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It is shown that the description of a relativistic fluid at local
thermodynamic equilibrium depends on the particular quantum stress-energy
tensor operator chosen, e.g., the canonical or symmetrized Belinfante
stress-energy tensor. We argue that the Belinfante tensor is not appropriate to
describe a relativistic fluid whose macroscopic polarization relaxes slowly to
thermodynamic equilibrium and that a spin tensor, like the canonical spin
tensor, is required. As a consequence, the description of a polarized
relativistic fluid involves an extension of relativistic hydrodynamics
including a new antisymmetric rank-two tensor as a dynamical field. We show
that the canonical and Belinfante tensors lead to different predictions for
measurable quantities such as spectrum and polarization of particles produced
in relativistic heavy-ion collisions.
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Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of
power utility-based prices and hedging strategies can be computed by solving a
mean-variance hedging problem under a specific equivalent martingale measure
and relative to a suitable numeraire. In order to avoid the introduction of an
additional state variable necessitated by the change of numeraire, we propose
an alternative representation in terms of the original numeraire. More
specifically, we characterize the relevant quantities using semimartingale
characteristics similarly as in Cerny and Kallsen (2007) for mean-variance
hedging. These results are illustrated by applying them to exponential L\'evy
processes and stochastic volatility models of Barndorff-Nielsen and Shephard
type.
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Here we investigate the spin-dependent subband structure of newly-developed
Mn-based modulation-doped quantum wells. In the presence of an external
magnetic field, the s-d exchange coupling between carriers and localized d
electrons of the Mn impurities gives rise to large spin splittings resulting in
a magnetic-field dependent subband structure. Within the framework of the
effective-mass approximation, we self-consistently calculate the subband
structure at zero temperature using Density Functional Theory (DFT) with a
Local Spin Density Approximation (LSDA). We present results for the
magnetic-field dependence of the subband structure of shallow ZnSe/ZnCdMnSe
modulation doped quantum wells. Our results show a significant contribution to
the self-consistent potential due to the exchange-correlation term. These
calculations are the first step in the study of a variety of interesting
spin-dependent phenomena, e.g., spin-resolved transport and many-body effects
in polarized two-dimensional electron gases.
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Consider the problem of reconstructing a multidimensional signal from an
underdetermined set of measurements, as in the setting of compressed sensing.
Without any additional assumptions, this problem is ill-posed. However, for
signals such as natural images or movies, the minimal total variation estimate
consistent with the measurements often produces a good approximation to the
underlying signal, even if the number of measurements is far smaller than the
ambient dimensionality. This paper extends recent reconstruction guarantees for
two-dimensional images to signals of arbitrary dimension d>1 and to isotropic
total variation problems. To be precise, we show that a multidimensional signal
x can be reconstructed from O(sd*log(N^d)) linear measurements using total
variation minimization to within a factor of the best s-term approximation of
its gradient. The reconstruction guarantees we provide are necessarily optimal
up to polynomial factors in the spatial dimension d.
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Semidefinite programs (SDPs) can be solved in polynomial time by interior
point methods. However, when the dimension of the problem gets large, interior
point methods become impractical in terms of both computational time and memory
requirements. Certain first-order methods, such as Alternating Direction
Methods of Multipliers (ADMMs), established as suitable algorithms to deal with
large-scale SDPs and gained growing attention over the past decade. In this
paper, we focus on an ADMM designed for SDPs in standard form and extend it to
deal with inequalities when solving SDPs in general form. Beside numerical
results on randomly generated instances, where we show that our method compares
favorably with respect to the state-of-the-art solver SDPNAL+, we present
results on instances from SDP relaxations of classical combinatorial problems
such as the graph coloring problem and the maximum clique problem. Through
extensive numerical experiments, we show that even an inaccurate dual solution,
obtained at a generic iteration of our proposed ADMM, can represent an
efficiently recovered valid bound on the optimal solution of the combinatorial
problems considered, as long as an appropriate post-processing procedure is
applied.
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We study the long-run properties of optimal control problems in continuous
time, where the running cost of a control problem is evaluated by a probability
measure over R_+. Li, Quincampoix and Renault [DCDS-A, 2016] introduced an
asymptotic regularity condition for a sequence of probability measures to study
the limit properties of the value functions with respect to the evaluation. In
the particular case of t-horizon Ces\`aro mean or rho-discounted Abel mean,
this condition implies that the horizon t tends to infinity or the discount
factor rho tends to zero. For the control system defined on a compact domain
and satisfying some nonexpansive condition, Li, Quincampoix and Renault
[DCDS-A, 2016] proved the existence of general limit value, i.e. the value
function uniform converges as the evaluation becomes more and more regular.
Within the same context, we prove the existence of general uniform value, i.e.
for any epsilon>0, there is an optimal control that guarantees the general
limit value up to epsilon for all control problems where the cost is evaluated
by sufficiently regular probability measures.
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In this note we discuss the combination of the usual renormalization and
factorization scale uncertainties of Higgs-pair production via gluon fusion
with the novel uncertainties originating from the scheme and scale choice of
the virtual top mass. Moreover, we address the uncertainties related to the
top-mass definition for different values of the trilinear Higgs coupling and
their combination with the other uncertainties.
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In this paper, the two dimensional Euler flow under a simple symmetry
condition with hyperbolic structure in a unit square
$D=\{(x_1,x_2):0<x_1+x_2<\sqrt{2},0<-x_1+x_2<\sqrt{2}\}$ is considered. It is
shown that the Lipschitz estimate of the vorticity on the boundary is at most
single exponential growth near the stagnation point.
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We introduce a new second-order inertial optimization method for machine
learning called INNA. It exploits the geometry of the loss function while only
requiring stochastic approximations of the function values and the generalized
gradients. This makes INNA fully implementable and adapted to large-scale
optimization problems such as the training of deep neural networks. The
algorithm combines both gradient-descent and Newton-like behaviors as well as
inertia. We prove the convergence of INNA for most deep learning problems. To
do so, we provide a well-suited framework to analyze deep learning loss
functions involving tame optimization in which we study a continuous dynamical
system together with its discrete stochastic approximations. We prove sublinear
convergence for the continuous-time differential inclusion which underlies our
algorithm. Additionally, we also show how standard optimization mini-batch
methods applied to non-smooth non-convex problems can yield a certain type of
spurious stationary points never discussed before. We address this issue by
providing a theoretical framework around the new idea of $D$-criticality; we
then give a simple asymptotic analysis of INNA. Our algorithm allows for using
an aggressive learning rate of $o(1/\log k)$. From an empirical viewpoint, we
show that INNA returns competitive results with respect to state of the art
(stochastic gradient descent, ADAGRAD, ADAM) on popular deep learning benchmark
problems.
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We derive the exact ground-state energy of the one-dimensional Ising model in
random fields taking values h, 0 and -h with general probabilities. The
random-field Ising model on a ladder is also analyzed by showing its
equivalence to the random-field Ising chain with field values h, -h and 0 for
h<J. The zero-temperature transger matrix is used to obtain the results.
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It has been suggested that strongly magnetised and rapidly rotating
protoneutron stars (PNSs) may produce long duration gamma-ray bursts (GRBs)
originating from stellar core collapse. We explore the steady-state properties
and heavy element nucleosynthesis in neutrino-driven winds from such PNSs whose
magnetic axis is generally misaligned with the axis of rotation. We consider a
wide variety of central engine properties such as surface dipole field
strength, initial rotation period and magnetic obliquity to show that heavy
element nuclei can be synthesised in the radially expanding wind. This process
is facilitated provided the outflow is Poynting-flux dominated such that its
low entropy and fast expansion timescale enables heavy nuclei to form in a more
efficient manner as compared to the equivalent thermal GRB outflows. We also
examine the acceleration and survival of these heavy nuclei and show that they
can reach sufficiently high energies $\gtrsim 10^{20}\ {\rm eV}$ within the
same physical regions that are also responsible for powering gamma-ray
emission, primarily through magnetic dissipation processes. Although these
magnetised outflows generally fail to achieve the production of elements
heavier than lanthanides for our explored electron fraction range 0.4-0.6, we
show that they are more than capable of synthesizing nuclei near and beyond
iron peak elements.
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In academic research, systematic literature reviews are foundational and
highly relevant, yet tedious to create due to the high volume of publications
and labor-intensive processes involved. Systematic selection of relevant papers
through conventional means like keyword-based filtering techniques can
sometimes be inadequate, plagued by semantic ambiguities and inconsistent
terminology, which can lead to sub-optimal outcomes. To mitigate the required
extensive manual filtering, we explore and evaluate the potential of using
Large Language Models (LLMs) to enhance the efficiency, speed, and precision of
literature review filtering, reducing the amount of manual screening required.
By using models as classification agents acting on a structured database only,
we prevent common problems inherent in LLMs, such as hallucinations. We
evaluate the real-world performance of such a setup during the construction of
a recent literature survey paper with initially more than 8.3k potentially
relevant articles under consideration and compare this with human performance
on the same dataset. Our findings indicate that employing advanced LLMs like
GPT-4o, Claude 3.5 Sonnet, Gemini 1.5 Flash, or Llama3 with simple prompting
can significantly reduce the time required for literature filtering - from
usually weeks of manual research to only a few minutes. Simultaneously, we
crucially show that false negatives can indeed be controlled through a
consensus scheme, achieving recalls >98.8% at or even beyond the typical human
error threshold, thereby also providing for more accurate and relevant articles
selected. Our research not only demonstrates a substantial improvement in the
methodology of literature reviews but also sets the stage for further
integration and extensive future applications of responsible AI in academic
research practices.
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Some finite series of harmonic numbers involving certain reciprocals are
evaluated. Products of such reciprocals are expanded in a sum of the individual
reciprocals, leading to a computer program. A list of examples is provided.
|
In the present paper we study the production of $\chi_b + c\bar c$ at the LHC
within single parton scattering approach. A special attention payed to the
feed-down from $\chi_b$ states to the associated $\Upsilon + c\bar c$
production, which was recently studied by the LHCb. We have found that this
feed-down is about percents of the total cross section seen in the experiment.
It is shown that the shapes of the differential distributions are almost same
as found by the LHCb except the azimuthal asymmetry, which is almost flat in
the experiment. We conclude that the precise study of the single parton
scattering contributions is necessary for the correct isolation of other
possible production channels such as double parton scattering.
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Meiotic recombination is a fundamental feature of sexually reproducing
species. It is often required for proper chromosome segregation and plays
important role in adaptation and the maintenance of genetic diversity. The
molecular mechanisms of recombination are remarkably conserved across
eukaryotes, yet meiotic genes and proteins show substantial variation in their
sequence and function, even between closely related species. Furthermore, the
rate and distribution of recombination shows a huge diversity within and
between chromosomes, individuals, sexes, populations, and species. This
variation has implications for many molecular and evolutionary processes, yet
how and why this diversity has evolved is not well understood. A key step in
understanding trait evolution is to determine its genetic basis - that is, the
number, effect sizes, and distribution of loci underpinning variation. In this
perspective, I discuss past and current knowledge on the genetic basis of
variation in recombination rate and distribution, explore its evolutionary
implications, and present open questions for future research.
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Causal reversibility blends reversibility and causality for concurrent
systems. It indicates that an action can be undone provided that all of its
consequences have been undone already, thus making it possible to bring the
system back to a past consistent state. Time reversibility is instead
considered in the field of stochastic processes, mostly for efficient analysis
purposes. A performance model based on a continuous-time Markov chain is time
reversible if its stochastic behavior remains the same when the direction of
time is reversed. We bridge these two theories of reversibility by showing the
conditions under which causal reversibility and time reversibility are both
ensured by construction. This is done in the setting of a stochastic process
calculus, which is then equipped with a variant of stochastic bisimilarity
accounting for both forward and backward directions.
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We have compared far-ultraviolet (FUV), near-ultraviolet (NUV), and Halpha
measurements for star forming regions in 21 galaxies, in order to characterise
the properties of their discs at radii beyond the main optical radius (R25). In
our representative sample of extended and non-extended UV discs we find that
half of the extended UV discs also exhibit extended Halpha emission. We find
that extended UV discs fall into two categories, those with a sharp truncation
in the Halpha disc close to the optical edge (R25), and those with extended
emission in Halpha as well as in the ultraviolet. Although most galaxies with
strong Halpha truncations near R25 show a significant corresponding falloff in
UV emission (factor 10--100), the transition tends to be much smoother than in
Halpha, and significant UV emission often extends well beyond this radius,
confirming earlier results by Thilker et al. (2007) and others. After
correcting for dust attenuation the median fraction of total FUV emission from
regions outside of R25 is 1.7%, but it can be as high as 35% in the most
extreme cases. The corresponding fractions of Halpha emission are approximately
half as large on average. This difference reflects both a slightly lower ratio
of Halpha to UV emission in the HII regions in the outer discs, as well as a
lower fraction of star clusters showing HII regions. Most HII regions in the
extended disc have fluxes consistent with small numbers of ionising O-type
stars, and this poor sampling of the upper initial mass function in small
clusters can probably account for the differences in the emission properties,
consistent with earlier conclusions by Zaritsky & Christlein (2007), without
needing to invoke a significant change in the stellar IMF itself. Consistent
Ha/FUV ratios and brightest HII region to total Halpha fluxes in the inner and
extended discs across our whole galaxy sample demonstrate no evidence for a
change in the cluster luminosity function or the IMF in the low gas density
outer disc.
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The Robinson-Schensted (RS) correspondence and its variants naturally give
rise to integrable dynamics of non-intersecting particle systems.
In previous work, the author exhibited a RS correspondence for geometric
crystals by constructing a Littelmann path model, in general Lie type. Since
this representation-theoretic map takes as input a continuous path on a
Euclidian space, the natural starting measure is the Wiener measure. In this
paper, we characterize the measures induced by Brownian motion through the RS
map.
On the one hand, the highest weight in the output is a remarkable Markov
process (the Whittaker process), and can be interpreted as a weakly
non-intersecting particle system which deforms Brownian motion in a Weyl
chamber. One the other hand, the measure induced on geometric crystals is given
by the Landau-Ginzburg potential for complete flag manifolds which appear in
mirror symmetry. The measure deforms the uniform measure on string polytopes.
Whittaker functions, which appear as volumes of geometric crystals, play the
role of characters in the theory.
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The talk is about the power corrections in QCD. Renormalons, both infrared
and ultraviolet, provide with a kind of a kinematical framework to fix
exponents of the leading power corrections to various observables. Any viable
dynamical framework is to reproduce this pattern of the power corrections. In
this mini-review, we emphasize that a simple dynamical framework satisfying
this requirement may well be provided by the strings inherent to the Abelian
Higgs model. This model comes naturally into consideration within the U(1)
projection of QCD which makes explicit the dual-superconductor model of the
confinement. At large distances (compared to $\LQ^{-1}$) there are
Abrikosov-Nielsen-Olesen strings which develop a characteristic
non-perturbative transverse size of order $\LQ^{-1}$ and match in this way the
infrared renormalons. At short distances there are no ANO strings but there
still exist dynamical manifestations of the stringy topological condition that
(external) quarks are connected by a mathematically thin line along which the
vacuum is trivial. These manifestations may match ultraviolet renormalons.
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We report the discovery of a thin stellar stream - which we name the Jet
stream - crossing the constellations of Hydra and Pyxis. The discovery was made
in data from the SLAMS survey, which comprises deep $g$ and $r$ imaging for a
$650$ square degree region above the Galactic disc performed by the CTIO Blanco
+ DECam. SLAMS photometric catalogues will be made publicly available. The
stream is approximately 0.18 degrees wide and 10 degrees long, though it is
truncated by the survey footprint. Its colour-magnitude diagram is consistent
with an old, metal-poor stellar population at a heliocentric distance of
approximately 29 kpc. We corroborate this measurement by identifying a
spatially coincident overdensity of likely blue horizontal branch stars at the
same distance. There is no obvious candidate for a surviving stream progenitor.
|
Knowledge Distillation (KD) refers to transferring knowledge from a large
model to a smaller one, which is widely used to enhance model performance in
machine learning. It tries to align embedding spaces generated from the teacher
and the student model (i.e. to make images corresponding to the same semantics
share the same embedding across different models). In this work, we focus on
its application in face recognition. We observe that existing knowledge
distillation models optimize the proxy tasks that force the student to mimic
the teacher's behavior, instead of directly optimizing the face recognition
accuracy. Consequently, the obtained student models are not guaranteed to be
optimal on the target task or able to benefit from advanced constraints, such
as large margin constraints (e.g. margin-based softmax). We then propose a
novel method named ProxylessKD that directly optimizes face recognition
accuracy by inheriting the teacher's classifier as the student's classifier to
guide the student to learn discriminative embeddings in the teacher's embedding
space. The proposed ProxylessKD is very easy to implement and sufficiently
generic to be extended to other tasks beyond face recognition. We conduct
extensive experiments on standard face recognition benchmarks, and the results
demonstrate that ProxylessKD achieves superior performance over existing
knowledge distillation methods.
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We consider UV divergences for the on-shell planar gluon-gluon scattering
amplitudes in the gauge theory in arbitrary D-dimensions in the one-loop order.
The amplitudes are evaluated using the standard Feynman diagram technique for
several choices of external gluon polarizations. Using the Passarino - Veltman
reduction, the expansion in terms of the scalar master integrals is constructed
and their calculation is performed within dimensional regularization. The
resulting expressions are confronted with existing results for various cases,
including maximally supersymmetric theories in D=4, 6, 8, and 10 dimensions.
One finds that, contrary to the D=4 case, in D=6 one-loop UV divergences
cancel, while in D=8 and 10 the contributions of gauge, scalar and fermion
loops have the same sign.
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We classify all finite simple subgroups in the Cremona group of rank 3
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We use near infrared spectroscopy to obtain concentration dependent glucose
absorption spectra in their aqueous solutions in the near-infrared range (3800
- 7500 cm^{-1}). We introduce a new method to obtain reliable glucose
absorption bands from aqueous glucose solutions without measuring the water
displacement coefficients of glucose separately. Additionally, we are able to
extract the water displacement coefficients of glucose, and this may give a new
general method using spectroscopy techniques applicable to other water soluble
materials. We also observe red shifts in the absorption bands of water in the
hydration shell around solute molecules, which comes from contribution of the
interacting water molecules around the glucose molecules in solutions. The
intensity of the red shift get larger as the concentration increases, which
indicates that as the concentration increases more water molecules are involved
in the interaction. However, the red shift in frequency does not seem to depend
significantly on the concentration up to our highest concentration. We also
performed the same measurements and analysis with sucrose instead of glucose as
solute and compare.
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We study exotic superconducting states in SrTiO$_3$ heterostructures on the
basis of the three-orbital model, which reproduces the band structure of
two-dimensional electron gases. We show various
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states induced by the broken inversion
symmetry and orbital degree of freedom. In particular, a novel
orbital-dependent FFLO state is stabilized in a magnetic field along the
[110]-axis. The field angle dependence of the FFLO state is clarified on the
basis of the spin and orbital texture in the momentum space. It is shown that
the orbital degree of freedom in Cooper pairs gives rise to in-plane anisotropy
of the critical magnetic field. The carrier density dependence of the
superconducting state is also discussed.
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We prove that the variety defined by the determinant of the matrix of
diagonals is $F$-pure for matrices of all sizes and in all positive prime
characteristics. Moreover, we find a system of parameters for it.
|
We derive a system of coupled partial differential equations for the
equal-time Wigner function in an arbitrary strong electromagnetic field using
the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a
3+1-system of four coupled partial differential equations, which are completed
by Ampere's law. This electrostatic system is further studied for two different
cases. In the first case, we consider linearized wave propagation in plasma
accounting for the nonzero vacuum expectation values. We then derive the
dispersion relation and compare it with well-known limiting cases. In the
second case, we consider Schwinger pair production using the local density
approximation to allow for analytical treatment. The dependence of the pair
production rate on the perpendicular momentum is investigated and it turns out
that the spread of the produced pairs along with perpendicular momentum depends
on the strength of the applied electric field.
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This paper studies an unmanned aerial vehicle (UAV)-enabled wireless sensor
network, in which one UAV flies in the sky to collect the data transmitted from
a set of sensors via distributed beamforming. We consider the delay-sensitive
application scenario, in which the sensors transmit the common/shared messages
by using fixed data rates and adaptive transmit powers. Under this setup, we
jointly optimize the UAV's trajectory design and the sensors' transmit power
allocation, in order to minimize the transmission outage probability, subject
to the UAV's flight speed constraints and the sensors' individual average power
constraints. However, the formulated outage probability minimization problem is
non-convex and thus difficult to be optimally solved in general. To tackle this
issue, we first consider the special problem in the ideal case with the UAV's
flight speed constraints ignored, for which the well-structured optimal
solution is obtained to reveal the fundamental performance upper bound. Next,
for the general problem with the UAV's flight speed constraints considered, we
propose an efficient algorithm to solve it sub-optimally by using the
techniques of convex optimization and approximation. Finally, numerical results
show that our proposed design achieves significantly reduced outage probability
than other benchmark schemes.
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We test the history of structure formation from redshift 1 to today by
matching galaxies from VIPERS and SDSS with dark matter haloes in the MultiDark
SMDPL N-body simulation. We first show that the standard subhalo abundance
matching (SHAM) recipe implemented with MultiDark characterizes the clustering
of galaxies well both at redshift 0 for SDSS and at redshift 1 for VIPERS. This
is an important validation of the SHAM model at high redshift. We then remap
the simulation timesteps to test alternative growth histories and infer the
growth index $\gamma=0.6\pm0.3$. This analysis demonstrates the power of using
N-body simulations to forward model galaxy surveys for cosmological inference.
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The magnification induced by gravitational microlensing is sensitive to the
size of a source relative to the Einstein radius, the natural microlensing
scale length. This paper investigates the effect of source size in the case
where the microlensing masses are distributed with a bimodal mass function,
with solar mass stars representing the normal stellar masses, and smaller
masses (down to $8.5\times 10^{-5}$M$_\odot$) representing a dark matter
component. It is found that there exists a critical regime where the dark
matter is initially seen as individual compact masses, but with an increasing
source size the compact dark matter acts as a smooth mass component. This study
reveals that interpretation of microlensing light curves, especially claims of
small mass dark matter lenses embedded in an overall stellar population, must
consider the important influence of the size of the source.
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We show that the complete Segal model structure extends to a model structure
on bimplicial presheaves on a small site $\mathscr{C}$, for which the weak
equivalences are local (or stalkwise) weak equivalences. This model structure
can be realized as a left Bousfield localization of the Jardine model structure
on the simplicial presheaves on a site $\mathscr{C}/ \Delta^{op}$. Furthermore,
it is shown that this model structure is Quillen equivalent to the model
structure of the author's previous preprint entitled 'the Local Joyal Model
Structure'. This Quillen equivalence extends an equivalence between the
complete Segal space and Joyal model structures, due to Joyal and Tierney.
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In this paper we determine the signed Roman domination number of the join of
cycles, wheels, fans and friendship graphs.
|
We investigated photon-helicity-induced magnetization precession in
Co$_{1-x}$Pt$_{x}$ alloy thin films. In addition to field-like torque,
attributable to magnetic field generation owing to {\it the inverse Faraday
effect}, we observed non-trivial and large damping-like torque which has never
been discussed for single ferromagnetic layer. The composition dependence of
those two torques is effectively elucidated by a model that considers mutual
coupling via spin-orbit interaction between magnetization and the electronic
orbital angular momentum generated by photon-helicity. This work significantly
enhances our understanding of the physics relevant to the interplay of
photon-helicity and magnetization in magnetic metals.
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Natural Language Generation tools, such as chatbots that can generate
human-like conversational text, are becoming more common both for personal and
professional use. However, there are concerns about their trustworthiness and
ethical implications. The paper addresses the problem of understanding how
different users (e.g., linguists, engineers) perceive and adopt these tools and
their perception of machine-generated text quality. It also discusses the
perceived advantages and limitations of Natural Language Generation tools, as
well as users' beliefs on governance strategies. The main findings of this
study include the impact of users' field and level of expertise on the
perceived trust and adoption of Natural Language Generation tools, the users'
assessment of the accuracy, fluency, and potential biases of machine-generated
text in comparison to human-written text, and an analysis of the advantages and
ethical risks associated with these tools as identified by the participants.
Moreover, this paper discusses the potential implications of these findings for
enhancing the AI development process. The paper sheds light on how different
user characteristics shape their beliefs on the quality and overall
trustworthiness of machine-generated text. Furthermore, it examines the
benefits and risks of these tools from the perspectives of different users.
|
A systematic search for 22 GHz H2O megamaser emission is reported for 50
nearby (z < 0.15) FR I galaxies. No detection was obtained, implying that
ultraluminous H2O masers (L_H2O>10^3 L_sun) must be rare in early-type galaxies
with FR I radio morphology. Despite higher radio core luminosities the
detection rate for our sample is much lower than in similar surveys of
late-type Seyfert galaxies. This puzzling difference between Seyferts and
low-power radio galaxies could be explained in several ways: a) the maser
emission is saturated and therefore independent of the radio core luminosity,
b) the masers are unsaturated and the background continuum source is associated
with the counter jet which is beamed away and relativistically dimmed in
radio-galaxies, or c) the amount, kinematics, or the distribution of the
molecular gas in the nuclei of Seyferts and radio galaxies is different.
Further studies of maser properties may therefore hold a clue for morphological
differences between active nuclei of Seyfert and early-type radio galaxies.
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We study the multi-component Ising model, which is also known as the block
Ising model. In this model, the particles are partitioned into a fixed number
of groups with a fixed proportion, and the interaction strength is determined
by the group to which each particle belongs. We demonstrate that the Glauber
dynamics on our model exhibits the cutoff$\mbox{--}$metastability phase
transition as passing the critical inverse-temperature $\beta_{cr}$, which is
determined by the proportion of the groups and their interaction strengths,
regardless of the total number of particles. For $\beta<\beta_{cr}$, the
dynamics shows a cutoff at $\alpha n\log n$ with a window size $O(n)$, where
$\alpha$ is a constant independent of $n$. For $\beta=\beta_{cr}$, we prove
that the mixing time is of order $n^{3/2}$. In particular, we deduce the
so-called non-central limit theorem for the block magnetizations to validate
the optimal bound at $\beta=\beta_{cr}$. For $\beta>\beta_{cr}$, we examine the
metastability, which refers to the exponential mixing time. Our results, based
on the position of the employed Ising model on the complete multipartite graph,
generalize the results of previous versions of the model.
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In this paper, we consider a general multiple input multiple output (MIMO)
system with channel state information (CSI) feedback over time-correlated
Rayleigh block-fading channels. Specifically, we first derive the closed-form
expression of the minimum differential feedback rate to achieve the maximum
erdodic capacity in the presence of channel estimation errors and quantization
distortion at the receiver. With the feedback-channel transmission rate
constraint, in the periodic feedback system, we further investigate the
relationship of the ergodic capacity and the differential feedback interval,
and we find by theoretical analysis that there exists an optimal differential
feedback interval to maximize ergodic capacity. Finally, analytical results are
verified through simulations in a practical periodic differential feedback
system using Lloyd's quantization algorithm.
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In this paper, we present the design and the evaluation of an authoring tool
for End-User Development, which supports the definition of Trigger-Actions
rules that combines events and states in the triggers. The possibility of using
either states or events in triggers has already been discussed in the
literature. However, it is recognized that the state/event distinction is
difficult to manage for users. In this paper, we propose an authoring tool that
provides explicit support for managing this distinction. We compare it with a
state-of-the-art authoring tool that implements the classical event-event
paradigm.
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The linear and renormalized nonlinear analysis of the temporal evolution of
drift-type modes in plasma flows with strong time-varying velocity shear is
developed. Analysis is performed in the time domain without spectral
decomposition in time and admits time variation of the flow velocity with time
scales which may be comparable with turbulent time scales. 52.35.Ra
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Motivated by the recent experiment [Wright et al., Phys. Rev. A 88, 063633
(2013)], we investigate formation of vortices in an annular BEC stirred by a
narrow blue-detuned optical beam. In the framework of a two-dimensional mean
field model, we study the dissipative dynamics of the condensate with
parameters matched to the experimental conditions. Vortex-antivortex pairs
appear near the center of the stirrer in the bulk of the condensate for slow
motion of the stirring beam. When the barrier angular velocity is above some
critical value, an outer edge surface mode develops and breaks into the
vortices entering the condensate annulus. We determine the conditions for
creation of the vortex excitations in the stirred toroidal condensate and
compare our results with the experimental observations.
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We use the theory of skew duality to show that decomposing the tensor product
of $k$ irreducible representations of the symplectic group $Sp_{2m} =
Sp_{2m}(C)$ is equivalent to branching from $Sp_{2n}$ to
$Sp_{2n_1}\times\cdots\times Sp_{2n_k}$ where $n, n_1,\ldots, n_k$ are positive
integers such that $n = n_1+\cdots+n_k$ and the $n_j$'s depend on $m$ as well
as the representations in the tensor product. Using this result and a work of
J. Lepowsky, we obtain a skew Pieri rule for $Sp_{2m}$, i.e., a description of
the irreducible decomposition of the tensor product of an irreducible
representation of the symplectic group $Sp_{2m}$ with a fundamental
representation.
|
In natural language processing (NLP), the semantic similarity task requires
large-scale, high-quality human-annotated labels for fine-tuning or evaluation.
By contrast, in cases of music similarity, such labels are expensive to collect
and largely dependent on the annotator's artistic preferences. Recent research
has demonstrated that embedding calibration technique can greatly increase
semantic similarity performance of the pre-trained language model without
fine-tuning. However, it is yet unknown which calibration method is the best
and how much performance improvement can be achieved. To address these issues,
we propose using composer information to construct labels for automatically
evaluating music similarity. Under this paradigm, we discover the optimal
combination of embedding calibration which achieves superior metrics than the
baseline methods.
|
We study the scattering resonances of one-dimensional deterministic aperiodic
chains of electric dipoles using the vectorial Green's matrix method, which
accounts for both short- and long-range electromagnetic interactions in open
scattering systems. We discover the existence of edge-localized scattering
states within fractal energy gaps with characteristic topological band
structures. Notably, we report and characterize edge-localized modes in the
classical wave analogues of the Su-Schrieffer-Heeger (SHH) dimer model,
quasiperiodic Harper and Fibonacci crystals, as well as in more complex
Thue-Morse aperiodic systems. Our study demonstrates that topological
edge-modes with characteristic power-law envelope appear in open aperiodic
systems and coexist with traditional exponentially localized ones. Our results
extend the concept of topological states to the scattering resonances of
complex open systems with aperiodic order, thus providing an important step
towards the predictive design of topological optical metamaterials and devices
beyond tightbinding models.
|
We show that the recently proposed matrix model for M theory obeys the cyclic
trace assumptions underlying generalized quantum or trace dynamics. This
permits a verification of supersymmetry as an operator calculation, and a
calculation of the supercharge density algebra by using the generalized Poisson
bracket, in a basis-independent manner that makes no reference to individual
matrix elements. Implications for quantization of the model are discussed. Our
results are a special case of a general result presented elsewhere, that all
rigid supersymmetry theories can be extended to give supersymmetric trace
dynamics theories, in which the supersymmetry algebra is represented by the
generalized Poisson bracket of trace supercharges, constructed from fields that
form a noncommutative trace class graded operator algebra.
|
We delineate a procedure to classify 6d N=(1,0) gauge theories composed, in
part, of a semi-simple gauge group and hypermultiplets. We classify these
theories by requiring that they satisfy some consistency conditions. The
primary consistency condition is that the gauge anomaly can be cancelled by
adding tensor multiplets which couple to the gauge fields by acting as sources
of instanton strings. Based on the number of tensor multiplets required to
cancel the anomaly, we conjecture that the UV completion of these consistent
gauge theories (if it exists) should be either a 6d N=(1,0) SCFT or a 6d
N=(1,0) little string theory.
|
With the recent proliferation of Large Language Models (LLMs), there has been
an increasing demand for tools to detect machine-generated text. The effective
detection of machine-generated text face two pertinent problems: First, they
are severely limited in generalizing against real-world scenarios, where
machine-generated text is produced by a variety of generators, including but
not limited to GPT-4 and Dolly, and spans diverse domains, ranging from
academic manuscripts to social media posts. Second, existing detection
methodologies treat texts produced by LLMs through a restrictive binary
classification lens, neglecting the nuanced diversity of artifacts generated by
different LLMs. In this work, we undertake a systematic study on the detection
of machine-generated text in real-world scenarios. We first study the
effectiveness of state-of-the-art approaches and find that they are severely
limited against text produced by diverse generators and domains in the real
world. Furthermore, t-SNE visualizations of the embeddings from a pretrained
LLM's encoder show that they cannot reliably distinguish between human and
machine-generated text. Based on our findings, we introduce a novel system,
T5LLMCipher, for detecting machine-generated text using a pretrained T5 encoder
combined with LLM embedding sub-clustering to address the text produced by
diverse generators and domains in the real world. We evaluate our approach
across 9 machine-generated text systems and 9 domains and find that our
approach provides state-of-the-art generalization ability, with an average
increase in F1 score on machine-generated text of 19.6\% on unseen generators
and domains compared to the top performing existing approaches and correctly
attributes the generator of text with an accuracy of 93.6\%.
|
While state-of-the-art monocular depth estimation approaches achieve
impressive results in ideal settings, they are highly unreliable under
challenging illumination and weather conditions, such as at nighttime or in the
presence of rain. In this paper, we uncover these safety-critical issues and
tackle them with md4all: a simple and effective solution that works reliably
under both adverse and ideal conditions, as well as for different types of
learning supervision. We achieve this by exploiting the efficacy of existing
methods under perfect settings. Therefore, we provide valid training signals
independently of what is in the input. First, we generate a set of complex
samples corresponding to the normal training ones. Then, we train the model by
guiding its self- or full-supervision by feeding the generated samples and
computing the standard losses on the corresponding original images. Doing so
enables a single model to recover information across diverse conditions without
modifications at inference time. Extensive experiments on two challenging
public datasets, namely nuScenes and Oxford RobotCar, demonstrate the
effectiveness of our techniques, outperforming prior works by a large margin in
both standard and challenging conditions. Source code and data are available
at: https://md4all.github.io.
|
Two-dimensional (2D) materials are known to possess emergent properties that
are not found in their bulk counterparts. Recent experiments have shown a
$\sqrt7 \times \sqrt3$ charge density wave (CDW) in monolayer 1T-VSe$_2$, in
contrast to the $4\times 4\times 3$ phase in bulk. Here, via first-principles
calculations, we show that multiple CDW phases compete in monolayer VSe$_2$,
the ground state of which can be tuned by charge doping and in-plane biaxial
strain. With doping, the $\sqrt7 \times \sqrt3$ CDW of the pristine VSe$_2$
transfers to a $3 \times \sqrt3$ and $4\times 4$ phase, the latter of which is
a projection of the bulk counterpart, at critical doping concentrations of
around 0.2 holes per formula unit and 0.25 electrons per formula unit,
respectively. The $4\times 4$ CDW phase can also be stabilized under
compressive strain. Although electron-phonon coupling is prevailing in the CDW
formation, we show that Fermi surface nesting is a good starting point to
explain most of these transitions in monolayer 1T-VSe$_2$. These results make
VSe$_2$ an appealing material for electronic devices based on controllable CDW
phase transitions.
|
Witten- Helffer-Sj\"ostrand theory is a considerable addition to the De Rham-
Hodge theory for Riemannian manifolds and can serve as a general tool to prove
results about comparison of numerical invariants associated to compact
manifolds analytically, i.e. by using a Riemannian metric, or combinatorially,
i.e by using a triangulation. In this presentation a triangulation, or a
partition of a smooth manifold in cells, will be viewed in a more analytic
spirit, being provided by the stable manifolds of the gradient of a nice Morse
function. WHS theory was recently used both for providing new proofs for known
but difficult results in topology, as well as new results and a positive
solution for an important conjecture about $L_2-$torsion, cf [BFKM]. This
presentation is a short version of a one quarter course I have given during the
spring of 1997 at OSU.
|
We develop a theory of tame vanishing cycles for schemes over
$[\mathbb{A}^1_{S}/\mathbb{G}_{m,S}]$ in the context of \'etale sheaves. We
show some desired properties of this formalism, among which: a compatibility
with tame vanishing cycles over a (strctly) henselian trait, a compatibility
with the theory of tame vanishing cycles over $\mathbb{A}^1_{S}$, a
compatibility with tensor product and with duality. In the last section, we
prove that monodromy-invariant vanishing cycles, introduced by the second named
author, are the homotopy fixed points with respect to a canonical continuous
action of $\mu_{\infty}$ of tame vanishing cycles over
$[\mathbb{A}^1_{S}/\mathbb{G}_{m,S}]$.
|
The emergence of nanoscience has increased the importance of experiments able
to probe the very local structure of materials, especially for disordered and
heterogeneous systems. This is technologically important; for example, the
nanoscale structure of glassy polymers has a direct correlation with their
macroscopic physical properties. We have discovered how a local, high frequency
dynamic process can be used to monitor and even predict macroscopic behavior in
glassy polymers. Polyvinylethylenes vitrified by different chemical and
thermodynamic pathways exhibit different densities in the glassy state. We find
that the rate and amplitude of a high frequency relaxation mode (the
Johari-Goldstein process involving local motion of segments of the chain
backbone) can either correlate or anti-correlate with the density. This implies
that neither the unoccupied (free) volume nor the configurational entropy
governs the local dynamics in any general sense. Rather it is the magnitude of
the fluctuations in local density that underlie these nm-scale motions. We show
how properties of the dynamics and the density fluctuations can both be
interpreted in terms of an asymmetric double well potential. Finally, since
fluctuations underlie the macroscopic properties, we argue that information
about the latter should be obtainable from characterization of the local
dynamics.
|
We present an approximate method for calculating the electrostatic free
energy of concentrated protein solutions. Our method uses a cell model and
accounts for both the coulomb energy and the entropic cost of Donnan salt
partitioning. The former term is calculated by linearizing the
Poisson-Boltzmann equation around a nonzero average potential, while the second
term is calculated using a jellium approximation that is empirically modified
to reproduce the dilute solution limit. When combined with a short-ranged
binding interaction, calculated using the mean spherical approximation, our
model reproduces osmotic pressure measurements of bovine serum albumin
solutions. We also use our free energy to calculate the salt-dependent shift in
the critical temperature of lysozyme solutions and show why the predicted salt
partitioning between the dilute and dense phases has proven experimentally
elusive.
|
The orientation of the magnetic field (B-field) in the filamentary dark cloud
GF 9 was traced from the periphery of the cloud into the L1082C dense core that
contains the low-mass, low-luminosity Class 0 young stellar object (YSO) GF 9-2
(IRAS 20503+6006). This was done using SOFIA HAWC+ dust thermal emission
polarimetry (TEP) at 216 um in combination with Mimir near-infrared background
starlight polarimetry (BSP) conducted at H-band (1.6 um) and K-band (2.2 um).
These observations were augmented with published I-band (0.77 um) BSP and
Planck 850 um TEP to probe B-field orientations with offset from the YSO in a
range spanning 6000 AU to 3 pc. No strong B-field orientation change with
offset was found, indicating remarkable uniformity of the B-field from the
cloud edge to the YSO environs. This finding disagrees with weak-field models
of cloud core and YSO formation. The continuity of inferred B-field
orientations for both TEP and BSP probes is strong evidence that both are
sampling a common B-field that uniformly threads the cloud, core, and YSO
region. Bayesian analysis of Gaia DR2 stars matched to the Mimir BSP stars
finds a distance to GF 9 of 270 +/- 10 pc. No strong wavelength dependence of
B-field orientation angle was found, contrary to previous claims.
|
This paper investigates the capacity problem for some multiple-access
scenarios with cooperative transmitters. First, a general Multiple-Access
Channel (MAC) with common information, i.e., a scenario where p transmitters
send private messages and also a common message to q receivers and each
receiver decodes all of the messages, is considered. The capacity region of the
discrete memoryless channel is characterized. Then, the general Gaussian fading
MAC with common information wherein partial Channel State Information (CSI) is
available at the transmitters (CSIT) and perfect CSI is available at the
receivers (CSIR) is investigated. A coding theorem is proved for this model
that yields an exact characterization of the throughput capacity region.
Finally, a two-transmitter/one-receiver Gaussian fading MAC with conferencing
encoders with partial CSIT and perfect CSIR is studied and its capacity region
is determined. For the Gaussian fading models with CSIR only (transmitters have
no access to CSIT), some numerical examples and simulation results are provided
for Rayleigh fading.
|
We investigate a Left-Right symmetric model respecting $SU(3)_C \otimes
SU(2)_L \otimes U(1)_L \otimes SU(2)_R \otimes U(1)_R$ local gauge symmetry. We
study the interactions of the heavy neutral and charged scalars of this model
along with their production at the hadron collider and their subsequent decays.
We analyze the collider searches of two heavy scalars, one of them is charge
neutral and another one is singly charged. In both the cases we consider their
associated production at the Large Hadron Collider (LHC) and finally
concentrate only on the leptonic final states. We perform both cut-based and
multivariate analysis using Boosted Decision Tree algorithm for 14 TeV as well
as as 27 TeV LHC run with 3000 fb$^{-1}$ integrated luminosity. As expected,
the multivariate analysis shows a better signal-background discrimination
compared to the cut-based analysis. In this article, we show that a charged
Higgs of mass 750 GeV and 1.2 TeV can be probed with $2.77 \sigma$ ($4.58
\sigma$) and $1.38 \sigma$ ($3.66 \sigma$) significance at 14 (27) TeV run of
LHC.
|
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are
prominent extensions of Linear Temporal Logic to specify properties about data
languages. In this paper, we consider the class of data languages of
non-monotonic data words over the natural numbers. We prove that, in this
setting, TPTL is strictly more expressive than MTL. To this end, we introduce
Ehrenfeucht-Fraisse (EF) games for MTL. Using EF games for MTL, we also prove
that the MTL definability decision problem ("Given a TPTL-formula, is the
language defined by this formula definable in MTL?") is undecidable. We also
define EF games for TPTL, and we show the effect of various syntactic
restrictions on the expressiveness of MTL and TPTL.
|
The quon algebra is an approach to particle statistics introduced by
Greenberg in order to provide a theory in which the Pauli exclusion principle
and Bose statistics are violated by a small amount. We generalize these models
by introducing a deformation of the quon algebra generated by a collection of
operators $\mathtt{a}_i$, $i \in \mathbb{N}^*$ the set of positive integers, on
an infinite dimensional module satisfying the $q_{i,j}$-mutator relations
$\mathtt{a}_i \mathtt{a}_j^{\dag} - q_{i,j}\, \mathtt{a}_j^{\dag} \mathtt{a}_i
= \delta_{i,j}$. The realizability of our model is proved by means of the
Aguiar-Mahajan bilinear form on the chambers of hyperplane arrangements. We
show that, for suitable values of $q_{i,j}$, the module generated by the
particle states obtained by applying combinations of $\mathtt{a}_i$'s and
$\mathtt{a}_i^{\dag}$'s to a vacuum state $|0\rangle$ is an indefinite Hilbert
module. Furthermore, we refind the extended Zagier's conjecture established
independently by Meljanac et al. and by Duchamp et al.
|
Here we describe how, utilizing a time-dependent opto-mechanical interaction,
a mechanical probe can provide an amplified measurement of the virtual photons
dressing the quantum ground state of an ultra strongly-coupled light-matter
system. We calculate the thermal noise tolerated by this measurement scheme,
and discuss a range of experimental setups in which it could be realized.
|
We like to develop model theory for $T$, a complete theory in
$\mathbb{L}_{\theta,\theta}(\tau)$ when $\theta$ is a compact cardinal. By
[Sh:300a] we have bare bones stability and it seemed we can go no further.
Dealing with ultrapowers (and ultraproducts) we restrict ourselves to ``$D$ a
$\theta$-complete ultrafilter on $I$, probably $(I,\theta)$-regular". The basic
theorems work, but can we generalize deeper parts of model theory? In
particular can we generalize stability enough to generalize [Sh:c, Ch.VI]? We
prove that at least we can characterize the $T$'s which are minimal under
Keisler's order, i.e. such that $\{D:D$ is a regular ultrafilter on $\lambda$
and $M \models T \Rightarrow M^\lambda/D$ is $\lambda$-saturated$\}$. Further
we succeed to connect our investigation with the logic $\mathbb{L}^1_{<
\theta}$ introduced in [Sh:797]: two models are $\mathbb{L}^1_{<
\theta}$-equivalent iff \, for some $\omega$- sequence of$\theta$-complete
ultrafilters, the iterated ultra-powers by it of those two models are
isomorphic.
|
Obtaining highly spin-polarized currents in molecular junctions is crucial
and desirable for nanoscale spintronics devices. Motivated by our recent
symmetry-based theoretical argument for complete blocking of one spin
conductance channel in atomic-scale junctions [A. Smogunov and Y. J. Dappe,
Nano Lett. 15, 3552 (2015)], we explore the generality of the proposed
mechanism and the degree of achieved spin-polarized current for various
ferromagnetic electrodes (Ni, Co, Fe) and two different molecules,
quaterthiophene and p-quaterphenyl. A simple analysis of the spin-resolved
local density of states of a free electrode allowed us to identify the Fe(110)
as the most optimal electrode, providing perfect spin filtering and high
conductance at the same time. These results are confirmed by $ab$ $initio$
quantum transport calculations and are similar to those reported previously for
model junctions. It is found, moreover, that the distortion of the
p-quaterphenyl molecule plays an important role, reducing significantly the
overall conductance.
|
We present deep HST/STIS coronagraphic images of the Beta Pic debris disk
obtained at two epochs separated by 15 years. The new images and the
re-reduction of the 1997 data provide the most sensitive and detailed views of
the disk at optical wavelengths as well as the yet smallest inner working angle
optical coronagraphic image of the disk. Our observations characterize the
large-scale and inner-disk asymmetries and we identify multiple breaks in the
disk radial surface brightness profile. We study in detail the radial and
vertical disk structure and show that the disk is warped. We explore the disk
at the location of the Beta Pic b super-jupiter and find that the disk surface
brightness slope is continuous between 0.5 and 2.0 arcsec, arguing for no
change at the separations where Beta Pic b orbits. The two epoch images
constrain the disk surface brightness evolution on orbital and radiation
pressure blow-out timescales. We place an upper limit of 3% on the disk surface
brightness change between 3-5 arcsec, including the locations of the disk warp,
and the CO and dust clumps. We discuss the new observations in the context of
high-resolution multi-wavelength images and divide the disk asymmetries in two
groups: axisymmetric and non-axisymmetric. The axisymmetric structures (warp,
large-scale butterfly, etc.) are consistent with disk structure models that
include interactions of a planetesimal belt and a non-coplanar giant planet.
The non-axisymmetric features, however, require a different explanation.
|
I will begin by conjecturing a cosmological generalization of black hole
complementarity (also known as the central dogma). I will then discuss three
theories and argue that they are inconsistent with second law of thermodynamics
if the cosmological version of the dogma is correct. The three theories are:
the big rip; cyclic cosmology; and the Farhi-Guth-Guven mechanism for creating
inflating universes behind black hole horizons.
|
A weak turbulence theory is derived for magnetohydrodynamics under rapid
rotation and in the presence of a large-scale magnetic field. The angular
velocity $\Omega_0$ is assumed to be uniform and parallel to the constant
Alfv\'en speed ${\bf b_0}$. Such a system exhibits left and right circularly
polarized waves which can be obtained by introducing the magneto-inertial
length $d \equiv b_0/\Omega_0$. In the large-scale limit ($kd \to 0$; $k$ being
the wave number), the left- and right-handed waves tend respectively to the
inertial and magnetostrophic waves whereas in the small-scale limit ($kd \to +
\infty$) pure Alfv\'en waves are recovered. By using a complex helicity
decomposition, the asymptotic weak turbulence equations are derived which
describe the long-time behavior of weakly dispersive interacting waves {\it
via} three-wave interaction processes. It is shown that the nonlinear dynamics
is mainly anisotropic with a stronger transfer perpendicular ($\perp$) than
parallel ($\parallel$) to the rotating axis. The general theory may converge to
pure weak inertial/magnetostrophic or Alfv\'en wave turbulence when the large
or small-scales limits are taken respectively. Inertial wave turbulence is
asymptotically dominated by the kinetic energy/helicity whereas the
magnetostrophic wave turbulence is dominated by the magnetic energy/helicity.
For both regimes a family of exact solutions are found for the spectra which do
not correspond necessarily to a maximal helicity state. It is shown that the
hybrid helicity exhibits a cascade whose direction may vary according to the
scale $k_f$ at which the helicity flux is injected with an inverse cascade if
$k_fd < 1$ and a direct cascade otherwise. The theory is relevant for the
magnetostrophic dynamo whose main applications are the Earth and giant planets
for which a small ($\sim 10^{-6}$) Rossby number is expected.
|
Probabilistic modeling enables combining domain knowledge with learning from
data, thereby supporting learning from fewer training instances than purely
data-driven methods. However, learning probabilistic models is difficult and
has not achieved the level of performance of methods such as deep neural
networks on many tasks. In this paper, we attempt to address this issue by
presenting a method for learning the parameters of a probabilistic program
using backpropagation. Our approach opens the possibility to building deep
probabilistic programming models that are trained in a similar way to neural
networks.
|
Segmenting text into semantically coherent segments is an important task with
applications in information retrieval and text summarization. Developing
accurate topical segmentation requires the availability of training data with
ground truth information at the segment level. However, generating such labeled
datasets, especially for applications in which the meaning of the labels is
user-defined, is expensive and time-consuming. In this paper, we develop an
approach that instead of using segment-level ground truth information, it
instead uses the set of labels that are associated with a document and are
easier to obtain as the training data essentially corresponds to a multilabel
dataset. Our method, which can be thought of as an instance of distant
supervision, improves upon the previous approaches by exploiting the fact that
consecutive sentences in a document tend to talk about the same topic, and
hence, probably belong to the same class. Experiments on the text segmentation
task on a variety of datasets show that the segmentation produced by our method
beats the competing approaches on four out of five datasets and performs at par
on the fifth dataset. On the multilabel text classification task, our method
performs at par with the competing approaches, while requiring significantly
less time to estimate than the competing approaches.
|
High-resolution mass spectra of helium droplets doped with C$_{60}$ and
formic acid (FA) are ionized by electrons. Positive ion mass spectra reveal
cluster ions [(C$_{60}$)$_p$FA$_n$]$^+$ together with their hydrogenated and
dehydrogenated counterparts. Also observed are ions containing one or more
water (W) molecules. The abundance distributions of these ions reveal several
interesting features: i) [(C$_{60}$)$_p$FA$_n$]$^+$ ions are more abundant than
hydrogenated [(C$_{60}$)$_p$FA$_n$H]$^+$ ions even though the opposite is true
in the absence of C$_{60}$ (i.e. if $p$ = 0); ii) although [C$_{60}$FA]$^+$ is
the most abundant ion containing a single C$_{60}$, multiple C$_{60}$ suppress
the [(C$_{60}$)$_p$FA]$^+$ signal; iii) an enhanced stability of
[(C$_{60}$)$_p$W$_1$FA$_5$H]$^+$ and [(C$_{60}$)$_p$W$_2$FA$_6$H]$^+$ mirrors
that of [W$_1$FA$_5$H]$^+$ and [W$_2$FA$_6$H]$^+$, respectively. On the other
hand, the enhanced stability of [C$_{60}$FA$_6$H]$^+$ finds no parallel in the
stability pattern of [FA$_n$H]$^+$ or FA$_n$$^+$. Negative ion mass spectra
indicate a propensity for non-dissociated [(C$_{60}$)$_p$FA$_n$]$^-$ anions if
$p \geq 1$ which contrasts with the dominance of dehydrogenated [FA$_n$-H]$^-$
anions.
|
We have investigated whether motion of gas in a bar-like potential can
account for the peculiar but systematic velocity field observed in the nuclear
region of the starburst galaxy NGC 253. This unusual velocity field with
gradients along both major and minor axes was revealed in a high resolution
($1.8^{\arcsec}\times 1.0^{\arcsec}$) H92$\alpha$ recombination line
observation by Anantharamiah and Goss (1996). A simple logarithmic potential is
used to model the bar. Assuming that the bulk of the gas flows along closed and
non-intersecting x1 (bar) and x2 (anti-bar) orbits of the bar potential, we
have computed the expected velocity field and position-velocity diagrams and
compared them with the observations. A comparison of the integrated CO
intensity maps with the spatial distribution of the x1 and x2 orbits in the
model indicates that the nuclear molecular gas in NGC 253 lies mainly on the x2
orbits. We also find that the velocity field observed in the central 100 pc
region in the H92$\alpha$ recombination line is well accounted for by the bar
model if most of the ionized gas resides in the inner x2 orbits. However, the
model is unable to explain the velocity field on a larger scale of $\sim 500$
pc observed using the OVRO interferometer with a resolution of
$5^{\arcsec}\times 3^{\arcsec}$. The direction of the observed CO velocity
field appears twisted compared to the model. We suggest that this perturbation
in the velocity field may be due to an accretion event that could have occurred
$10^7$ years ago.
|
The drying dynamics in three dimensional porous media are studied with
confocal microscopy. We observe abrupt air invasions in size from single
particle to hundreds of particles. We show that these result from the strong
flow from menisci in large pores to menisci in small pores during drying. This
flow causes air invasions to start in large menisci and subsequently spread
throughout the entire system. We measure the size and structure of the air
invasions and show that they are in accord with invasion percolation. By
varying the particle size and contact angle we unambiguously demonstrate that
capillary pressure dominates the drying process.
|
A theoretical study is performed on the entropy $S_{\rm s}$ and the spin
susceptibility $\chi_{\rm s}$ near the upper critical field $H_{c2}$ of s-wave
type-II superconductors with arbitrary impurity concentrations. The changes of
these quantities through $H_{c2}$ may be expressed as $[S_{\rm s}(T,B)-S_{\rm
s}(T,0)]/[S_{\rm n}(T)-S_{\rm s}(T,0)]=1-\alpha_{S}(1-B/H_{c2})\approx
(B/H_{c2})^{\alpha_{S}}$, for example, where $B$ is the average flux density
and $S_{\rm n}$ denotes entropy in the normal state. It is found that the
slopes $\alpha_{S}$ and $\alpha_{\chi}$ at T=0 are identical, connected
directly with the zero-energy density of states, and vary from 1.72 in the
dirty limit to $0.5\sim 0.6$ in the clean limit. This mean-free-path dependence
of $\alpha_{S}$ and $\alpha_{\chi}$ at T=0 is quantitatively the same as that
of the slope $\alpha_{\rho}(T=0)$ for the flux-flow resistivity studied
previously. The result suggests that $S_{\rm s}(B)$ and $\chi_{\rm s}(B)$ near
T=0 are convex downward (upward) in the dirty (clean) limit, deviating
substantially from the linear behavior $\propto B/H_{c2}$. The specific-heat
jump at $H_{c2}$ also shows fairly large mean-free-path dependence.
|
This paper continues the investigation of the configuration space of two
distinct points on a graph. We analyze the process of adding an additional edge
to the graph and the resulting changes in the topology of the configuration
space. We introduce a linking bilinear form on the homology group of the graph
with values in the cokernel of the intersection form (introduced in Part I of
this work). For a large class of graphs, which we call mature graphs, we give
explicit expressions for the homology groups of the configuration space. We
show that under a simple condition, adding an edge to a mature graph yields
another mature graph.
|
We carry out realistic coupled-channels calculations for
$^{11}$Be + $^{208}$Pb reaction in order to discuss the effects of break-up
of the projectile nucleus on sub-barrier fusion.
We discretize in energy the particle continuum states, which are associated
with the break-up process, and construct the coupling form factors to these
states on a microscopic basis.
The incoming boundary condition is employed in solving coupled-channels
equations, which enables us to define the flux for complete fusion inside the
Coulomb barrier. It is shown that complete fusion cross sections are
significantly enhanced due to the couplings to the continuum states compared
with the no coupling case at energies below the Coulomb barrier, while they are
hindered at above barrier energies.
|
We compute explicit upper bounds on the distance between the law of a
multivariate Gaussian distribution and the joint law of wavelets/needlets
coefficients based on a homogeneous spherical Poisson field. In particular, we
develop some results from Peccati and Zheng (2011), based on Malliavin calculus
and Stein's methods, to assess the rate of convergence to Gaussianity for a
triangular array of needlet coefficients with growing dimensions. Our results
are motivated by astrophysical and cosmological applications, in particular
related to the search for point sources in Cosmic Rays data.
|
HI absorption systems are great targets for direct measurement of the
Sandage-Loeb (SL) effect throughout a wide range of redshift for ground-based
radio telescopes. We demonstrate the significance of improving the accuracy of
SL effect measurement in cosmological model selection. With its wide sky
coverage and high sensitivity, we forecast that for 1 year of the upcoming
commensal survey (CRAFTS) the FAST telescope is capable of discovering about
800 HI absorption systems thereby improving the SL measurement accuracy. Aiming
to measurement the cosmic redshift drift rate at the precision of $\dot{z} \sim
10^{-10} \mathrm{decade^{-1}}$, we propose combined observation mode with
blind-searching and targeted observation. For a decade of consecutive targeted
spectroscopic observation with the frequency resolution at a level of sub-$0.1\
\rm Hz$, we could detect the first-order derivative of the cosmological
redshift with the expected precision.
|
Urban rail transit provides significant comprehensive benefits such as large
traffic volume and high speed, serving as one of the most important components
of urban traffic construction management and congestion solution. Using real
passenger flow data of an Asian subway system from April to June of 2018, this
work analyzes the space-time distribution of the passenger flow using
short-term traffic flow prediction. Stations are divided into four types for
passenger flow forecasting, and meteorological records are collected for the
same period. Then, machine learning methods with different inputs are applied
and multivariate regression is performed to evaluate the improvement effect of
each weather element on passenger flow forecasting of representative metro
stations on hourly basis. Our results show that by inputting weather variables
the precision of prediction on weekends enhanced while the performance on
weekdays only improved marginally, while the contribution of different elements
of weather differ. Also, different categories of stations are affected
differently by weather. This study provides a possible method to further
improve other prediction models, and attests to the promise of data-driven
analytics for optimization of short-term scheduling in transit management.
|
Solar flares are extremely energetic phenomena in our Solar System. Their
impulsive, often drastic radiative increases, in particular at short
wavelengths, bring immediate impacts that motivate solar physics and space
weather research to understand solar flares to the point of being able to
forecast them. As data and algorithms improve dramatically, questions must be
asked concerning how well the forecasting performs; crucially, we must ask how
to rigorously measure performance in order to critically gauge any
improvements. Building upon earlier-developed methodology (Barnes et al, 2016,
Paper I), international representatives of regional warning centers and
research facilities assembled in 2017 at the Institute for Space-Earth
Environmental Research, Nagoya University, Japan to - for the first time -
directly compare the performance of operational solar flare forecasting
methods. Multiple quantitative evaluation metrics are employed, with focus and
discussion on evaluation methodologies given the restrictions of operational
forecasting. Numerous methods performed consistently above the "no skill"
level, although which method scored top marks is decisively a function of flare
event definition and the metric used; there was no single winner. Following in
this paper series we ask why the performances differ by examining
implementation details (Leka et al. 2019, Paper III), and then we present a
novel analysis method to evaluate temporal patterns of forecasting errors in
(Park et al. 2019, Paper IV). With these works, this team presents a
well-defined and robust methodology for evaluating solar flare forecasting
methods in both research and operational frameworks, and today's performance
benchmarks against which improvements and new methods may be compared.
|
Given $\beta\in(1,2],$ the $\beta$-transformation $T_\beta: x\mapsto \beta
x\pmod 1$ on the circle $[0, 1)$ with a hole $[0, t)$ was investigated by Kalle
et al.~(2019). They described the set-valued bifurcation set
\[
\mathcal E_\beta:=\{t\in[0, 1): K_\beta(t')\ne K_\beta(t)~\forall t'>t\},
\]
where $K_\beta(t):=\{x\in[0, 1): T_\beta^n(x)\ge t~\forall n\ge 0\}$ is the
survivor set. In this paper we investigate the dimension bifurcation set
\[
\mathcal B_\beta:=\{t\in[0, 1): \dim_H K_\beta(t')\ne \dim_H
K_\beta(t)~\forall t'>t\},
\]
where $\dim_H$ denotes the Hausdorff dimension.
We show that if $\beta\in(1,2]$ is a multinacci number then the two
bifurcation sets $\mathcal B_\beta$ and $\mathcal E_\beta$ coincide. Moreover
we give a complete characterization of these two sets. As a corollary of our
main result we prove that for $\beta$ a multinacci number we have
$\dim_H(\mathcal E_\beta\cap[t, 1])=\dim_H K_\beta(t)$ for any $t\in[0, 1)$.
This confirms a conjecture of Kalle et al.~for $\beta$ a multinacci number.
|
We investigate polytopes inscribed into a sphere that are normally equivalent
(or strongly isomorphic) to a given polytope $P$. We show that the associated
space of polytopes, called the inscribed cone of $P$, is closed under Minkowski
addition. Inscribed cones are interpreted as type cones of ideal hyperbolic
polytopes and as deformation spaces of Delaunay subdivisions. In particular,
testing if there is an inscribed polytope normally equivalent to $P$ is
polynomial time solvable.
Normal equivalence is decided on the level of normal fans and we study the
structure of inscribed cones for various classes of polytopes and fans,
including simple, simplicial, and even. We classify (virtually) inscribable
fans in dimension $2$ as well as inscribable permutahedra and nestohedra.
A second goal of the paper is to introduce inscribed virtual polytopes.
Polytopes with a fixed normal fan $\mathcal{N}$ form a monoid with respect to
Minkowski addition and the associated Grothendieck group is called the type
space of $\mathcal{N}$. Elements of the type space correspond to formal
Minkowski differences and are naturally equipped with vertices and hence with a
notion of inscribability. We show that inscribed virtual polytopes form a
subgroup, which can be non-trivial even if $\mathcal{N}$ does not have actual
inscribed polytopes.
We relate inscribed virtual polytopes to routed particle trajectories, that
is, piecewise-linear trajectories of particles in a ball with restricted
directions. The state spaces gives rise to connected groupoids generated by
reflections, called reflection groupoids. The endomorphism groups of reflection
groupoids can be thought of as discrete holonomy groups of the trajectories and
we determine when they are reflection groups.
|
The fission processes of thermal excited nuclei are conventionally studied by
statistical models which rely on inputs of phenomenological level densities and
potential barriers. Therefore the microscopic descriptions of spontaneous
fission and induced fission are very desirable for a unified understanding of
various fission processes.
We propose to study the fission rates, at both low and high temperatures,
with microscopically calculated temperature-dependent fission barriers and
collective mass parameters.
The fission barriers are calculated by the finite-temperature
Skyrme-Hartree-Fock+BCS method. The mass parameters are calculated by the
temperature-dependent cranking approximation. The thermal fission rates can be
obtained by the imaginary free energy approach at all temperatures, in which
fission barriers are naturally temperature dependent. The fission at low
temperatures can be described mainly as a barrier-tunneling process. While the
fission at high temperatures has to incorporate the reflection above barriers.
Our results of spontaneous fission rates reasonably agree with other studies
and experiments. The temperature dependencies of fission barrier heights and
curvatures have been discussed. The temperature dependent behaviors of mass
parameters have also been discussed. The thermal fission rates from low to high
temperatures with a smooth connection have been given by different approaches.
\item[Conclusions] Since the temperature dependencies of fission barrier
heights and curvatures, and the mass parameters can vary rapidly for different
nuclei, the microscopic descriptions of thermal fission rates are very
valuable. Our studies without free parameters provide a consistent picture to
study various fissions such as that in fast-neutron reactors, astrophysical
environments and fusion reactions for superheavy nuclei.
|
Getting rid of the fundamental limitations in fitting to the paired training
data, recent unsupervised low-light enhancement methods excel in adjusting
illumination and contrast of images. However, for unsupervised low light
enhancement, the remaining noise suppression issue due to the lacking of
supervision of detailed signal largely impedes the wide deployment of these
methods in real-world applications. Herein, we propose a novel
Cycle-Interactive Generative Adversarial Network (CIGAN) for unsupervised
low-light image enhancement, which is capable of not only better transferring
illumination distributions between low/normal-light images but also
manipulating detailed signals between two domains, e.g.,
suppressing/synthesizing realistic noise in the cyclic enhancement/degradation
process. In particular, the proposed low-light guided transformation
feed-forwards the features of low-light images from the generator of
enhancement GAN (eGAN) into the generator of degradation GAN (dGAN). With the
learned information of real low-light images, dGAN can synthesize more
realistic diverse illumination and contrast in low-light images. Moreover, the
feature randomized perturbation module in dGAN learns to increase the feature
randomness to produce diverse feature distributions, persuading the synthesized
low-light images to contain realistic noise. Extensive experiments demonstrate
both the superiority of the proposed method and the effectiveness of each
module in CIGAN.
|
In this paper, we study the complexity of evaluating Conjunctive Queries with
negation (\cqneg). First, we present an algorithm with linear preprocessing
time and constant delay enumeration for a class of CQs with negation called
free-connex signed-acyclic queries. We show that no other queries admit such an
algorithm subject to lower bound conjectures. Second, we extend our algorithm
to Conjunctive Queries with negation and aggregation over a general semiring,
which we call Functional Aggregate Queries with negation (\faqneg). Such an
algorithm achieves constant delay enumeration for the same class of queries,
but with a slightly increased preprocessing time which includes an inverse
Ackermann function. We show that this surprising appearance of the Ackermmann
function is probably unavoidable for general semirings, but can be removed when
the semiring has specific structure. Finally, we show an application of our
results to computing the difference of CQs.
|
Purpose: To demonstrate an alternative to the rinse and rub (RR) method for
cleaning pollutants from the exterior surface of soft contact lenses. This
proposed technique is termed Polymer on Polymer Pollutant Removal (PoPPR),
which utilizes the elastic properties of polydimethylsiloxane (PDMS) to
physically remove contaminants from contact lens surfaces through non-adhesive
unpeeling.
Methods: Three different ratios of setting agent to polymer PDMS (1:30, 1:40,
and 1:50) were evaluated using the PoPPR method against the control method of
RR with a commercial multi-purpose lens cleaning solution. Three simulated
pollutants of different sizes: pollen (25-40 {\mu}m), microbeads (1-5 {\mu}m),
and nanoparticles (5-10 nm), were used to test the effectiveness of both
cleaning methods. The fraction of pollutants removed from each contact lens was
recorded and evaluated for significance.
Results: PDMS 1:40 was found to be the optimal ratio for lens cleaning using
the PoPPR method. For larger particles (>10 {\mu}m), no difference was observed
between conventional RR and proposed PoPPR method (p > 0.05). However, the new
PoPPR technique was significantly better at removing small PM2.5 particles
(<2.5 {\mu}m) compared to the RR method, specifically for microbeads (p =
0.006) and nanoparticles (p < 0.001).
Conclusion: This proof-of-concept work demonstrates that the PoPPR method of
cleaning contact lenses is as effective as the conventional cleaning method for
larger particles such as pollen. The PoPPR method is more effective at removing
extremely fine particulate pollutants, including microplastics and
nanoparticles. This method offers a potentially more efficient cleaning
protocol that could enhance the safety, health, and comfort of contact lens
users, especially those living in regions with significant air pollution.
|
Oncolytic virotherapy, utilizing genetically modified viruses to combat
cancer and trigger anti-cancer immune responses, has garnered significant
attention in recent years. In our previous work arXiv:2305.12386, we developed
a stochastic agent-based model elucidating the spatial dynamics of infected and
uninfected cells within solid tumours. Building upon this foundation, we
present a novel stochastic agent-based model to describe the intricate
interplay between the virus and the immune system; the agents' dynamics are
coupled with a balance equation for the concentration of the chemoattractant
that guides the movement of immune cells. We formally derive the continuum
limit of the model and carry out a systematic quantitative comparison between
this system of PDEs and the individual-based model in two spatial dimensions.
Furthermore, we describe the traveling waves of the three populations, with the
uninfected proliferative cells trying to escape from the infected cells while
immune cells infiltrate the tumour.
Simulations show a good agreement between agent-based approaches and
numerical results for the continuum model. Some parameter ranges give rise to
oscillations of cell number in both models, in line with the behaviour of the
corresponding nonspatial model, which presents Hopf bifurcations. Nevertheless,
in some situations the behaviours of the two models may differ significantly,
suggesting that stochasticity plays a key role in the dynamics. Our results
highlight that a too rapid immune response, before the infection is
well-established, appears to decrease the efficacy of the therapy and thus some
care is needed when oncolytic virotherapy is combined with immunotherapy. This
further suggests the importance of clinically improving the modulation of the
immune response according to the tumour's characteristics and to the immune
capabilities of the patients.
|
We present a computational scheme for predicting the ligands that bind to a
pocket of known structure. It is based on the generation of a general abstract
representation of the molecules, which is invariant to rotations, translations
and permutations of atoms, and has some degree of isometry with the space of
conformations. We use these representations to train a non-deep machine
learning algorithm to classify the binding between pockets and molecule pairs,
and show that this approach has a better generalization capability than
existing methods.
|
We report three new transiting hot-Jupiter planets discovered from the WASP
surveys combined with radial velocities from OHP/SOPHIE and Euler/CORALIE and
photometry from Euler and TRAPPIST. All three planets are inflated, with radii
1.7-1.8 Rjup. All orbit hot stars, F5-F7, and all three stars have evolved,
post-MS radii (1.7-2.2 Rsun). Thus the three planets, with orbits of 1.8-3.9 d,
are among the most irradiated planets known. This reinforces the correlation
between inflated planets and stellar irradiation.
|
This paper studies local derivations on the Schr{\"o}dinger algebra $\ms_n$
in $(n+1)$-dimensional space-time of Schr{\"o}dinger Lie groups for any integer
$n$. The purpose of this work is to prove that every local derivation on
$\ms_n$ is a derivation.
|
The limiting magnitude of the HST data set used by Cochran et al. (1995) to
detect small objects in the Kuiper belt is reevaluated, and the methods used
are described in detail. It is shown, by implanting artificial objects in the
original HST images, and re-reducing the images using our original algorithm,
that the limiting magnitude of our images (as defined by the 50% detectability
limit) is $V=28.4$. This value is statistically the same as the value found in
the original analysis. We find that $\sim50%$ of the moving Kuiper belt objects
with $V=27.9$ are detected when trailing losses are included. In the same data
in which these faint objects are detected, we find that the number of false
detections brighter than $V=28.8$ is less than one per WFPC2 image. We show
that, primarily due to a zero-point calibration error, but partly due to
inadequacies in modeling the HST'S data noise characteristics and Cochran et
al.'s reduction techniques, Brown et al. 1997 underestimate the SNR of objects
in the HST dataset by over a factor of 2, and their conclusions are therefore
invalid.
|
Neutrino-induced reactions on $^{40}$Ar are investigated by shell model for
Gamow-Teller transitions and random-phase-approximation (RPA) for forbidden
transitions. For the 1$^{+}$ multipole, an effective interaction in $sd$-$pf$
shell obtained by the extended Kuo-Krenciglowa (EKK) method from chiral
interactions is used to study $B(GT)$, charged-current reaction $^{40}$Ar
($\nu_e$, $e^{-}$) $^{40}$K, $B(M1)$ in $^{40}$Ar and neutral-current reaction
$^{40}$Ar ($\nu$, $\nu$') $^{40}$Ar. A considerable quenching for spin modes is
found in the analysis of $B(M1)$, and this quenching is taken into account for
the evaluation of the cross sections of the neutral-current reaction. The
sensitive dependence of the reaction cross sections on the quenching of the
axial-vector coupling constant, $g_A$, is pointed out.
|
This paper addresses the problem of finding the optimal Eco-Driving (ED)
speed profile of an electric Connected and Automated Vehicle (CAV) in an
isolated urban un-signalized intersection. The problem is formulated as a
single-level optimization and solved using Pontryagin's Minimum Principle
(PMP). Analytical solutions are presented for various conflicts that occur at
an intersection. Cooperation is introduced amongst CAVs as the ability to share
intentions. Two levels of cooperation, namely the Cooperative ED (C-ED) and
Non-Cooperative (NC-ED) algorithms are evaluated, in a simulation environment,
for energy efficiency with Intelligent Driver Model (IDM) as the baseline.
|
We consider the one-sided matching problem, where n agents have preferences
over n items, and these preferences are induced by underlying cardinal
valuation functions. The goal is to match every agent to a single item so as to
maximize the social welfare. Most of the related literature, however, assumes
that the values of the agents are not a priori known, and only access to the
ordinal preferences of the agents over the items is provided. Consequently,
this incomplete information leads to loss of efficiency, which is measured by
the notion of distortion. In this paper, we further assume that the agents can
answer a small number of queries, allowing us partial access to their values.
We study the interplay between elicited cardinal information (measured by the
number of queries per agent) and distortion for one-sided matching, as well as
a wide range of well-studied related problems. Qualitatively, our results show
that with a limited number of queries, it is possible to obtain significant
improvements over the classic setting, where only access to ordinal information
is given.
|
We prove that if G is a compact connected Lie group and X is a compact
connected hyper-Kahler manifold, then the L^2 metric on (the smooth locus of)
the moduli space of flat G-bundles on X is a hyper-Kahler metric.
|
In this paper, we consider linear $q$-difference systems with coefficients
that are germs of meromorphic functions, with Newton polygon that has two
slopes. Then, we explain how to compute similar meromorphic gauge
transformations than those appearing in the work of Bugeaud, using a
$q$-analogue of the Borel-Laplace summation.
|
Heavy-metal hot subdwarfs (sdB and sdO) represent a small group of stars with
unusually high concentrations of trans-iron elements in their atmospheres,
having abundances ~ 10000 times solar. One example is LS IV-14$^{\circ}$ 116,
where a number of heavy-metal absorption lines of Sr II, Y III and Zr IV have
been observed in the optical band 4000 - 5000 A. We use a fully relativistic
Dirac atomic R-Matrix (DARC) to calculate photoionization cross sections of
Sr$^{0}$, Y$^{+}$ and Zr$^{2+}$ from their ground state to the twentieth
excited level. We use the cross sections and the oscillator strengths to
simulate the spectrum of a hot subdwarf. We obtain complete sets of
photoionization cross sections for the three ions under study. We use these
data to calculate the opacity of the stellar atmospheres of hot subdwarf stars,
and show that for overabundances observed in some heavy-metal subdwarves,
photo-excitation from zirconium, in particular, does contribute some back
warming in the model.
|
In this paper we give an algorithm of how to determine a Weierstrass equation
with minimal discriminant for superelliptic curves generalizing work of Tate
for elliptic curves and Liu for genus 2 curves.
|
We study unit ball graphs (and, more generally, so-called noisy uniform ball
graphs) in $d$-dimensional hyperbolic space, which we denote by $\mathbb{H}^d$.
Using a new separator theorem, we show that unit ball graphs in $\mathbb{H}^d$
enjoy similar properties as their Euclidean counterparts, but in one dimension
lower: many standard graph problems, such as Independent Set, Dominating Set,
Steiner Tree, and Hamiltonian Cycle can be solved in $2^{O(n^{1-1/(d-1)})}$
time for any fixed $d\geq 3$, while the same problems need $2^{O(n^{1-1/d})}$
time in $\mathbb{R}^d$. We also show that these algorithms in $\mathbb{H}^d$
are optimal up to constant factors in the exponent under ETH.
This drop in dimension has the largest impact in $\mathbb{H}^2$, where we
introduce a new technique to bound the treewidth of noisy uniform disk graphs.
The bounds yield quasi-polynomial ($n^{O(\log n)}$) algorithms for all of the
studied problems, while in the case of Hamiltonian Cycle and $3$-Coloring we
even get polynomial time algorithms. Furthermore, if the underlying noisy disks
in $\mathbb{H}^2$ have constant maximum degree, then all studied problems can
be solved in polynomial time. This contrasts with the fact that these problems
require $2^{\Omega(\sqrt{n})}$ time under ETH in constant maximum degree
Euclidean unit disk graphs.
Finally, we complement our quasi-polynomial algorithm for Independent Set in
noisy uniform disk graphs with a matching $n^{\Omega(\log n)}$ lower bound
under ETH. This shows that the hyperbolic plane is a potential source of
NP-intermediate problems.
|
Given a metric space $(X,d_X)$, $c\ge 1$, $r>0$, and $p,q\in [0,1]$, a
distribution over mappings $\h:X\to \mathbb N$ is called a
$(r,cr,p,q)$-sensitive hash family if any two points in $X$ at distance at most
$r$ are mapped by $\h$ to the same value with probability at least $p$, and any
two points at distance greater than $cr$ are mapped by $\h$ to the same value
with probability at most $q$. This notion was introduced by Indyk and Motwani
in 1998 as the basis for an efficient approximate nearest neighbor search
algorithm, and has since been used extensively for this purpose. The
performance of these algorithms is governed by the parameter
$\rho=\frac{\log(1/p)}{\log(1/q)}$, and constructing hash families with small
$\rho$ automatically yields improved nearest neighbor algorithms. Here we show
that for $X=\ell_1$ it is impossible to achieve $\rho\le \frac{1}{2c}$. This
almost matches the construction of Indyk and Motwani which achieves $\rho\le
\frac{1}{c}$.
|
In this paper, we revisit the split decomposition of graphs and give new
combinatorial and algorithmic results for the class of totally decomposable
graphs, also known as the distance hereditary graphs, and for two non-trivial
subclasses, namely the cographs and the 3-leaf power graphs. Precisely, we give
strutural and incremental characterizations, leading to optimal fully-dynamic
recognition algorithms for vertex and edge modifications, for each of these
classes. These results rely on a new framework to represent the split
decomposition, namely the graph-labelled trees, which also captures the modular
decomposition of graphs and thereby unify these two decompositions techniques.
The point of the paper is to use bijections between these graph classes and
trees whose nodes are labelled by cliques and stars. Doing so, we are also able
to derive an intersection model for distance hereditary graphs, which answers
an open problem.
|
We prove an explicit integral formula for computing the product of two
shifted Riemann zeta functions everywhere in the complex plane. We show that
this formula implies the existence of infinite families of exact exponential
sum identities involving the divisor functions, and we provide examples of
these identities. We conjecturally propose a method to compute divisor
functions by matrix inversion, without employing arithmetic techniques.
|
For a continuous map $T$ of a compact metrizable space $X$ with finite
topological entropy, the order of accumulation of entropy of $T$ is a countable
ordinal that arises in the context of entropy structure and symbolic
extensions. We show that every countable ordinal is realized as the order of
accumulation of some dynamical system. Our proof relies on functional analysis
of metrizable Choquet simplices and a realization theorem of Downarowicz and
Serafin. Further, if $M$ is a metrizable Choquet simplex, we bound the ordinals
that appear as the order of accumulation of entropy of a dynamical system whose
simplex of invariant measures is affinely homeomorphic to $M$. These bounds are
given in terms of the Cantor-Bendixson rank of $\overline{\ex(M)}$, the closure
of the extreme points of $M$, and the relative Cantor-Bendixson rank of
$\overline{\ex(M)}$ with respect to $\ex(M)$. We also address the optimality of
these bounds.
|
Let M be a compact manifold of dimension n, P = P(h) a semiclassical
pseudodifferential operator on M, and u = u(h) an L^2 normalised family of
functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact
submanifold of M. In a previous article, the second-named author proved
estimates on the L^p norms, p > 2, of u restricted to H, under the assumption
that the u are semiclassically localised and under some natural structural
assumptions about the principal symbol of P. These estimates are of the form
Ch^d(n;k;p) where k=dimH (except for a logarithmic divergence in the case k =
n-2; p = 2). When H is a hypersurface, i.e. k = n-1, we have d(n;n-1;2)=1/4,
which is sharp when M is the round n-sphere and H is an equator. In this
article, we assume that H is a hypersurface, and make the additional geometric
assumption that H is curved with respect to the bicharacteristic flow of P.
Under this assumption we improve the estimate from d=1/4 to 1/6, generalising
work of Burq-Gerard-Tzvetkov and Hu for Laplace eigenfunctions. To do this we
apply the Melrose-Taylor theorem, as adapted by Pan and Sogge, for Fourier
integral operators with folding canonical relations.
|
This paper introduces {\em fusion subspace clustering}, a novel method to
learn low-dimensional structures that approximate large scale yet highly
incomplete data. The main idea is to assign each datum to a subspace of its
own, and minimize the distance between the subspaces of all data, so that
subspaces of the same cluster get {\em fused} together. Our method allows low,
high, and even full-rank data; it directly accounts for noise, and its sample
complexity approaches the information-theoretic limit. In addition, our
approach provides a natural model selection {\em clusterpath}, and a direct
completion method. We give convergence guarantees, analyze computational
complexity, and show through extensive experiments on real and synthetic data
that our approach performs comparably to the state-of-the-art with complete
data, and dramatically better if data is missing.
|
Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.