and highlight the role of the nodal radius and the smoothness of the interface.
We also suggest material-independent ways to detect and identify these states,
using optical conductivity and infrared absorption spectroscopy in magnetic
field.
|
The notions of "motion" and "conserved quantities", if applied to extended
objects, are already quite non-trivial in Special Relativity. This contribution
is meant to remind us on all the relevant mathematical structures and
constructions that underlie these concepts, which we will review in some
detail. Next to the prerequisites from Special Relativity, like Minkowski space
and its automorphism group, this will include the notion of a body in Minkowski
space, the momentum map, a characterisation of the habitat of globally
conserved quantities associated with Poincar\'e symmetry -- so called
Poincar\'e charges --, the frame-dependent decomposition of global angular
momentum into Spin and an orbital part, and, last not least, the likewise
frame-dependent notion of centre of mass together with a geometric description
of the Moeller Radius, of which we also list some typical values. Two
Appendices present some mathematical background material on Hodge duality and
group actions on manifolds. This is a contribution to the book: "Equations of
Motion in Relativistic Gravity", edited by Dirk Puetzfeld and Claus
Laemmerzahl, to be published by Springer Verlag.
|
Electronic Health Records (EHR) data analysis plays a crucial role in
healthcare system quality. Because of its highly complex underlying causality
and limited observable nature, causal inference on EHR is quite challenging.
Deep Learning (DL) achieved great success among the advanced machine learning
methodologies. Nevertheless, it is still obstructed by the inappropriately
assumed causal conditions. This work proposed a novel method to quantify
clinically well-defined causal effects as a generalized estimation vector that
is simply utilizable for causal models. We incorporated it into DL models to
achieve better predictive performance and result interpretation. Furthermore,
we also proved the existence of causal information blink spots that regular DL
models cannot reach.
|
A new inverse iteration algorithm that can be used to compute all the
eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is
developed. The modified Gram-Schmidt orthogonalization is used in the classical
inverse iteration. This algorithm is sequential and causes a bottleneck in
parallel computing. In this paper, the use of the compact WY representation is
proposed in the orthogonalization process of the inverse iteration with the
Householder transformation. This change results in drastically reduced
synchronization cost in parallel computing. The new algorithm is evaluated on
both an 8-core and a 32-core parallel computer, and it is shown that the new
algorithm is greatly faster than the classical inverse iteration algorithm in
computing all the eigenvectors of matrices with several thousand dimensions.
|
Dabconium hybrid perovskites include a number of recently-discovered
ferroelectric phases with large spontaneous polarisations. The origin of
ferroelectric response has been rationalised in general terms in the context of
hydrogen bonding, covalency, and strain coupling. Here we use a combination of
simple theory, Monte Carlo simulations, and density functional theory
calculations to assess the ability of these microscopic ingredients---together
with the always-present through-space dipolar coupling---to account for the
emergence of polarisation in these particular systems whilst not in other
hybrid perovskites. Our key result is that the combination of A-site polarity,
preferred orientation along $\langle111\rangle$ directions, and ferroelastic
strain coupling drives precisely the ferroelectric transition observed
experimentally. We rationalise the absence of polarisation in many hybrid
perovskites, and arrive at a set of design rules for generating FE examples
beyond the dabconium family alone.
|
We develop a theoretical background to treat exciton states of semiconductor
single-walled carbon nanotubes (SWCNTs) in presence of a periodic potential
induced by the surface acoustic wave (SAW) propagating along semiconducting
SWCNT. The formalism naturally accounts for the electronic bands splitting into
the Floquet sub-bands brought about by the Bragg scattering on the SAW
potential. Optically induced transitions within the Floquet states and
formation of correlated electron-hole pairs, i.e., exciton states, are examined
numerically. We discuss dynamical formation of new van Hove singularities
within electron-hole continuum and associated reduction of the exciton
oscillator strengths and its effect on the photoluminescence quenching in
presence of the SAW. We argue that SAW induced dynamical gaps in the single
particle dispersion leads to redistribution of the oscillator strength from
excitons to the Floquet edge states. The simulations also confirm exciton
energy Stark red shift as well as reduction in the binding energy. Comparison
of our results with previous theoretical and experimental studies is provided.
|
Isolated quantum system in a pure state may be perceived as thermal if only
substantially small fraction of all degrees of freedom is probed. We propose
that in a chaotic quantum many-body system all states with sufficiently small
energy fluctuations are approximately thermal. We refer to this hypothesis as
Canonical Universality (CU). The CU hypothesis complements the Eigenstate
Thermalization Hypothesis (ETH) which proposes that for chaotic systems
individual energy eigenstates are thermal. Integrable and MBL systems do not
satisfy CU. We provide theoretical and numerical evidence supporting the CU
hypothesis.
|
We have shown previously (Bobylev et al 2011) that some of the stars in the
Solar neighborhood today may have originated in the same star cluster as the
Sun, and could thus be called Solar Siblings. In this work we investigate the
sensitivity of this result to Galactic models and to parameters of these
models, and also extend the sample of orbits. There are a number of good
candidates for the Sibling category, but due to the long period of orbit
evolution since the break-up of the birth cluster of the Sun, one can only
attach probabilities of membership. We find that up to 10% (but more likely
around 1 %) of the members of the Sun's birth cluster could be still found
within 100 pc from the Sun today.
|
Presented is a method to compute certain classes of Hamilton-Jacobi equations
that result from optimal control and trajectory generation problems with time
delays. Many robotic control and trajectory problems have limited information
of the operating environment a priori and must continually perform online
trajectory optimization in real time after collecting measurements. The sensing
and optimization can induce a significant time delay, and must be accounted for
when computing the trajectory. This paper utilizes the generalized Hopf
formula, which avoids the exponential dimensional scaling typical of other
numerical methods for computing solutions to the Hamilton-Jacobi equation. We
present as an example a robot that incrementally predicts a communication
channel from measurements as it travels. As part of this example, we introduce
a seemingly new generalization of a non-parametric formulation of robotic
communication channel estimation. New communication measurements are used to
improve the channel estimate and online trajectory optimization with time-delay
compensation is performed.
|
In this paper we address the vector problem of a 2D half-plane interfacial
crack loaded by a general asymmetric distribution of forces acting on its
faces. It is shown that the general integral formula for the evaluation of
stress intensity factors, as well as high-order terms, requires both symmetric
and skew-symmetric weight function matrices. The symmetric weight function
matrix is obtained via the solution of a Wiener-Hopf functional equation,
whereas the derivation of the skew-symmetric weight function matrix requires
the construction of the corresponding full field singular solution. The weight
function matrices are then used in the perturbation analysis of a crack
advancing quasi-statically along the interface between two dissimilar media. A
general and rigorous asymptotic procedure is developed to compute the
perturbations of stress intensity factors as well as high-order terms.
|
Cameras are an essential part of sensor suite in autonomous driving.
Surround-view cameras are directly exposed to external environment and are
vulnerable to get soiled. Cameras have a much higher degradation in performance
due to soiling compared to other sensors. Thus it is critical to accurately
detect soiling on the cameras, particularly for higher levels of autonomous
driving. We created a new dataset having multiple types of soiling namely
opaque and transparent. It will be released publicly as part of our WoodScape
dataset \cite{yogamani2019woodscape} to encourage further research. We
demonstrate high accuracy using a Convolutional Neural Network (CNN) based
architecture. We also show that it can be combined with the existing object
detection task in a multi-task learning framework. Finally, we make use of
Generative Adversarial Networks (GANs) to generate more images for data
augmentation and show that it works successfully similar to the style transfer.
|
In the context of task-oriented communications we advocate the development of
waveforms for Federated Edge Learning (FEEL). Over-the-air computing (AirComp)
has emerged as a communication scheme that allows to compute a function out of
distributed data and can be applied to FEEL. However, the design of modulations
for AirComp is still in its infancy and most of the literature ignores this
topic. In this work we employ frequency modulation (FM) and type based multiple
access (TMBA) for FEEL and demonstrate its advantages with respect to the state
of the art in terms of convergence and peak-to-average power ratio (PAPR).
|
Magnetic fields are ubiquitous in the universe and are thought to play an
important role in various astrophysical processes. Polarization of thermal dust
emission from dust grains aligned with the magnetic field is widely used to
measure the two-dimensional magnetic field projected onto the plane of the sky
(POS), but the component along the line of sight (LOS) is not yet reliably
constrained with dust polarization. Here, we introduce a new method to infer
three-dimensional (3D) magnetic fields using thermal dust polarization and
grain alignment physics. We first develop a physical model of thermal dust
polarization using the modern grain alignment theory based on the magnetically
enhanced radiative torque (MRAT) alignment theory. We then test this model with
synthetic observations of magnetohydrodynamic (MHD) simulations of a
filamentary cloud with our updated POLARIS code. Combining the tested physical
polarization model with synthetic polarization, we show that the B-field
inclination angle can be accurately constrained by the polarization degree from
synthetic observations. Compared to the true 3D magnetic fields, our method
with grain alignment is more accurate than the previous methods that assume
uniform grain alignment. This new technique paves the way for tracing 3D
B-fields using thermal dust polarization and grain alignment theory and for
constraining dust properties and grain alignment physics.
|
In the molecular picture the hidden-charm, pentaquark-like $P_c(4450)$
resonance is a $\bar{D}^* \Sigma_c$ bound state with quantum numbers
$I=\tfrac{1}{2}$ and $J^P = \tfrac{3}{2}^-$. If this happens to be the case, it
will be natural to expect the existence of $\bar{D}^* \bar{D}^* \Sigma_c$
three-body bound states. The most probable quantum numbers for a bound
$\bar{D}^* \bar{D}^* \Sigma_c$ trimer are the isoscalar $J^P = \tfrac{1}{2}^+$,
$\tfrac{5}{2}^+$ and the isovector $J^P = \tfrac{3}{2}^+$, $\tfrac{5}{2}^+$
configurations. Calculations within a contact-range theory indicate a trimer
binding energy $B_3 \sim 3-5\,{\rm MeV}$ and $14-16\,{\rm MeV}$ for the
isoscalar $\tfrac{1}{2}^+$ and $\tfrac{5}{2}^+$ states and $B_3 \sim 1-3\,{\rm
MeV}$ and $3-5\,{\rm MeV}$ for the isovector $\tfrac{3}{2}^+$ and
$\tfrac{5}{2}^+$ states, respectively, with $B_3$ relative to the $\bar{D}^*
P_c(4450)$ threshold. These predictions are affected by a series of error
sources that we discuss in detail.
|
The CMS detector at the CERN LHC features a silicon pixel detector as its
innermost subdetector. The original CMS pixel detector has been replaced with
an upgraded pixel system (CMS Phase-1 pixel detector) in the extended year-end
technical stop of the LHC in 2016/2017. The upgraded CMS pixel detector is
designed to cope with the higher instantaneous luminosities that have been
achieved by the LHC after the upgrades to the accelerator during the first long
shutdown in 2013-2014. Compared to the original pixel detector, the upgraded
detector has a better tracking performance and lower mass with four barrel
layers and three endcap disks on each side to provide hit coverage up to an
absolute value of pseudorapidity of 2.5. This paper describes the design and
construction of the CMS Phase-1 pixel detector as well as its performance from
commissioning to early operation in collision data-taking.
|
This paper investigates the capacity region of the optical intensity
broadcast channels (OI-BCs), where the input is subject to a peak-intensity
constraint, an average-intensity constraint, or both. By leveraging the
decomposition results of several random variables, i.e., uniform, exponential,
and truncated exponential random variables, and adopting a superposition coding
(SC) scheme, the inner bound on the capacity region is derived. Then, the outer
bound is derived by applying the conditional entropy power inequality (EPI). In
the high signal-to-noise ratio (SNR) regime, the inner bound asymptotically
matches the outer bound, thus characterizing the high-SNR asymptotic capacity
region. The bounds are also extended to the general K-user BCs without loss of
high-SNR asymptotic optimality.
|
We investigate the Schrodinger equation for a particle with a nonuniform
solitonic mass density. First, we discuss in extent the (nontrivial)
position-dependent mass $V(x)=0$ case whose solutions are hypergeometric
functions in $\tanh^2(x)$. Then, we consider an external hyperbolic-tangent
potential. We show that the effective quantum mechanical problem is given by a
Heun class equation and find analytically an eigenbasis for the space of
solutions. We also compute the eigenstates for a potential of the form
$V(x)=V_0 \sinh^2(x)$.
|
We investigate testing of the hypothesis of independence between a covariate
and the marks in a marked point process. It would be rather straightforward if
the (unmarked) point process were independent of the covariate and the marks.
In practice, however, such an assumption is questionable and possible
dependence between the point process and the covariate or the marks may lead to
incorrect conclusions. Therefore, we propose to investigate the complete
dependence structure in the triangle points--marks--covariates together. We
take advantage of the recent development of the nonparametric random shift
methods, namely the new variance correction approach, and propose tests of the
null hypothesis of independence between the marks and the covariate and between
the points and the covariate. We present a detailed simulation study showing
the performance of the methods and provide two theorems establishing the
appropriate form of the correction factors for the variance correction.
Finally, we illustrate the use of the proposed methods in two real
applications.
|
We derive a series of quantitative bulk-boundary correspondences for 3D
bosonic and fermionic symmetry-protected topological (SPT) phases under the
assumption that the surface is gapped, symmetric and topologically ordered,
i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases
that are protected by the mirror symmetry and continuous symmetries that form a
group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases
correspond to a crystalline version of 3D topological insulators and
topological superconductors in the famous ten-fold-way classification, with the
time-reversal symmetry replaced by the mirror symmetry and with strong
interaction taken into account. For surface SETs, the most general interplay
between symmetries and anyon excitations is considered. Based on the previously
proposed dimension reduction and folding approaches, we re-derive the
classification of bulk SPT phases and define a \emph{complete} set of bulk
topological invariants for every symmetry group under consideration, and then
derive explicit expressions of the bulk invariants in terms of surface
topological properties (such as topological spin, quantum dimension) and
symmetry properties (such as mirror fractionalization, fractional charge or
spin). These expressions are our quantitative bulk-boundary correspondences.
Meanwhile, the bulk topological invariants can be interpreted as \emph{anomaly
indicators} for the surface SETs which carry 't Hooft anomalies of the
associated symmetries whenever the bulk is topologically non-trivial. Hence,
the quantitative bulk-boundary correspondences provide an easy way to compute
the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators
are complete. Our derivations of the bulk-boundary correspondences and anomaly
indicators are explicit and physically transparent.
|
We show how the superembedding formalism can be applied to construct
manifestly kappa-symmetric higher derivative corrections for the D9-brane. We
also show that all correction terms appear at even powers of the fundamental
length scale $l$. We explicitly construct the first potential correction, which
corresponds to the kappa-symmetric version of the $\partial^4 F^4$, which one
finds from the four-point amplitude of the open superstring.
|
The moment-angle complex Z_K is cell complex with a torus action constructed
from a finite simplicial complex K. When this construction is applied to a
triangulated sphere K or, in particular, to the boundary of a simplicial
polytope, the result is a manifold. Moment-angle manifolds and complexes are
central objects in toric topology, and currently are gaining much interest in
homotopy theory, complex and symplectic geometry.
The geometric aspects of the theory of moment-angle complexes are the main
theme of this survey. We review constructions of non-Kahler complex-analytic
structures on moment-angle manifolds corresponding to polytopes and complete
simplicial fans, and describe invariants of these structures, such as the Hodge
numbers and Dolbeault cohomology rings. Symplectic and Lagrangian aspects of
the theory are also of considerable interest. Moment-angle manifolds appear as
level sets for quadratic Hamiltonians of torus actions, and can be used to
construct new families of Hamiltonian-minimal Lagrangian submanifolds in a
complex space, complex projective space or toric varieties.
|
When the output of an atomistic simulation (such as the Gillespie stochastic
simulation algorithm, SSA) can be approximated as a diffusion process, we may
be interested in the dynamic features of the deterministic (drift) component of
this diffusion. We perform traditional scientific computing tasks (integration,
steady state and closed orbit computation, and stability analysis) on such a
drift component using a SSA simulation of the Cyclic Lotka-Volterra system as
our illustrative example. The results of short bursts of appropriately
initialized SSA simulations are used to fit local diffusion models using
Ait-Sahalia's transition density expansions \cite{ait2,aitECO,aitVEC} in a
maximum likelihood framework. These estimates are then coupled with standard
numerical algorithms (such as Newton-Raphson or numerical integration routines)
to help design subsequent SSA experiments. A brief discussion of the validity
of the local diffusion approximation of the SSA simulation (a jump process) is
included.
|
Although more than 5000 TESS Objects of Interest have been cataloged, no
comprehensive survey of the flare rates of their host stars exists. We perform
the first flare survey of all 2250 non-retired TOIs with 2 min cadence light
curves to measure or place upper limits on their flare rates. We find 93
candidates orbit flare stars and measure their flare frequency distributions.
Across the sample, TOIs of <1.5R_Earth orbit flare stars more frequently than
do TOIs of 1.5<R<2.75R_Earth, 2.75<R<4R_Earth, or R<4R_Earth. We sort all TOI
host stars by their flare rate/upper limit, stellar mass, and distance to
create a flare ranking metric (FRM) to determine suitability for follow-up. The
FRM of each TOI is then checked against the expected signal-to-noise of
atmospheric features in transmission spectroscopy to locate the most promising
targets. We find 1/4 of terrestrial M-dwarf planets amenable to transmission
spectroscopy orbit flare stars. However, none of the M-dwarf hosts to
terrestrial planets are currently flaring at sufficient levels for >99.9%
atmospheric ozone depletion. We give the first upper limits on the flare rate
of the host star to TOI 700 d and explore the flare rates incident on young
planets such as DS Tuc Ab.
|
A parallel 2D+1 split-step Fourier method with Crank-Nicholson scheme running
on multi-core shared memory architectures is developed to study the propagation
of ultra-short high-intensity laser pulses in air. The parallel method achieves
a near linear speed-up with results for the efficiency of more than 95% on a
24-core machine. This method is of great potential application in studying the
long-distance propagation of the ultra-short high intensity laser pulses.
|
An algorithm for obtaining the Taylor coefficients of an expansion of Feynman
diagrams is proposed. It is based on recurrence relations which can be applied
to the propagator as well as to the vertex diagrams. As an application, several
coefficients of the Taylor series expansion for the two-loop propagator and
two-loop non-planar vertex diagrams are calculated. The results of the
numerical evaluation of these diagrams using conformal mapping and Pade
approximants are given.
|
The geomagnetic Kp index is derived from the K index measurements obtained
from thirteen stations located around the Earth geomagnetic latitudes between
$48^\circ$ and $63^\circ$. This index is processed every three hours, is
quasi-logarithmic and estimates the geomagnetic activity. The Kp values fall
within a range of 0 to 9 and are organized as a set of 28 discrete values. The
data set is important because it is used as one of the many input parameters of
magnetospheric and ionospheric models. The objective of this work is to use
historical data from the Kp index to develop a methodology to make a prediction
in a time interval of at least three hours. Five different models to forecast
geomagnetic indices Kp and ap are tested. Time series of values of Kp index
from 1932 to 15/12/2012 at 21:00 UT are used as input to the models. The
purpose of the model is to predict the three measured values after the last
measured value of the Kp index (it means the next 9 hours values). The AR model
provides the lowest computational cost with satisfactory results. The ARIMA
model is efficient for predicting Kp index during geomagnetic disturbance
conditions. This paper provides a quick and efficient way to make a prediction
of Kp index, without using satellite data. Although it is reported that the
forecast results are better when satellite data are used. In the literature we
find that the linear correlation between predicted values and actual values is
$77\%$, which is better than the $68.5\%$ obtained in this work. However,
taking into account that our results are based only on Kp stochastic time
series, the correlation value can be considered satisfactory.
|
We define and study the categorical sequence of a space, which is a new
formalism that streamlines the computation of the Lusternik-Schnirelmann
category of a space X by induction on its CW skeleta. The k-th term in the
categorical sequence of a CW complex X, \sigma_X(k), is the least integer n for
which cat_X(X_n) >= k. We show that \sigma_X is a well-defined homotopy
invariant of X.
We prove that \sigma_X(k+l) >= \sigma_X(k) + \sigma_X(l), which is one of
three keys to the power of categorical sequences. In addition to this formula,
we provide formulas relating the categorical sequences of spaces and some of
their algebraic invariants, including their cohomology algebras and their
rational models; we also find relations between the categorical sequences of
the spaces in a fibration sequence and give a preliminary result on the
categorical sequence of a product of two spaces in the rational case. We
completely characterize the sequences which can arise as categorical sequences
of formal rational spaces. The most important of the many examples that we
offer is a simple proof of a theorem of Ghienne: if X is a member of the Mislin
genus of the Lie group Sp(3), then cat(X) = cat(Sp(3)).
|
Let $A \to B$ be a $G$-Galois extension of rings, or more generally of
$\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in
algebraic $K$-theory asks how close the map $K(A) \to K(B)^{hG}$ is to being an
equivalence, i.e., how close algebraic $K$-theory is to satisfying Galois
descent. An elementary argument with the transfer shows that this equivalence
is true rationally in most cases of interest. Motivated by the classical
descent theorem of Thomason, one also expects such a result after periodic
localization.
We formulate and prove a general result which enables one to promote rational
descent statements as above into descent statements after periodic
localization. This reduces the localized descent problem to establishing an
elementary condition on $K_0(-)\otimes \mathbb{Q}$. As applications, we prove
various descent results in the periodic localized $K$-theory, $TC$, $THH$, etc.
of structured ring spectra, and verify several cases of a conjecture of Ausoni
and Rognes.
|
Topological superconductors are gapped superconductors with protected
Majorana surface/edge states on the boundary. In this paper, we study the
Josephson coupling between time-reversal invariant topological superconductors
and s-wave superconductors. The Majorana edge/surface states of time-reversal
invariant topological superconductors in all physical dimensions 1, 2, 3 have a
generic topological property which we named as time-reversal anomaly. Due to
the time-reversal anomaly, the Josephson coupling prefers a nonzero phase
difference between topological and trivial superconductors. The nontrivial
Josesphon coupling leads to a current-flux relation with a half period in a
SQUID geometry, and also a half period Fraunhofer effect in dimension higher
than one. We also show that an in-plane magnetic field restores the ordinary
Josephson coupling, as a sharp signature that the proposed effect is a
consequence of the unique time-reversal property of the topological
edge/surface states. Our proposal provides a general approach to experimentally
verify whether a superconductor is topological or not.
|
We consider a model for the decay Bbar^0 -> rho^0 gamma in which the
short-distance amplitude determined by the Hamiltonian describing b -> d gamma
is combined with a typical long-distance contribution Bbar^0 -> D^+ D^- ->
rho^0 gamma. The latter possesses a significant dynamical phase which induces a
CP-violating asymmetry A_CP, as well as an important modification of the Stokes
vector of the photon. The components S_1 and S_3 of the Stokes vector S = (S_1,
S_2, S_3) can be measured in the decay Bbar^0 -> rho^0 gamma^* -> pi^+ pi^- e^+
e^- where they produce a characteristic effect in the angular distribution d
Gamma / d phi, phi being the angle between the pi^+ pi^- and e^+ e^- planes. A
similar analysis is carried out for the decays Bbar^0 -> Kbar^* gamma and
Bbar^0 -> Kbar^* gamma^* -> pi^+ K^- e^+ e^-
|
Light transport in a disordered ensemble of resonant atoms placed in a
waveguide is found to be very sensitive to the sizes of cross section of a
waveguide. Based on self-consistent quantum microscopic model treating atoms as
coherent radiating dipoles, we have shown that the nature of radiation transfer
changes from Anderson localization regime in a single-mode waveguide to a
traditional diffuse transfer in a multi-mode one. Moreover, the transmittance
magnitude undergoes complex step-like dependence on the transverse sizes of a
waveguide.
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We investigate hadron attenuation in deep-inelastic lepton scattering off
complex nuclei in the kinematic regime of the HERMES experiment. Our transport
theoretical simulations reveal strong prehadronic final state interactions of
the reaction products with the surrounding nuclear medium early after the
initial photon-nucleon interaction has taken place. In this work we compare our
model results with the measured hadron multiplicity ratios for a Kr target at
HERMES and provide an extended discussion of the double-hadron attenuation
recently observed at HERMES.
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We present In NMR measurements in a novel thermodynamic phase of CeCoIn5 in
high magnetic field, where exotic superconductivity coexists with the
incommensurate spin-density wave order. We show that the NMR spectra in this
phase provide direct evidence for the emergence of the spatially distributed
normal quasiparticle regions. The quantitative analysis for the field evolution
of the paramagnetic magnetization and newly-emerged low-energy quasiparticle
density of states is consistent with the nodal plane formation, which is
characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state. The NMR spectra also suggest that the spatially uniform
spin-density wave is induced in the FFLO phase.
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Given an RCD$(K,N)$ space $({X},\mathsf{d},\mathfrak{m})$, one can use its
heat kernel $\rho$ to map it into the $L^2$ space by a locally Lipschitz map
$\Phi_t(x):=\rho(x,\cdot,t)$. The space $(X,\mathsf{d},\mathfrak{m})$ is said
to be an isometrically heat kernel immersing space, if each $\Phi_t$ is an
isometric immersion {}{after a normalization}. A main result states that any
compact isometrically heat kernel immersing RCD$(K,N)$ space is isometric to an
unweighted closed smooth Riemannian manifold. This is justified by a more
general result: if a compact non-collapsed RCD$(K, N)$ space has an
isometrically immersing eigenmap, then the space is isometric to an unweighted
closed Riemannian manifold, which greatly improves a regularity result in
\cite{H21} by Honda. As an application of these results, we give a
$C^\infty$-compactness theorem for a certain class of Riemannian manifolds with
a curvature-dimension-diameter bound and an isometrically immersing eigenmap.
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This paper is devoted to the study of the embeddings of a complex submanifold
$S$ inside a larger complex manifold $M$; in particular, we are interested in
comparing the embedding of $S$ in $M$ with the embedding of $S$ as the zero
section in the total space of the normal bundle $N_S$ of $S$ in $M$. We
explicitely describe some cohomological classes allowing to measure the
difference between the two embeddings, in the spirit of the work by Grauert,
Griffiths, and Camacho-Movasati-Sad; we are also able to explain the
geometrical meaning of the separate vanishing of these classes. Our results
holds for any codimension, but even for curves in a surface we generalize
previous results due to Laufert and Camacho-Movasati-Sad.
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In the low-dimensional case, the generalized additive coefficient model
(GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been
demonstrated to be a powerful tool for studying nonlinear interaction effects
of variables. In this paper, we propose estimation and inference procedures for
the GACM when the dimension of the variables is high. Specifically, we propose
a groupwise penalization based procedure to distinguish significant covariates
for the "large $p$ small $n$" setting. The procedure is shown to be consistent
for model structure identification. Further, we construct simultaneous
confidence bands for the coefficient functions in the selected model based on a
refined two-step spline estimator. We also discuss how to choose the tuning
parameters. To estimate the standard deviation of the functional estimator, we
adopt the smoothed bootstrap method. We conduct simulation experiments to
evaluate the numerical performance of the proposed methods and analyze an
obesity data set from a genome-wide association study as an illustration.
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Node localization plays an important role in many practical applications of
wireless underground sensor networks (WUSNs), such as finding the locations of
earthquake epicenters, underground explosions, and microseismic events in
mines. It is more difficult to obtain the time-difference-of-arrival (TDOA)
measurements in WUSNs than in terrestrial wireless sensor networks because of
the unfavorable channel characteristics in the underground environment. The
robust Chinese remainder theorem (RCRT) has been shown to be an effective tool
for solving the phase ambiguity problem and frequency estimation problem in
wireless sensor networks. In this paper, the RCRT is used to robustly estimate
TDOA or range difference in WUSNs and therefore improves the ranging accuracy
in such networks. After obtaining the range difference, distributed source
localization algorithms based on a diffusion strategy are proposed to decrease
the communication cost while satisfying the localization accuracy requirement.
Simulation results confirm the validity and efficiency of the proposed methods.
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We study the Einstein equations coupled with the scalar field equations,
$\hbox{Ein}(g)=T$, $T=T(g,\phi)+F^1$, and $\square_g\phi^\ell-m^2\phi^\ell=
F^2$, where the sources $F=(F^1, F^2)$ correspond to perturbations of the
physical fields which we control. Here $\phi=(\phi^\ell)_{\ell=1}^L$ and
$(M,g)$ is a 4-dimensional globally hyperbolic Lorentzian manifold. The sources
$F$ need to be such that the fields $(g,\phi,F)$ satisfy the conservation law
$\hbox{div}_g(T)=0$. If $(g_\epsilon,\phi_\epsilon)$ solves the above
equations, $\dot g=\partial_\epsilon g_\epsilon|_{\epsilon=0}$,
$\dot\phi=\phi_\epsilon|_{\epsilon=0}$, and $f=(f^1,f^2)= \partial_\epsilon
F_\epsilon|_{\epsilon=0}$ solve the linearized Einstein equations and the
linearized conservation law $$ \frac 12 \hat g^{pk}\hat \nabla_p f^1_{kj}+
\sum_{\ell=1}^L f^2_\ell \, \partial_j\hat\phi_\ell=0, $$ where $\hat g=
g_\epsilon|_{\epsilon=0}$ and $\hat \phi= \phi_\epsilon|_{\epsilon=0}$. Then
$(\hat g,\hat \phi)$ and $f$ have the linearization stability property. Here
ask the converse: If $\dot g$, $\dot \phi$, and $f$ solve the linearized
Einstein equations and the linearized conservation law, are there
$F_\epsilon=(F^1_\epsilon,F^2_\epsilon)$ and $(g_\epsilon,\phi_\epsilon)$
depending on $\epsilon\in [0,\epsilon_0)$, $\epsilon_0>0$, such that
$(g_\epsilon,\phi_\epsilon)$ solves the Einstein-scalar field equations and the
conservation law. When $\hat g$ and $\hat \phi$ vary enough and $L\geq 5$, we
prove a microlocal version of this: When $Y\subset M$ is a 2-surface and
$(y,\eta)\in N^*Y$, there is $f$ that is a conormal distibutions wrt. the
surface $Y$ with a given principal symbol at $(y,\eta)$ such that $(\hat g,\hat
\phi)$ and $f$ have the linearization stability property.
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Resting-state fMRI is commonly used for diagnosing Autism Spectrum Disorder
(ASD) by using network-based functional connectivity. It has been shown that
ASD is associated with brain regions and their inter-connections. However,
discriminating based on connectivity patterns among imaging data of the control
population and that of ASD patients' brains is a non-trivial task. In order to
tackle said classification task, we propose a novel deep learning architecture
(MHATC) consisting of multi-head attention and temporal consolidation modules
for classifying an individual as a patient of ASD. The devised architecture
results from an in-depth analysis of the limitations of current deep neural
network solutions for similar applications. Our approach is not only robust but
computationally efficient, which can allow its adoption in a variety of other
research and clinical settings.
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The Feynman-Hellmann theorem and semiempirical mass formulas are used to
predict the masses of baryons containing one or two heavy quarks. In
particular, the mass of the $\Lambda_b$ is predicted to be $5620 \pm 40$ MeV, a
value consistent with measurements.
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In this paper, we introduce a method for finding all edge-transitive graphs
of small order, using faithful representations of transitive permutation groups
of small degree, and we explain how we used this method to find all
edge-transitive graphs of order up to $47$, and all bipartite edge-transitive
graphs of order up to $63$. We also give an answer to a 1967 question of
Folkman about semi-symmetric graphs of large valency; in fact we show that for
semi-symmetric graphs of order $2n$ and valency $d$, the ratio $d/n$ can be
arbitrarily close to $1$.
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One of the solutions to the cosmological Polonyi problem is to introduce a
large coupling between the Polonyi field and the inflaton so that the Polonyi
field adiabatically tracks the temporal minimum of the potential. We study
general conditions for the adiabatic suppression mechanism to work, and find
that a non-negligible amount of the Polonyi field is induced in the form of
coherent oscillations at the end of inflation. In the case of low reheating
temperature, this contribution is so small that it does not cause cosmological
problems. On the other hand, this contribution may be significant for a
relatively high reheating temperature and we still need some amount of tuning
in order to avoid the Polonyi problem. We also point out that Polonyi particles
produced from thermal plasma pose a severe constraint on the reheating
temperature. Furthermore, we extend the original framework to include enhanced
couplings of the Polonyi field with the visible particles as well as with
itself, and derive upper bounds on the reheating temperature after inflation.
We also investigate the adiabatic solution to the cosmological moduli problem
in gauge and anomaly mediation.
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Binary neutron star (NS) mergers are among the most promising sources of
gravitational waves (GWs), as well as candidate progenitors for short Gamma-Ray
Bursts (SGRBs). Depending on the total initial mass of the system, and the NS
equation of state (EOS), the post-merger phase can see a prompt collapse to a
black hole, or the formation of a supramassive NS, or even a stable NS. In the
case of post-merger NS (PMNS) formation, magnetic field amplification during
the merger will produce a magnetar with a large induced mass quadrupole moment,
and millisecond spin. If the timescale for orthogonalization of the magnetic
symmetry axis with the spin axis is sufficiently short the NS will radiate its
spin down energy primarily via GWs. Here we study this scenario for various
outcomes of NS formation: we generalise the set of equilibrium states for a
twisted torus magnetic configuration to include solutions that, at a fixed
exterior dipole field, carry a larger magnetic energy reservoir; we hence
compute their magnetic ellipticity and the strength of the expected GW signal
as a function of the magnitude of the dipole and toroidal field. The relative
number of GW detections from PMNSs and from binary NSs is a strong function of
the NS equation of state (EOS), being higher (~ 1%) for the stiffest EOSs and
negligibly small for the softest ones. For intermediate-stiffness EOSs, such as
the n=4/7 polytrope recently used by Giacomazzo \& Perna or the GM1 used by
Lasky et al., the relative fraction is ~0.3%; correspondingly we estimate a GW
detection rate from stable PMNSs of ~ (0.1-1) yr$^{-1}$ with Advanced
detectors, and of ~ (100-1000) yr$^{-1}$ with third generation detectors such
as the Einstein Telescope. Measurement of such GW signal would provide strong
constraints on the NS EOS and on the nature of the binary progenitors giving
rise to SGRBs.
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The initial value problem for an evolution equation of type $v' + Av + BKv =
f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and
where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not
required to be embedded in $V_B$ or vice versa. The operator $K$ incorporates a
Volterra integral operator in time of convolution type with an exponentially
decaying kernel. Existence of a global-in-time solution is shown by proving
convergence of a suitable time discretisation. Moreover, uniqueness as well as
stability results are proved. Appropriate integration-by-parts formulae are a
key ingredient for the analysis.
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In this paper, we develop a method to obtain the algebraic classification of
compatible pre-Lie algebras from the classification of pre-Lie algebras of the
same dimension. We use this method to obtain the algebraic classification of
complex $2$-dimensional compatible pre-Lie algebras. As a byproduct, we obtain
the classification of complex $2$-dimensional compatible commutative
associative, compatible associative, and compatible Novikov algebras. In
addition, we consider the geometric classification of varieties of cited
algebras, that is the description of its irreducible components.
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Bladder cancer ranks within the top 10 most diagnosed cancers worldwide and
is among the most expensive cancers to treat due to the high recurrence rates
which require lifetime follow-ups. The primary tool for diagnosis is
cystoscopy, which heavily relies on doctors' expertise and interpretation.
Therefore, annually, numerous cases are either undiagnosed or misdiagnosed and
treated as urinary infections. To address this, we suggest a deep learning
approach for bladder cancer detection and segmentation which combines CNNs with
a lightweight positional-encoding-free transformer and dual attention gates
that fuse self and spatial attention for feature enhancement. The architecture
suggested in this paper is efficient making it suitable for medical scenarios
that require real time inference. Experiments have proven that this model
addresses the critical need for a balance between computational efficiency and
diagnostic accuracy in cystoscopic imaging as despite its small size it rivals
large models in performance.
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In this work we aim at quantifying quantum channel output similarity. In
order to achieve this, we introduce the notion of quantum channel
superfidelity, which gives us an upper bound on the quantum channel fidelity.
This quantity is expressed in a clear form using the Kraus representation of a
quantum channel. As examples, we show potential applications of this quantity
in the quantum control field.
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In this paper we will look at the distribution with which passwords are
chosen. Zipf's Law is commonly observed in lists of chosen words. Using
password lists from four different on-line sources, we will investigate if
Zipf's law is a good candidate for describing the frequency with which
passwords are chosen. We look at a number of standard statistics, used to
measure the security of password distributions, and see if modelling the data
using Zipf's Law produces good estimates of these statistics. We then look at
the the similarity of the password distributions from each of our sources,
using guessing as a metric. This shows that these distributions provide
effective tools for cracking passwords. Finally, we will show how to shape the
distribution of passwords in use, by occasionally asking users to choose a
different password.
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We provide the combinatorial proofs of the log-convexity for the derangement
numbers in the symmetric group $\mathfrak{S}_n$, hyperoctahedral group
$\mathfrak{B}_n$, and the demihyperoctahedral group $\mathfrak{D}_n$. We also
show that the sequences of the even and odd derangement numbers in
$\mathfrak{S}_n$ and $\mathfrak{B}_n$ are log-convex.
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We have examined cobalt based valence tautomer molecules such as
Co(SQ)$_2$(phen) using density functional theory (DFT) and variational
configuration interaction (VCI) approaches based upon a model Hamiltonian. Our
DFT results extend earlier work by finding a reduced total energy gap (order
0.6 eV) between high temperature and low temperature states when we fully relax
the coordinates (relative to experimental ones). Futhermore we demonstrate that
the charge transfer picture based upon formal valence arguments succeeds
qualitatively while failing quantitatively due to strong covalency between the
Co 3$d$ orbitals and ligand $p$ orbitals. With the VCI approach, we argue that
the high temperature, high spin phase is strongly mixed valent, with about 30 %
admixture of Co(III) into the predominantly Co(II) ground state. We confirm
this mixed valence through a fit to the XANES spectra. Moreover, the strong
electron correlations of the mixed valent phase provide an energy lowering of
about 0.2-0.3 eV of the high temperature phase relative to the low temperature
one. Finally, we use the domain model to account for the extraordinarily large
entropy and enthalpy values associated with the transition.
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A stochastic optimal control based model with velocity tracking and internal
feedback for saccadic eye movements is presented in this paper. Recent evidence
from neurophysiological studies of superior colliculus suggests the presence of
a dynamic input to the saccade generation system that encodes saccade velocity,
rather than just the saccade amplitude and direction. The new evidence makes it
imperative to test if saccade control can use a desired velocity input which is
the basis for the proposed velocity tracking model. The model is validated
using behavioral data of saccades generated by healthy human subjects. It
generates trajectories of horizontal saccades made to different amplitudes as
well as predicts vertical and oblique saccade behavior. This paper presents the
first-ever model of the saccadic system in an optimal control framework using
an alternate interpretation of velocity-based control, contrary to the dominant
end-point based models available in the literature.
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Th$_3$Te$_4$ materials are potential candidates for commercial thermoelectric
(TE) materials at high-temperature due to their superior physical properties.
We incorporate the multiband Boltzmann transport equations with firstprinciples
calculations to theoretically investigate the TE properties of Th$_3$Te$_4$
materials. As a demonstration of our method, the TE properties of La$_3$Te$_4$
are similar with that of Ce$_3$Te$_4$ at low-temperature, which is consistent
with the experiment. Then we systematically calculate the electrical
conductivity, the Seebeck coefficient, and the power factor of the two
materials above based on parameters obtained from first-principles calculations
as well as several other fitting parameters. Our results reveal that for the
electron--optical-phonon scattering at high temperatures, a linear dependence
of optical phonon energy on temperature explains better the experimental
results than a constant optical phonon energy. Based on this, we predict that
the TE properties of Ce$_3$Te$_4$ is better than La$_3$Te$_4$ at high
temperatures and the optimal carrier concentration corresponding to
Ce$_3$Te$_4$ shifts upward with increasing temperature. The optimal carrier
concentration of Ce$_3$Te$_4$ is around $1.6\times10^{21}$cm$^{-3}$ with the
peak power factor 13.07 $\mu$Wcm$^{-1}$K$^{-2}$ at $T=1200$K.
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In quantum information processing, it is vital to protect the coherence of
qubits in noisy environments. Dynamical decoupling (DD), which applies a
sequence of flips on qubits and averages the qubit-environment coupling to
zero, is a promising strategy compatible with other desired functionalities
such as quantum gates. Here we review the recent progresses in theories of
dynamical decoupling and experimental demonstrations. We give both
semiclassical and quantum descriptions of the qubit decoherence due to coupling
to noisy environments. Based on the quantum picture, a geometrical
interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD
and the concatenated DD are reviewed, followed by a detailed exploration of the
recently developed Uhrig DD, which employs the least number of pulses in an
unequally spaced sequence to suppress the qubit-environment coupling to a given
order of the evolution time. Some new developments and perspectives are also
discussed.
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We consider suspension semi-flows of angle-multiplying maps on the circle.
Under a $C^r$generic condition on the ceiling function, we show that there
exists an anisotropic Sobolev space contained in the $L^2$ space such that the
Perron-Frobenius operator for the time-$t$-map acts on it and that the
essential spectral radius of that action is bounded by the square root of the
inverse of the minimum expansion rate. This leads to a precise description on
decay of correlations and extends the result of M. Pollicott.
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We investigate the generalized tree properties and guessing model properties
introduced by Wei\ss\ and Viale, as well as natural weakenings thereof,
studying the relationships among these properties and between these properties
and other prominent combinatorial principles. We introduce a weakening of Viale
and Wei\ss's Guessing Model Property, which we call the Almost Guessing
Property, and prove that it provides an alternate formulation of the slender
tree property in the same way that the Guessing Model Property provides and
alternate formulation of the ineffable slender tree property. We show that
instances of the Almost Guessing Property have sufficient strength to imply,
for example, failures of square or the nonexistence of weak Kurepa trees. We
show that these instances of the Almsot Guessing Property hold in the Mitchell
model starting from a strongly compact cardinal and prove a number of other
consistency results showing that certain implications between the principles
under consideration are in general not reversible. In the process, we provide a
new answer to a question of Viale by constructing a model in which, for all
regular $\theta \geq \omega_2$, there are stationarily many $\omega_2$-guessing
models $M \in \mathscr{P}_{\omega_2} H(\theta)$ that are not
$\omega_1$-guessing models.
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Let $N \subset M$ be a submanifold embedding of spin manifolds of some
codimension $k \geq 1$. A classical result of Gromov and Lawson, refined by
Hanke, Pape and Schick, states that $M$ does not admit a metric of positive
scalar curvature if $k = 2$ and the Dirac operator of $N$ has non-trivial
index, provided that suitable conditions are satisfied. In the cases $k=1$ and
$k=2$, Zeidler and Kubota, respectively, established more systematic results:
There exists a transfer $\mathrm{KO}_\ast(\mathrm{C}^{\ast} \pi_1 M)\to
\mathrm{KO}_{\ast - k}(\mathrm{C}^\ast \pi_1 N)$ which maps the index class of
$M$ to the index class of $N$. The main goal of this article is to construct
analogous transfer maps $E_\ast(\mathrm{B}\pi_1M) \to
E_{\ast-k}(\mathrm{B}\pi_1N)$ for different generalized homology theories $E$
and suitable submanifold embeddings. The design criterion is that it is
compatible with the transfer $E_\ast(M) \to E_{\ast-k}(N)$ induced by the
inclusion $N \subset M$ for a chosen orientation on the normal bundle. Under
varying restrictions on homotopy groups and the normal bundle, we construct
transfers in the following cases in particular: In ordinary homology, it works
for all codimensions. This slightly generalizes a result of Engel and
simplifies his proof. In complex K-homology, we achieve it for $k \leq 3$. For
$k \leq 2$, we have a transfer on the equivariant KO-homology of the
classifying space for proper actions.
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We consider for the first time the ability of present-day cosmic microwave
background (CMB) anisotropies data to determine the primordial helium mass
fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160
< Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as
measured by CMB and discuss the implications for big bang nucleosynthesis. We
identify and discuss correlations between the helium mass fraction and both the
redshift of reionization and the spectral index. We forecast the precision of
future CMB observations, and find that Planck alone will measure Y_p with
error-bars of 5%. We point out that the uncertainty in the determination of the
helium fraction will have to be taken into account in order to correctly
estimate the baryon density from Planck-quality CMB data.
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The Permuted Kernel Problem (PKP) asks to find a permutation of a given
vector belonging to the kernel of a given matrix. The PKP is at the basis of
PKP-DSS, a post-quantum signature scheme deriving from the identification
scheme proposed by Shamir in 1989. The most efficient solver for PKP is due to
a recent paper by Koussa et al. In this paper we propose an improvement of such
an algorithm, which we achieve by considering an additional collision search
step applied on kernel equations involving a small number of coordinates. We
study the conditions for such equations to exist from a coding theory
perspective, and we describe how to efficiently find them with methods borrowed
from coding theory, such as information set decoding. We assess the complexity
of the resulting algorithm and show that it outperforms previous approaches in
several cases. We also show that, taking the new solver into account, the
security level of some instances of PKP-DSS turns out to be slightly
overestimated.
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