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The phenomenon of dynamical quark mass generation is studied in QCD within
the framework of a gauge invariant formalism. An exact relationship is
established between the equation satisfied by the scalar part of the two-point
gauge invariant quark Green's function and the quark-antiquark bound state
equation in the chiral limit. A possible nontrivial solution of the former
yields a massless pseudoscalar solution of the bound state equation with
vanishing total momentum. The result is also corroborated by the corresponding
Ward-Takahashi identity. The problem is explicitly solved in two-dimensional
QCD in the large-$N_c$ limit.
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Let $P$ be an orthogonal polygon. Consider a sliding camera that travels back
and forth along an orthogonal line segment $s\in P$ as its \emph{trajectory}.
The camera can see a point $p\in P$ if there exists a point $q\in s$ such that
$pq$ is a line segment normal to $s$ that is completely inside $P$. In the
\emph{minimum-cardinality sliding cameras problem}, the objective is to find a
set $S$ of sliding cameras of minimum cardinality to guard $P$ (i.e., every
point in $P$ can be seen by some sliding camera) while in the
\emph{minimum-length sliding cameras problem} the goal is to find such a set
$S$ so as to minimize the total length of trajectories along which the cameras
in $S$ travel.
In this paper, we first settle the complexity of the minimum-length sliding
cameras problem by showing that it is polynomial tractable even for orthogonal
polygons with holes, answering a question asked by Katz and Morgenstern (2011).
We next show that the minimum-cardinality sliding cameras problem is
\textsc{NP}-hard when $P$ is allowed to have holes, which partially answers
another question asked by Katz and Morgenstern (2011).
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Near-equilibrium thermal detectors operate as classical calorimeters, with
energy deposition and internal equilibration times short compared to the
thermal time constant of the device. Advances in fabrication techniques,
cryogenics, and electronics have made it practical to measure deposited energy
with unprecedented sensitivity and precision. In this chapter we discuss
performance considerations for these devices, including optimal filtering and
energy resolution calculations. We begin with the basic theory of simple
equilibrium calorimeters with ideal resistive thermometers. This provides a
starting point for a brief discussion of electrothermal feedback, other noise
sources, various non-ideal effects, and nonlinearity. We then describe other
types of thermometers and show how they fit into this theoretical framework and
why they may require different optimizations and figures of merit. Most of this
discussion is applicable also to power detectors, or bolometers, where the
detector time constants may be short compared to variations in the incident
signal power.
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Vortex dynamics in 3He-B is divided by the temperature dependent damping into
a high-temperature regime, where the number of vortices is conserved, and a
low-temperature regime, where rapid vortex multiplication takes place in a
turbulent burst. We investigate experimentally the hydrodynamic transition
between these two regimes by injecting seed vortex loops into vortex-free
rotating flow. The onset temperature of turbulence is dominated by the roughly
exponential temperature dependence of vortex friction, but its exact value is
found to depend on the injection method.
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For settings with a binary treatment and a binary outcome, instrumental
variables can be used to construct bounds on a causal treatment effect. With
continuous outcomes, meaningful bounds are more difficult to obtain because the
domain of the outcome is typically unrestricted. In this paper, we combine an
instrumental variable and subjective assumptions in the context of an obser-
vational cohort study of HIV-infected women to construct meaningful bounds on
the initial-stage causal effect of antiretroviral therapy on CD4 count. The
subjective assumptions are encoded in terms of the potential outcomes that are
identified by observed data as well as a sensitivity parameter that captures
the impact of unmeasured confounding. Measured confounding is adjusted using
the method of inverse probability weighting (IPW). With extra information from
an IV, we quantify both the causal treatment effect and the degree of the
unmea- sured confounding. We demonstrate our method by analyzing data from the
HIV Epidemiology Research Study.
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SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS)
polynomial optimizations. This document briefly describes the use and
functionality of this toolbox. Section 1 introduces the problem formulations
for SOS tests, SOS feasibility problems, SOS optimizations, and generalized SOS
problems. Section 2 reviews the SOSOPT toolbox for solving these optimizations.
This section includes information on toolbox installation, formulating
constraints, solving SOS optimizations, and setting optimization options.
Finally, Section 3 briefly reviews the connections between SOS optimizations
and semidefinite programs (SDPs). It is the connection to SDPs that enables SOS
optimizations to be solved in an efficient manner
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We report results of an extended spectropolarimetric and photometric
monitoring of the weak-line T Tauri star V830 Tau and its recently-detected
newborn close-in giant planet. Our observations, carried out within the MaTYSSE
programme, were spread over 91d, and involved the ESPaDOnS and Narval
spectropolarimeters linked to the 3.6m Canada-France-Hawaii, the 2m Bernard
Lyot and the 8-m Gemini-North Telescopes. Using Zeeman-Doppler Imaging, we
characterize the surface brightness distributions, magnetic topologies and
surface differential rotation of V830 Tau at the time of our observations, and
demonstrate that both distributions evolve with time beyond what is expected
from differential rotation. We also report that near the end of our
observations, V830 Tau triggered one major flare and two weaker precursors,
showing up as enhanced red-shifted emission in multiple spectral activity
proxies. With 3 different filtering techniques, we model the radial velocity
(RV) activity jitter (of semi-amplitude 1.2km/s) that V830 Tau generates,
successfully retrieve the 68m/s RV planet signal hiding behind the jitter,
further confirm the existence of V830 Tau b and better characterize its orbital
parameters. We find that the method based on Gaussian-process regression
performs best thanks to its higher ability at modelling not only the activity
jitter, but also its temporal evolution over the course of our observations,
and succeeds at reproducing our RV data down to a rms precision of 35m/s. Our
result provides new observational constraints on scenarios of star / planet
formation and demonstrates the scientific potential of large-scale searches for
close-in giant planets around T Tauri stars.
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We study the comparison problem of distribution equality between two random
samples under a right censoring scheme. To address this problem, we design a
series of tests based on energy distance and kernel mean embeddings. We
calibrate our tests using permutation methods and prove that they are
consistent against all fixed continuous alternatives. To evaluate our proposed
tests, we simulate survival curves from previous clinical trials. Additionally,
we provide practitioners with a set of recommendations on how to select
parameters/distances for the delay effect problem. Based on the method for
parameter tunning that we propose, we show that our tests demonstrate a
considerable gain of statistical power against classical survival tests.
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A multivariable hypergeometric-type formula for raising operators of the
Macdonald polynomials is conjectured. It is proved that this agrees with Jing
and Jozefiak's expression for the two-row Macdonald polynomials, and also with
Lassalle and Schlosser's formula for partitions with length three.
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We report complex band structure (CBS) calculations for the four late
transition metal monoxides, MnO, FeO, CoO and NiO, in their paramagnetic phase.
The CBS is obtained from density functional theory plus dynamical mean field
theory (DMFT) calculations to take into account correlation effects. The
so-called $\beta$ parameters, governing the exponential decay of the
transmission probability in the non-resonant tunneling regime of these oxides,
are extracted from the CBS. Different model constructions are examined in the
DMFT part of the calculation. The calculated $\beta$ parameters provide
theoretical estimation for the decay length in the evanescent channel, which
would be useful for tunnel junction applications of these materials.
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Topic evolution modeling has received significant attentions in recent
decades. Although various topic evolution models have been proposed, most
studies focus on the single document corpus. However in practice, we can easily
access data from multiple sources and also observe relationships between them.
Then it is of great interest to recognize the relationship between multiple
text corpora and further utilize this relationship to improve topic modeling.
In this work, we focus on a special type of relationship between two text
corpora, which we define as the "lead-lag relationship". This relationship
characterizes the phenomenon that one text corpus would influence the topics to
be discussed in the other text corpus in the future. To discover the lead-lag
relationship, we propose a jointly dynamic topic model and also develop an
embedding extension to address the modeling problem of large-scale text corpus.
With the recognized lead-lag relationship, the similarities of the two text
corpora can be figured out and the quality of topic learning in both corpora
can be improved. We numerically investigate the performance of the jointly
dynamic topic modeling approach using synthetic data. Finally, we apply the
proposed model on two text corpora consisting of statistical papers and the
graduation theses. Results show the proposed model can well recognize the
lead-lag relationship between the two corpora, and the specific and shared
topic patterns in the two corpora are also discovered.
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Newborn stars form within the localized, high density regions of molecular
clouds. The sequence and rate at which stars form in dense clumps and the
dependence on local and global environments are key factors in developing
descriptions of stellar production in galaxies. We seek to observationally
constrain the rate and latency of star formation in dense massive clumps that
are distributed throughout the Galaxy and to compare these results to proposed
prescriptions for stellar production. A sample of 24 micron-based Class~I
protostars are linked to dust clumps that are embedded within molecular clouds
selected from the APEX Telescope Large Area Survey of the Galaxy. We determine
the fraction of star-forming clumps, f*, that imposes a constraint on the
latency of star formation in units of a clump's lifetime. Protostellar masses
are estimated from models of circumstellar environments of young stellar
objects from which star formation rates are derived. Physical properties of the
clumps are calculated from 870 micron dust continuum emission and NH_3 line
emission. Linear correlations are identified between the star formation rate
surface density, Sigma_{SFR}, and the quantities Sigma_{H2}/tau_{ff} and
Sigma_{H2}/tau_{cross}, suggesting that star formation is regulated at the
local scales of molecular clouds. The measured fraction of star forming clumps
is 23%. Accounting for star formation within clumps that are excluded from our
sample due to 24 micron saturation, this fraction can be as high as 31%. Dense,
massive clumps form primarily low mass (< 1-2 msun) stars with emergent 24
micron fluxes below our sensitivity limit or are incapable of forming any stars
for the initial 70% of their lifetimes. The low fraction of star forming clumps
in the Galactic center relative to those located in the disk of the Milky Way
is verified.
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We consider nonholonomic geodesic flows of left-invariant metrics and
left-invariant nonintegrable distributions on compact connected Lie groups. The
equations of geodesic flows are reduced to the Euler-Poincare-Suslov equations
on the corresponding Lie algebras. The Poisson and symplectic structures give
raise to various algebraic constructions of the integrable Hamiltonian systems.
On the other hand, nonholonomic systems are not Hamiltonian and the integration
methods for nonholonomic systems are much less developed. In this paper, using
chains of subalgebras, we give constructions that lead to a large set of first
integrals and to integrable cases of the Euler-Poincare-Suslov equations.
Further, we give examples of nonholonomic geodesic flows that can be seen as a
restrictions of integrable sub-Riemannian geodesic flows.
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To bridge the gap between single/isolated pore systems to multi-pore systems,
such as membranes/electrodes, we studied an array of nanochannels with varying
interchannel spacing that controlled the degree of channel communication.
Instead of treating them as individual channels connected in parallel or an
assembly like a homogeneous membrane, this study resolves the pore-pore
interaction. We found that increased channel isolation leads to current
intensification whereas at high voltages electro-convective effects control the
degree of communication via suppression of the diffusion layer growth
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We present the results of sub-mm, mm (850 um, 450 um and 1250 um) and radio
(1.4 and 4.8 GHz) continuum observations of a sample of 27 K-selected Extremely
Red Objects, or EROs, (14 of which form a complete sample with K < 20 and I-K >
5) aimed at detecting dusty starbursts, deriving the fraction of UltraLuminous
Infrared Galaxies (ULIGs) in ERO samples, and constraining their redshifts
using the radio-FIR correlation. One ERO was tentatively detected at 1250 um
and two were detected at 1.4 GHz, one of which has a less secure identification
as an ERO counterpart. Limits on their redshifts and their star forming
properties are derived and discussed. We stacked the observations of the
undetected objects at 850 um, 1250 um and 4.8 GHz in order to search for
possible statistical emission from the ERO population as a whole, but no
significant detections were derived either for the whole sample or as a
function of the average NIR colours. These results strongly suggest that the
dominant population of EROs with K < 20 is not comprised of ULIGs like HR 10,
but is probably made of radio-quiet ellipticals and weaker starburst galaxies
with L < 10^{12} L_sun and SFR < 100 M_sun/yr.
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We report that low frequency (up to 200 kHz) noise spectra of magnetic tunnel
junctions with areas ~10^{-10}cm^2$ at 10 Kelvin deviate significantly from the
typical 1/f behavior found in large area junctions at room temperature. In most
cases, a Lorentzian-like shape with characteristic time between 0.1 and 10 ms
is observed, which indicates only a small number of fluctuators contribute to
the measured noise. By investigating the dependence of noise on both the
magnitude and orientation of an applied magnetic field, we find that
magnetization fluctuations in both free and reference layers are the main
sources of noise in these devices. At small fields, where the noise from the
free layer is dominant, a linear relation between the measured noise and
angular magnetoresistance susceptibility can be established.
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We construct explicit examples of elementary extremal contractions, both
birational and of fiber type, from smooth projective n-dimensional varieties,
n\geq 4, onto smooth projective varieties, arising from classical projective
geometry and defined over sufficiently small fields, not necessarily
algebraically closed.
The examples considered come from particular special homaloidal and
subhomaloidal linear systems, which usually are degenerations of general
phenomena classically investigated by Bordiga, Severi, Todd, Room, Fano, Semple
and Tyrrell and more recently by Ein and Shepherd-Barron.
The first series of examples is associated to particular codimension 2
determinantal smooth subvarieties of P^m, 3\leq m\leq 5. We get another series
of examples by considering special cubic hypersurfaces through some surfaces in
P^5, or some 3-folds in P^7 having one apparent double point. The last examples
come from an intriguing birational elementary extremal contraction in dimension
6, studied by Semple and Tyrrell and fully described in the last section.
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We characterize the absolute retracts in the category of reflexive oriented
graphs, that is, antisymmetric reflexive graphs, where morphisms between
objects preserve arcs (which may be sent to loops). Here we show, by correcting
a much earlier attempt at a proof, that a reflexive oriented graph is an
absolute retract if and only if it is indeed a retract of some (direct) product
of reflexive oriented zigzags (which are concatenations of reflexive oriented
paths). Absolute retracts are therefore necessarily acyclic. In contrast to
other categories of graphs and ordered sets, not every acyclic oriented graph
can be embedded isometrically into some absolute retract. Embedding involves
isometry with respect to the zig-zag distances forming a particular "dual
quantale", which is a complete lattice of certain sets of words over the
alphabet $\{+, -\}$, endowed with an additional monoid operation (viz.,
compound concatenation of sets of words) and an involution (interchanging $+$
and $- $ and then mirroring words). As reflexive oriented zigzags have
MacNeille-closed distances, so do their products and retracts. So, the category
of reflexive oriented graphs and its full subcategory of reflexive acyclic
graphs do not have enough injectives, as the injective objects coincide with
the absolute retracts.
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Using the ground-based V and I photometry of a sample of stars from the Groth
Strip, we obtain the first empirical calibration of the F606W and F814W Hubble
Space Telescope WFPC2 filters for 0.5<V-I<4.5. We present results in the form
of corrections that need to be applied to the two synthetic calibrations
currently in use. Both calibrations are found to require corrections to zero
points and color-terms.
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The Holstein model on a square lattice at half-filling has a well-established
finite temperature phase transition to an insulating state with long range
charge density wave (CDW) order. Because this CDW formation suppresses pairing,
a superconducting (SC) phase emerges only with doping. In this work, we study
the effects of dilution of the local phonon degrees of freedom in the Holstein
model while keeping the system at half filling. We find not only that the CDW
remains present up to a dilution fraction $f \sim 0.15$, but also that long
range pairing is stabilized with increasing $f$, resulting in a {\it
supersolid} regime centered at $f \approx 0.10$, where long range diagonal and
off-diagonal correlations coexist. Further dilution results in a purely SC
phase, and ultimately in a normal metal. Our results provide a new route to the
supersolid phase via the introduction of impurities at fixed positions which
both increase quantum fluctuations and also are immune to the competing
tendency to phase separation often observed in the doped case.
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Tunneling measurements have been carried out on heavily underdoped, slightly
overdoped and partially Ni-substituted Bi2212 single crystals by using a
break-junction technique. We find that in-plane tunneling spectra below Tc are
the combination of incoherent part from the pseudogap and coherent
quasiparticle peaks. There is a clear correlation between the magnitude of the
pseudogap and the magnitude of the superconducting gap in Bi2212. The analysis
of the data suggests that the tunneling pseudogap in Bi2212 is predominantly a
charge-density-wave gap on dynamical charge stripes. The tunneling
characteristics corresponding to the quasiparticle peaks are in excellent
agreement with theoretical predictions made for a quasi-one dimensional
topological-excitation liquid. In addition, the analysis of data measured by
different techniques shows that the phase coherence along the c-axis is
established at Tc due to spin fluctuations in local antiferromagnetic domains
of CuO2 planes.
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Depending on the type of flow the transition to turbulence can take one of
two forms, either turbulence arises from a sequence of instabilities, or from
the spatial proliferation of transiently chaotic domains, a process analogous
to directed percolation. Both scenarios are inherently continuous and hence the
transformation from ordered laminar to fully turbulent fluid motion is only
accomplished gradually with flow speed. Here we show that these established
transition types do not account for the more general setting of shear flows
subject to body forces. By attenuating spatial coupling and energy transfer,
spatio-temporal intermittency is suppressed and with forcing amplitude the
transition becomes increasingly sharp and eventually discontinuous. We argue
that the suppression of the continuous range and the approach towards a first
order, discontinuous scenario applies to a wide range of situations where in
addition to shear, flows are subject to e.g. gravitational, centrifugal or
electromagnetic forces.
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In a recent paper Lehnert & Bremer have photometrically selected a sample of
galaxies at z>4.8 from a single VLT/FORS2 pointing and spectroscopically
confirmed half of them to be at 4.8<z<5.8. To study the properties of such
galaxies further, we have photometrically selected a similar sample (V(AB)>28,
i(AB)<26.3, i(AB)-z(AB)>0) from the HST ACS images of the Chandra Deep Field
South. This selection results in a sample of 44 sources from ~150 sq. arcmin.
We find that such galaxies are often barely resolved in the ACS images, having
half-light radii of 0.1-0.3 arcsec (<2 kpc). They show no difference in spatial
clustering from sources selected by i(AB)<26.3, i(AB)-z(AB)>0, which are
generally galaxies of lower redshift. However, their distribution over the
field is not uniform and their surface density varies considerably over areas
comparable to a single 8m or HST pointing. The reliable determination of the
surface and volume densities of such galaxies requires a sky area considerably
larger than the current ACS imaging of this field. No individual z>5 candidate
was detected to a 3-sigma limit of 6 x 10^-17 erg s^-1 cm^-2 at 0.5-5 keV by
Chandra (a limiting luminosity of below 2 x 10^43 erg s^-1 at z~5.3). By
summing over all positions, we find that the mean source must be undetected at
a level at least a factor 4 times fainter than this. This rules out anything
other than a weak AGN contribution to the emission from these objects and thus
luminous AGN made little contribution to the final stages of re-ionization of
the Universe.
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This paper investigates stability analysis of flapping flight. Due to
time-varying aerodynamic forces, such systems do not display fixed points of
equilibrium. The problem is therefore approached via a limit cycle analysis
based on Floquet theory. Stability is assessed from the eigenvalues of the
Jacobian matrix associated to the limit cycle, also known as the Floquet
multipliers. We developed this framework to analyze the flapping flight
equations of motion of a bird in the longitudinal plane. Such a system is known
to be not only non-linear and time-dependent, but also driven by
state-dependent forcing aerodynamic forces. A model accounting for wing
morphing under prescribed kinematics is developed for generating realistic
state-dependent aerodynamic forces. The morphing wing geometry results from the
envelope of continuously articulated rigid bodies, modeling bones and feather
rachises, and capturing biologically relevant degrees of freedom. A sensitivity
analysis is carried out which allows studying several flight configurations in
trimmed state. Our numerical results show that in such a system one instability
mode is ubiquitous, thus suggesting the importance of sensory feedback to
achieve steady-state flapping flight in birds. The effect of wingbeat
amplitude, governed by the shoulder joint, is found to be crucial in tuning the
gait towards level flight, but marginally affects stability. In contrast, the
relative position between the wing and the center of mass is found to
significantly affect the values of Floquet multipliers, suggesting that the
distribution of pitching moment plays a very important role in flapping flight
stability.
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The adiabatic hydrodynamization framework is a promising framework within
which to describe and characterize pre-hydrodynamic attractors in a
model-independent fashion. Using this framework, we define a procedure to
identify a time-dependent change in coordinates which reveals a dynamical
reduction in the number of active degrees of freedom. Applying this procedure
to the kinetic theory of a Bjorken-expanding gas of gluons in the small angle
elastic scattering limit, we are able to intuitively explain the self-similar
evolution of the gluon distribution function long before the applicability of
hydrodynamics, as well as the loss of memory of its initial condition.
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We characterize the formulas that are avoided by every $\alpha$-free word for
some $\alpha>1$. We study the avoidability index of formulas whose fragments
are of the form $XYX$. The largest avoidability index of an avoidable
palindrome pattern is known to be at least $4$ and at most $16$. We make
progress toward the conjecture that every avoidable palindrome pattern is
$4$-avoidable.
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Anomaly detection, a.k.a. outlier detection or novelty detection, has been a
lasting yet active research area in various research communities for several
decades. There are still some unique problem complexities and challenges that
require advanced approaches. In recent years, deep learning enabled anomaly
detection, i.e., deep anomaly detection, has emerged as a critical direction.
This paper surveys the research of deep anomaly detection with a comprehensive
taxonomy, covering advancements in three high-level categories and 11
fine-grained categories of the methods. We review their key intuitions,
objective functions, underlying assumptions, advantages and disadvantages, and
discuss how they address the aforementioned challenges. We further discuss a
set of possible future opportunities and new perspectives on addressing the
challenges.
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It has been shown that entanglement distillation of Gaussian entangled states
by means of local photon subtraction can be improved by local Gaussian
transformations. Here we show that a similar effect can be expected for the
distillation of an asymmetric Gaussian entangled state that is produced by a
single squeezed beam. We show that for low initial entanglement, our largely
simplified protocol generates more entanglement than previous proposed
protocols. Furthermore, we show that the distillation scheme also works
efficiently on decohered entangled states as well as with a practical photon
subtraction setup.
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We propose a simple modification to the conventional attention mechanism
applied by Transformers: Instead of quantifying pairwise query-key similarity
with scaled dot-products, we quantify it with the logarithms of scaled
dot-products of exponentials. Our modification linearizes attention with
exponential kernel feature maps, whose corresponding feature function is
infinite dimensional. We show that our modification is expressible as a
composition of log-sums of exponentials, with a latent space of constant size,
enabling application with constant time and space complexity per token. We
implement our modification, verify that it works in practice, and conclude that
it is a promising alternative to conventional attention.
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We prove that the evolution of weight vectors in online gradient descent can
encode arbitrary polynomial-space computations, even in very simple learning
settings. Our results imply that, under weak complexity-theoretic assumptions,
it is impossible to reason efficiently about the fine-grained behavior of
online gradient descent.
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Young's archetypal double-slit experiment forms the basis for modern
diffraction techniques: the elastic scattering of waves yields an interference
pattern that captures the real-space structure. Here, we report on an inelastic
incarnation of Young's experiment and demonstrate that resonant inelastic x-ray
scattering (RIXS) measures interference patterns which reveal the symmetry and
character of electronic excited states in the same way as elastic scattering
does for the ground state. A prototypical example is provided by the
quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural
Ir dimers and strong spin-orbit coupling. The double 'slits' in this resonant
experiment are the highly localized core levels of the two Ir atoms within a
dimer. The clear double-slit-type sinusoidal interference patterns that we
observe allow us to characterize the electronic excitations, demonstrating the
power of RIXS interferometry to unravel the electronic structure of solids
containing, e.g., dimers, trimers, ladders, or other superstructures.
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Recently, Hwang et al. [Eur. Phys. J. D. 61, 785 (2011)] and Yuan et al.
[Int. J. Theo. Phys. 50, 2403 (2011)] have proposed two efficient protocols of
secure quantum communication using 3-qubit and 4-qubit symmetric W state
respectively. These two dense coding based protocols are generalized and their
efficiencies are considerably improved. Simple bounds on the qubit efficiency
of deterministic secure quantum communication (DSQC) and quantum secure direct
communication (QSDC) protocols are obtained and it is shown that dense coding
is not essential for designing of maximally efficient DSQC and QSDC protocols.
This fact is used to design maximally efficient protocols of DSQC and QSDC
using 3-qubit and 4-qubit W states.
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The photon production arising due to time variation of the medium has been
considered. The Hamilton formalism for photons in time-variable medium (plasma)
has been developed with application to inclusive photon production. The results
have been used for calculation of the photon production in the course of
transition from quark-gluon phase to hadronic phase in relativistic heavy ion
collisions. The relative strength of the effect as well as specific two- photon
correlations have been evaluated. It has been demonstrated that the opposite
side two-photon correlations are indicative of the sharp transition from the
quark-gluon phase to hadrons.
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The large aperture and sensitive optical and near infrared imager
spectrographs will enable an ELT system to observe some supernovae at large
distances, deep into cosmological history when supernovae first began to occur.
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We used ALMA to observe the star-forming region GGD27 at 1.14 mm with an
unprecedented angular resolution, 40 mas (56 au) and sensitivity (0.002 Msun).
We detected a cluster of 25 continuum sources, most of which are likely tracing
disks around Class 0/I protostars. Excluding the two most massive objects,
disks masses are in the range 0.003-0.05 Msun. The analysis of the cluster
properties indicates that GGD27 displays moderate subclustering. This result
combined with the dynamical timescale of the radio jet (10000 years) suggests
the youthfulness of the cluster. The lack of disk mass segregation signatures
may support this too. We found a clear paucity of disks with Rdisk >100 au. The
median value of the radius is 34 au, smaller than the median of 92 au for
Taurus but comparable to the value found in Ophiuchus and in the Orion Nebula
Cluster. In GGD27 there is no evidence of a distance-dependent disk mass
distribution (i. e., disk mass depletion due to external photoevaporation),
most likely due to the cluster youth. There is a clear deficit of disks for
distances <0.02 pc. Only for distances >0.04 pc stars can form larger and more
massive disks, suggesting that dynamical interactions far from the cluster
center are weaker, although the small disks found could be the result of disk
truncation. This work demonstrates the potential to characterize disks from
low-mass YSOs in distant and massive (still deeply embedded) clustered
environments.
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This document presents the material of two lectures on statistical physics
and neural representations, delivered by one of us (R.M.) at the Fundamental
Problems in Statistical Physics XIV summer school in July 2017. In a first
part, we consider the neural representations of space (maps) in the
hippocampus. We introduce an extension of the Hopfield model, able to store
multiple spatial maps as continuous, finite-dimensional attractors. The phase
diagram and dynamical properties of the model are analyzed. We then show how
spatial representations can be dynamically decoded using an effective Ising
model capturing the correlation structure in the neural data, and compare
applications to data obtained from hippocampal multi-electrode recordings and
by (sub)sampling our attractor model. In a second part, we focus on the problem
of learning data representations in machine learning, in particular with
artificial neural networks. We start by introducing data representations
through some illustrations. We then analyze two important algorithms, Principal
Component Analysis and Restricted Boltzmann Machines, with tools from
statistical physics.
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It was as early as the 1980s that A V Gurevich and his group proposed a
theory to explain the magnetosphere of radio pulsars and the mechanism by which
they produce coherent radio emission. The theory has been sharply criticized
and is currently rarely mentioned when discussing the observational properties
of radio pulsars, even though all the criticisms were in their time disproven
in a most thorough and detailed manner. Recent results show even more
conclusively that the theory has no internal inconsistencies. New observational
data also demonstrate the validity of the basic conclusions of the theory.
Based on the latest results on the effects of wave propagation in the
magnetosphere of a neuron star, we show that the developed theory does indeed
allow quantitative predictions of the evolution of neutron stars and the
properties of the observed radio emission.
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We study the possibility of baryogenesis in the case of supersymmetry
breaking with large mixing between the right-handed scalar charm and
right-handed scalar top or right-handed scalar up and right-handed scalar top
squarks resulting in one light right-handed up-type squark mass eigenstate. We
argue that in this case the electroweak phase transition will be first order,
and that large phases already present in the quark mass matrices can generate a
baryon asymmetry of the correct magnitude without introducing any new phases
specifically for this purpose. We study in detail a particular ansatz for
supersymmetry breaking and CP violation where there is only one CP violating
phase in the theory: in the up-type quark mass matrix. We study the constraints
placed on this model by baryogenesis and flavor physics. This scenario has
robust implications for low energy flavor phsyics including D-Dbar mixing and
an electric dipole moment for the neutron that are close to the experimental
bounds, and CP violation in the B-Bbar system that is different from that in
the Standard Model.
|
To make arbitrarily accurate quantum computation possible, practical
realization of quantum computers will require suppressing noise in quantum
memory and gate operations to make it below a threshold value. A scheme based
on realistic quantum computer models is described for suppressing noise in
quantum computation without the cost of stringent quantum computing resources.
|
In this article, we investigate the problem of engineering synchronization in
non-Markovian quantum systems. First, a time-convoluted linear quantum
stochastic differential equation is derived which describes the Heisenberg
evolution of a localized quantum system driven by multiple colored noise
inputs. Then, we define quantum expectation synchronization in an augmented
system consisting of two subsystems. We prove that, for two homogenous
subsystems, synchronization can always be synthesized without designing direct
Hamiltonian coupling given that the degree of non-Markovianity is below a
certain threshold. System parameters are explicitly designed to achieve quantum
synchronization. Also, a numerical example is presented to illustrate our
results.
|
We prove a new class of inequalities, yielding bounds for the normal
approximation in the Wasserstein and the Kolmogorov distance of functionals of
a general Poisson process (Poisson random measure). Our approach is based on an
iteration of the classical Poincar\'e inequality, as well as on the use of
Malliavin operators, of Stein's method, and of an (integrated) Mehler's
formula, providing a representation of the Ornstein-Uhlenbeck semigroup in
terms of thinned Poisson processes. Our estimates only involve first and second
order differential operators, and have consequently a clear geometric
interpretation. In particular we will show that our results are perfectly
tailored to deal with the normal approximation of geometric functionals
displaying a weak form of stabilization, and with non-linear functionals of
Poisson shot-noise processes. We discuss two examples of stabilizing
functionals in great detail: (i) the edge length of the $k$-nearest neighbour
graph, (ii) intrinsic volumes of $k$-faces of Voronoi tessellations. In all
these examples we obtain rates of convergence (in the Kolmogorov and the
Wasserstein distance) that one can reasonably conjecture to be optimal, thus
significantly improving previous findings in the literature. As a necessary
step in our analysis, we also derive new lower bounds for variances of Poisson
functionals.
|
We observed total and polarized radio continuum emission from the spiral
galaxy M 101 at 6.2 cm and 11.1 cm wavelengths with the Effelsberg telescope.
We use these data to study various emission components in M 101 and properties
of the magnetic field. Separation of thermal and non-thermal emission shows
that the thermal emission is closely correlated with the spiral arms, while the
non-thermal emission is more smoothly distributed indicating diffusion of
cosmic ray electrons away from their places of origin. The radial distribution
of both emissions has a break near R=16 kpc, where it steepens to an
exponential scale length of about 5 kpc, which is about 2.5 times smaller than
at R<16 kpc. The distribution of the polarized emission has a broad maximum
near R=12 kpc and beyond R=16 kpc also decreases with about 5 kpc scalelength.
It seems that near R=16 kpc a major change in the structure of M 101 takes
place, which also affects the distributions of the strength of the random and
ordered magnetic field. Beyond R=16 kpc the radial scale length of both fields
is about 20 kpc, which implies that they decrease to about 0.3 \mu G at R=70
kpc, which is the largest optical extent. The equipartition strength of the
total field ranges from nearly 10 \mu G at R<2 kpc to 4 \mu G at R=22-24 kpc.
As the random field dominates in M 101, wavelength-independent polarization is
the main polarization mechanism. We show that energetic events causing HI
shells of mean diameter <625 pc could partly be responsible for this. At radii
<24 kpc, the random magnetic field depends on the star formation rate per area
with a power-law exponent of 0.28+-0.02. The ordered magnetic field is
generally aligned with the spiral arms with pitch angles that are about 8{\deg}
larger than those of HI filaments.
|
Restless multi-armed bandits (RMAB) have been widely used to model sequential
decision making problems with constraints. The decision maker (DM) aims to
maximize the expected total reward over an infinite horizon under an
"instantaneous activation constraint" that at most B arms can be activated at
any decision epoch, where the state of each arm evolves stochastically
according to a Markov decision process (MDP). However, this basic model fails
to provide any fairness guarantee among arms. In this paper, we introduce
RMAB-F, a new RMAB model with "long-term fairness constraints", where the
objective now is to maximize the long term reward while a minimum long-term
activation fraction for each arm must be satisfied. For the online RMAB-F
setting (i.e., the underlying MDPs associated with each arm are unknown to the
DM), we develop a novel reinforcement learning (RL) algorithm named Fair-UCRL.
We prove that Fair-UCRL ensures probabilistic sublinear bounds on both the
reward regret and the fairness violation regret. Compared with off-the-shelf RL
methods, our Fair-UCRL is much more computationally efficient since it contains
a novel exploitation that leverages a low-complexity index policy for making
decisions. Experimental results further demonstrate the effectiveness of our
Fair-UCRL.
|
As more Fast Radio Bursts (FRBs) are being localised, we are learning that
some fraction have persistent radio sources (PRSs). Such a discovery motivates
an improvement in our understanding of the nature of those counterparts, the
relation to the bursts themselves and why only some FRBs have PRSs. We report
on observations made of FRB 20121102A with the MeerKAT radio telescope. Across
five epochs, we detect the PRS associated with FRB 20121102A. Our observations
are split into a cluster of four epochs (MJD 58732 - 58764) and a separate
single epoch about 1000days later. The measured flux density is constant across
the first four observations but then decays by more than one-third in the final
observation. Our observations on MJD 58736 coincided with the detections of 11
bursts from FRB 20121102A by the MeerTRAP backend, seven of which we detected
in the image plane. We discuss the importance of image plane detections when
considering the commensal transient searches being performed with MeerKAT and
other radio facilities. We find that MeerKAT is so sensitive that within a
two-second image, we can detect any FRB with a flux density above 2.4mJy at
1.3GHz and so could localise every FRB that has been detected by CHIME to date.
|
We discuss Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT) and
possible fitting strategies to Lattice QCD data at next-to-next-to-leading
order (NNLO) in the mesonic sector. We also present a complete calculation of
the masses of the charged pseudoscalar mesons, in the supersymmetric
formulation of PQ$\chi$PT. Explicit analytical results are given for up to
three nondegenerate sea quark flavors, along with the previously unpublished
expression for the pseudoscalar meson decay constant for three nondegenerate
sea quark flavors. The numerical analysis in this paper demonstrates that the
corrections at NNLO are sizable, as expected from earlier work.
|
We present polarization resolved Raman scattering study of surface vibration
modes in the topological insulator Bi$_2$Se$_3$ single crystal and thick films.
Besides the four Raman active bulk phonons, we observed four additional modes
with much weaker intensity and slightly lower energy than the bulk
counterparts. Using symmetry analysis, we assigned these additional modes to
out-of-plane surface phonons. Comparing with first principle calculations, we
conclude that the appearance of these modes is due to $c$-axis lattice
distortion and van der Waals gap expansion near the crystal surface. Two of the
surface modes at 60 and 173 cm$^{-1}$ are associated with Raman active $A_{1g}$
bulk phonon modes, the other two at 136 and 158 cm$^{-1}$ are associated with
infrared active bulk phonons with $A_{2u}$ symmetry. The latter become Raman
allowed due to reduction of crystalline symmetry from $D_{3d}$ in the bulk to
$C_{3v}$ on the crystal surface. In particular, the 158 cm$^{-1}$ surface
phonon mode shows a Fano lineshape under resonant excitation, suggesting
interference in the presence of electron-phonon coupling of the surface
excitations.
|
To promote the benefits of the Internet of Things (IoT) in smart communities
and smart cities, a real-time data marketplace middleware platform, called the
Intelligent IoT Integrator (I3), has been recently proposed. While facilitating
the easy exchanges of real-time IoT data streams between device owners and
third-party applications through the marketplace, I3 is presently a monolithic,
centralized platform for a single community. Although the service oriented
architecture (SOA) has been widely adopted in the IoT and cyber-physical
systems (CPS), it is difficult for a monolithic architecture to provide
scalable, inter-operable and extensible services for large numbers of
distributed IoT devices and different application vendors. Traditional security
solutions rely on a centralized authority, which can be a performance
bottleneck or susceptible to a single point of failure. Inspired by
containerized microservices and blockchain technology, this paper proposed a
BLockchain-ENabled Secure Microservices for Decentralized Data Marketplaces
(BlendSM-DDM). Within a permissioned blockchain network, a microservices based
security mechanism is introduced to secure data exchange and payment among
participants in the marketplace. BlendSM-DDM is able to offer a decentralized,
scalable and auditable data exchanges for the data marketplace.
|
Various coarse-grained models have been proposed to study the spreading
dynamics in the network. A microscopic theory is needed to connect the
spreading dynamics with the individual behaviors. In this letter, we unify the
description of different spreading dynamics on complex networks by decomposing
the microscopic dynamics into two basic processes, the aging process and the
contact process. A microscopic dynamical equation is derived to describe the
dynamics of individual nodes on the network. The hierarchy of a duration
coarse-grained (DCG) approach is obtained to study duration-dependent
processes, where the transition rates depend on the duration of an individual
node on a state. Applied to the epidemic spreading, such formalism is feasible
to reproduce different epidemic models, e.g., the
susceptible-infected-recovered and the susceptible-infected-susceptible models,
and to associate with the corresponding macroscopic spreading parameters with
the microscopic transition rate. The DCG approach enables us to obtain the
steady state of the general SIS model with arbitrary duration-dependent
recovery and infection rates. The current hierarchical formalism can also be
used to describe the spreading of information and public opinions, or to model
a reliability theory in networks.
|
A general formalism is developed for constructing modified Hamiltonian
dynamical systems which preserve a canonical equilibrium distribution by adding
a time evolution equation for a single additional thermostat variable. When
such systems are ergodic, canonical ensemble averages can be computed as
dynamical time averages over a single trajectory. Systems of this type were
unknown until their recent discovery by Hoover and colleagues. The present
formalism should facilitate the discovery, construction, and classification of
other such systems by encompassing a wide class of them within a single unified
framework. This formalism includes both canonical and generalized Hamiltonian
systems in a state space of arbitrary dimensionality (either even or odd), and
therefore encompasses both few- and many-particle systems. Particular attention
is devoted to the physical motivation and interpretation of the formalism,
which largely determine its structure. An analogy to stochastic thermostats and
fluctuation-dissipation theorems is briefly discussed.
|
We extend the calculations of holographic entanglement entropy in AdS(4) for
entangling curves with singular non-smooth points that generalize cusps. Our
calculations are based on minimal surfaces that correspond to elliptic
solutions of the corresponding Pohlmeyer reduced system. For these minimal
surfaces, the entangling curve contains singular points that are not cusps, but
the joint point of two logarithmic spirals one being the rotation of the other
by a given angle. It turns out that, similarly to the case of cusps, the
entanglement entropy contains a logarithmic term, which is absent when the
entangling curve is smooth. The latter depends solely on the geometry of the
singular points and not on the global characteristics of the entangling curve.
The results suggest that a careful definition of the geometric characteristic
of such a singular point that determines the logarithmic term is required,
which does not always coincide with the definition of the angle. Furthermore,
it is shown that the smoothness of the dependence of the logarithmic terms on
this characteristic is not in general guaranteed, depending on the uniqueness
of the minimal surface for the given entangling curve.
|
Although the sensitivity of THz spectra to the crystal form of the sample
being analysed makes it an ideal tool for differentiating polymorphic forms of
crystalline materials, the lack of adequate knowledge about the THz response to
various materials often results in misinterpretations. The inclusion of
structural information in THz spectral databases of crystalline substances is
therefore suggested.
|
Seismic data noise processing is an important part of seismic exploration
data processing, and the effect of noise elimination is directly related to the
follow-up processing of data. In response to this problem, many authors have
proposed methods based on rank reduction, sparse transformation, domain
transformation, and deep learning. However, such methods are often not ideal
when faced with strong noise. Therefore, we propose to use diffusion model
theory for noise removal. The Bayesian equation is used to reverse the noise
addition process, and the noise reduction work is divided into multiple steps
to effectively deal with high-noise situations. Furthermore, we propose to
evaluate the noise level of blind Gaussian seismic data using principal
component analysis to determine the number of steps for noise reduction
processing of seismic data. We train the model on synthetic data and validate
it on field data through transfer learning. Experiments show that our proposed
method can identify most of the noise with less signal leakage. This has
positive significance for high-precision seismic exploration and future seismic
data signal processing research.
|
For the minimal O(N) sigma model, which is defined to be generated by the
O(N) scalar auxiliary field alone, all n-point functions, till order 1/N
included, can be expressed by elementary functions without logarithms.
Consequently, the conformal composite fields of m auxiliary fields possess at
the same order such dimensions, which are m times the dimension of the
auxiliary field plus the order of differentiation.
|
The presence of substructure in galaxy groups and clusters is believed to be
a sign of recent galaxy accretion and can be used not only to probe the
assembly history of these structures, but also the evolution of their member
galaxies. Using the Dressler-Shectman (DS) Test, we study substructure in a
sample of intermediate redshift (z ~ 0.4) galaxy groups from the Group
Environment and Evolution Collaboration (GEEC) group catalog. We find that 4 of
the 15 rich GEEC groups, with an average velocity dispersion of ~525 km s-1,
are identified as having significant substructure. The identified regions of
localized substructure lie on the group outskirts and in some cases appear to
be infalling. In a comparison of galaxy properties for the members of groups
with and without substructure, we find that the groups with substructure have a
significantly higher fraction of blue and star-forming galaxies and a parent
colour distribution that resembles that of the field population rather than the
overall group population. In addition, we observe correlations between the
detection of substructure and other dynamical measures, such as velocity
distributions and velocity dispersion profiles. Based on this analysis, we
conclude that some galaxy groups contain significant substructure and that
these groups have properties and galaxy populations that differ from groups
with no detected substructure. These results indicate that the substructure
galaxies, which lie preferentially on the group outskirts and could be
infalling, do not exhibit signs of environmental effects, since little or no
star-formation quenching is observed in these systems.
|
We observe two-fold shell filling in the spectra of closed one-dimensional
quantum dots formed in single-wall carbon nanotubes. Its signatures include a
bimodal distribution of addition energies, correlations in the excitation
spectra for different electron number, and alternation of the spins of the
added electrons. This provides a contrast with quantum dots in higher
dimensions, where such spin pairing is absent. We also see indications of an
additional fourfold periodicity indicative of K-K' subband shells. Our results
suggest that the absence of shell filling in most isolated nanotube dots
results from disorder or nonuniformity.
|
Collective behavior is studied in globally coupled maps with distributed
nonlinearity. It is shown that the heterogeneity enhances regularity in the
collective dynamics. Low-dimensional quasiperiodic motion is often found for
the mean-field, even if each element shows chaotic dynamics. The mechanism of
this order is due to the formation of an internal bifurcation structure, and
the self-consistent dynamics between the structures and the mean-field.
Keywords: Globally Coupled Map with heterogeneity, Collective behavior
|
We study tadpole potentials of non-supersymmetric strings, resorting to a
first-order formalism known in the literature as fake supersymmetry. We present
a detailed analysis for vacua with only gravity and the dilaton, displaying the
obstructions that forbid the simplest inclusion of form fluxes. Our focus is on
codimension-one vacua, for which we propose a definition of energy that might
be suitable for stability arguments. Our findings point to the central role of
boundary conditions when supersymmetry is absent or broken.
|
With the rise in popularity of public social media and micro-blogging
services, most notably Twitter, the people have found a venue to hear and be
heard by their peers without an intermediary. As a consequence, and aided by
the public nature of Twitter, political scientists now potentially have the
means to analyse and understand the narratives that organically form, spread
and decline among the public in a political campaign. However, the volume and
diversity of the conversation on Twitter, combined with its noisy and
idiosyncratic nature, make this a hard task. Thus, advanced data mining and
language processing techniques are required to process and analyse the data. In
this paper, we present and evaluate a technical framework, based on recent
advances in deep neural networks, for identifying and analysing
election-related conversation on Twitter on a continuous, longitudinal basis.
Our models can detect election-related tweets with an F-score of 0.92 and can
categorize these tweets into 22 topics with an F-score of 0.90.
|
Motivated by the fact that the origin of tiny Dirac neutrino masses via the
standard model Higgs field and non-thermal dark matter populating the Universe
via freeze-in mechanism require tiny dimensionless couplings of similar order
of magnitudes $(\sim 10^{-12})$, we propose a framework that can dynamically
generate such couplings in a unified manner. Adopting a flavour symmetric
approach based on $A_4$ group, we construct a model where Dirac neutrino
coupling to the standard model Higgs and dark matter coupling to its mother
particle occur at dimension six level involving the same flavon fields, thereby
generating the effective Yukawa coupling of same order of magnitudes. The
mother particle for dark matter, a complex scalar singlet, gets thermally
produced in the early Universe through Higgs portal couplings followed by its
thermal freeze-out and then decay into the dark matter candidates giving rise
to the freeze-in dark matter scenario. Some parts of the Higgs portal couplings
of the mother particle can also be excluded by collider constraints on
invisible decay rate of the standard model like Higgs boson. We show that the
correct neutrino oscillation data can be successfully produced in the model
which predicts normal hierarchical neutrino mass. The model also predicts the
atmospheric angle to be in the lower octant if the Dirac CP phase lies close to
the presently preferred maximal value.
|
Modern high-throughput sequencing assays efficiently capture not only gene
expression and different levels of gene regulation but also a multitude of
genome variants. Focused analysis of alternative alleles of variable sites at
homologous chromosomes of the human genome reveals allele-specific gene
expression and allele-specific gene regulation by assessing allelic imbalance
of read counts at individual sites. Here we formally describe an advanced
statistical framework for detecting the allelic imbalance in allelic read
counts at single-nucleotide variants detected in diverse omics studies
(ChIP-Seq, ATAC-Seq, DNase-Seq, CAGE-Seq, and others). MIXALIME accounts for
copy-number variants and aneuploidy, reference read mapping bias, and provides
several scoring models to balance between sensitivity and specificity when
scoring data with varying levels of experimental noise-caused overdispersion.
|
We here present a new version of the publicly available general relativistic
magnetohydrodynamic (GRMHD) code $\texttt{Spritz}$, which now includes an
approximate neutrino leakage scheme able to handle neutrino cooling and
heating. The leakage scheme is based on the publicly available
$\texttt{ZelmaniLeak}$ code, with a few modifications in order to properly work
with $\texttt{Spritz}$. We discuss the involved equations, physical
assumptions, and implemented numerical methods, along with a large battery of
general relativistic tests performed with and without magnetic fields. Our
tests demonstrate the correct implementation of the neutrino leakage scheme,
paving the way for further improvements of our neutrino treatment and the first
application to magnetized binary neutron star mergers. We also discuss the
implementation in the $\texttt{Spritz}$ code of high-order methods for a more
accurate evolution of hydrodynamical quantities.
|
We have observed the bright, magnetically active multiple star AB Doradus in
a multiwavelength campaign centring around two large facility allocations in
November 2006 and January, 2007. Our observations have covered at least three
large flares. These flares were observed to produce significant hardening of
the X-ray spectra during their very initial stages. We monitored flare-related
effects using the Suzaku X-ray satellite and the Australia Telescope Compact
Array at 3.6 and 6 cm. Observations at 11 and 21 cm were also included, but
they were compromised by interference. From our multiwavelength coverage we
find that the observed effects can be mainly associated with a large active
region near longitude zero. The second major X-ray and microwave flare of Jan
8, 2007 was observed with a favourable geometry that allowed its initial
high-energy impulsive phase to be observed in the higher frequency range of
Suzaku's XIS detectors. The fractional circular polarisation was measured for
the complete runs, for 25 min integrations and, at 4.80 GHz, for 5 min
integrations. Most of the full data sets showed circular polarisation fractions
from AB Dor B that were significant at greater than the 3 sigma level. In
several of the 5 min integrations at 4.80 and 8.64 GHz this fraction reached a
significance level between 3 and 9 sigma. Lack of angular resolution prevented
identification of these high V/I values with one or other of the two low-mass
red-dwarf components of AB Dor B.
|
We study the gravitomagnetism in the TeVeS theory. We compute the
gravitomagnetic field that a slow-moving mass distribution produces in its
Newtonian regime. We report that the consistency between the TeVeS
gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads
to a relation between the vector and scalar coupling constants of the theory.
We observe that requiring consistency between the near horizon geometry of a
black hole in TeVeS and the image of the black hole taken Event Horizon
Telescope leads to another relation between the coupling constants of the TeVeS
theory and enable us to identify the coupling constants of the theory.
|
Adaptable, low-cost, coils designed by carefully selecting the arrangements
and geometries of simple primitive units are used to generate magnetic fields
for diverse applications. These extend from magnetic resonance and fundamental
physics experiments to active shielding of quantum devices including
magnetometers, interferometers, clocks, and computers. However, finding optimal
arrangements and geometries of multiple primitive structures is time-intensive
and it is challenging to account for additional constraints, e.g. optical
access, during the design process. Here, we demonstrate a general method to
find these optimal arrangements. We encode specific symmetries into sets of
loops, saddles, and cylindrical ellipses and then solve exactly for the
magnetic field harmonics generated by each set. By combining these analytic
solutions using computer algebra, we can use numerical techniques to
efficiently map the landscape of parameters and geometries which the coils must
satisfy. Sets of solutions may be found which generate desired target fields
accurately while accounting for complexity and size restrictions. We
demonstrate this approach by employing simple configurations of loops, saddles,
and cylindrical ellipses to design target linear field gradients and compare
their performance with designs obtained using conventional methods. A case
study is presented where three optimized arrangements of loops, designed to
generate a uniform axial field, a linear axial field gradient, and a quadratic
axial field gradient, respectively, are hand-wound around a low-cost,
3D-printed coil former. These coils are used to null the background in a
typical laboratory environment, reducing the magnitude of the axial field along
the central half of the former's axis from $\left(7.8\pm0.3\right)$ $\mu$T
(mean $\pm$ st. dev.) to $\left(0.11\pm0.04\right)$ $\mu$T.
|
The N-point amplitudes for the Type II and Heterotic superstrings at two-loop
order and for $N \leq 4$ massless NS bosons are evaluated explicitly from first
principles, using the method of projection onto super period matrices
introduced and developed in the first five papers of this series. The
gauge-dependent corrections to the vertex operators, identified in paper V, are
carefully taken into account, and the crucial counterterms which are Dolbeault
exact in one insertion point and de Rham closed in the remaining points are
constructed explicitly. This procedure maintains gauge slice independence at
every stage of the evaluation.
Analysis of the resulting amplitudes demonstrates, from first principles,
that for $N\leq 3$, no two-loop corrections occur, while for N=4, no two-loop
corrections to the low energy effective action occur for $R^4$ terms in the
Type II superstrings, and for $F^4$, $F^2F^2$, $F^2R^2$, and $R^4$ terms in the
Heterotic strings.
|
Most governments employ a set of quasi-standard measures to fight COVID-19
including wearing masks, social distancing, virus testing, contact tracing, and
vaccination. However, combining these measures into an efficient holistic
pandemic response instrument is even more involved than anticipated. We argue
that some non-trivial factors behind the varying effectiveness of these
measures are selfish decision making and the differing national implementations
of the response mechanism. In this paper, through simple games, we show the
effect of individual incentives on the decisions made with respect to mask
wearing, social distancing and vaccination, and how these may result in
sub-optimal outcomes. We also demonstrate the responsibility of national
authorities in designing these games properly regarding data transparency, the
chosen policies and their influence on the preferred outcome. We promote a
mechanism design approach: it is in the best interest of every government to
carefully balance social good and response costs when implementing their
respective pandemic response mechanism; moreover, there is no one-size-fits-all
solution when designing an effective solution.
|
It is generally assumed in the thermoelectric community that the lattice
thermal conductivity of a given material is independent of the electronic
properties. This perspective is however questionable since the electron-phonon
coupling could have certain effects on both the carrier and phonon transport,
which in turn will affect the thermoelectric properties. Using SiGe compound as
a prototypical example, we give an accurate prediction of the carrier
relaxation time by considering scattering from all the phonon modes, as opposed
to the simple deformation potential theory. It is found that the carrier
relaxation time does not change much with the concentration, which is however
not the case for the phonon transport where the lattice thermal conductivity
can be significantly reduced by electron-phonon coupling at higher carrier
concentration. As a consequence, the figure-of-merit of SiGe compound is
obviously enhanced at optimized carrier concentration, and becomes more
pronounced at elevated temperature.
|
We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an
ensemble of fermionic walkers on a graph interacting with a structured infinite
reservoir of fermions $\mathcal{E}$ through an exchange of particles in
preferred states. We describe the asymptotic state of $\mathcal{S}$ in terms
the initial state of $\mathcal{E}$, with especially simple formulae in the
limit of small coupling strength. We also study the particle fluxes into the
different parts of the reservoir.
|
We calculate the equivariant instanton Floer homology, in the sense of Miller
Eismeier, for the trivial $SO(3)$-bundle over the binary polyhedral spaces with
coefficients in a PID $R$ for which $2\in R$ is invertible. Along the way we
modify a part of the algebraic construction needed to define the equivariant
instanton Floer groups.
|
We present a highly effective algorithmic approach for generating
$\varepsilon$-differentially private synthetic data in a bounded metric space
with near-optimal utility guarantees under the 1-Wasserstein distance. In
particular, for a dataset $X$ in the hypercube $[0,1]^d$, our algorithm
generates synthetic dataset $Y$ such that the expected 1-Wasserstein distance
between the empirical measure of $X$ and $Y$ is $O((\varepsilon n)^{-1/d})$ for
$d\geq 2$, and is $O(\log^2(\varepsilon n)(\varepsilon n)^{-1})$ for $d=1$. The
accuracy guarantee is optimal up to a constant factor for $d\geq 2$, and up to
a logarithmic factor for $d=1$. Our algorithm has a fast running time of
$O(\varepsilon dn)$ for all $d\geq 1$ and demonstrates improved accuracy
compared to the method in (Boedihardjo et al., 2022) for $d\geq 2$.
|
Noise sequences of infinite matrices associated with covariant phase and box
localization observables are defined and determined. The canonical observables
are characterized within the relevant classes of observables as those with
asymptotically minimal or minimal noise, i.e., the noise tending to 0 or having
the value 0.
|
We examine three equivalent constructions of a censored symmetric purely
discontinuous L\'evy process on an open set $D$; via the corresponding
Dirichlet form, through the Feynman-Kac transform of the L\'evy process killed
outside of $D$ and from the same killed process by the Ikeda-Nagasawa-Watanabe
piecing together procedure. By applying the trace theorem on $n$-sets for
Besov-type spaces of generalized smoothness associated with complete Bernstein
functions satisfying certain scaling conditions, we analyze the boundary
behaviour of the corresponding censored L\'evy process and determine conditions
under which the process approaches the boundary $\partial D$ in finite time.
Furthermore, we prove a stronger version of the 3G inequality and its
generalized version for Green functions of purely discontinuous L\'evy
processes on $\kappa$-fat open sets. Using this result, we obtain the scale
invariant Harnack inequality for the corresponding censored process.
|
We study optical Bloch oscillations in the one- and two-dimensional arrays of
helical waveguides with transverse refractive index gradient. Longitudinal
rotation of waveguides may lead to notable variations of the width of the band
of quasi-energies and even its complete collapse for certain radii of the
helix. This drastically affects the amplitude and direction of Bloch
oscillations. Thus, they can be completely arrested for certain helix radii or
their direction can be reversed. If the array of helical waveguides is
truncated and near-surface waveguide is excited, helix radius determines
whether periodic Bloch oscillations persist or replaced by the irregular
near-surface oscillations.
|
The purpose of this work is to describe the (category of) Higgs bundles on a
complex scheme X having a given cameral cover X~. We show that this category is
a T_{X~}-gerbe, where T_{X~} is a certain sheaf of abelian groups on X, and we
describe the class of this gerbe precisely. In particular, it follows that the
set of isomorphism classes of Higgs bundles with a fixed cameral cover X~ is a
torsor over the group H^1(X, T_{X~}), which itself parametrizes T_{X~}-torsors
on X. This underlying group can be described as a generalized Prym variety,
whose connected component is either an abelian variety or a degeneration
thereof.
|
We study a classical integrable (Neumann) model describing the motion of a
particle on the sphere, subject to harmonic forces. We tackle the problem in
the infinite dimensional limit by introducing a soft version in which the
spherical constraint is imposed only on average over initial conditions. We
show that the Generalized Gibbs Ensemble captures the long-time averages of the
soft model. We reveal the full dynamic phase diagram with extended,
quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The
scaling properties of the fluctuations allow us to establish in which cases the
strict and soft spherical constraints are equivalent, confirming the validity
of the GGE hypothesis for the Neumann model on a large portion of the dynamic
phase diagram.
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We have tuned in situ the proximity effect in a single graphene layer coupled
to two Pt/Ta superconducting electrodes. An annealing current through the
device changed the transmission coefficient of the electrode/graphene
interface, increasing the probability of multiple Andreev reflections. Repeated
annealing steps improved the contact sufficiently for a Josephson current to be
induced in graphene.
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We consider the contact process on a random graph with fixed degree
distribution given by a power law. We follow the work of Chatterjee and
Durrett, who showed that for arbitrarily small infection parameter $\lambda$,
the survival time of the process is larger than a stretched exponential
function of the number of vertices, $n$. We obtain sharp bounds for the typical
density of infected sites in the graph, as $\lambda$ is kept fixed and $n$
tends to infinity. We exhibit three different regimes for this density,
depending on the tail of the degree law.
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The main objective of this dissertation is to present an adaptation of some
finite volume methods used in the resolution of problems arising in
sedimentation processes of flocculated suspensions (or sedimentation with
compression).
This adaptation is based on the utilization of multiresolution techniques,
originally designed to reduce the computational cost incurred in solving using
high resolution schemes in the numerical solution of hyperbolic systems of
conservation laws.
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In recent years, physical informed neural networks (PINNs) have been shown to
be a powerful tool for solving PDEs empirically. However, numerical analysis of
PINNs is still missing. In this paper, we prove the convergence rate to PINNs
for the second order elliptic equations with Dirichlet boundary condition, by
establishing the upper bounds on the number of training samples, depth and
width of the deep neural networks to achieve desired accuracy. The error of
PINNs is decomposed into approximation error and statistical error, where the
approximation error is given in $C^2$ norm with $\mathrm{ReLU}^{3}$ networks
(deep network with activations function $\max\{0,x^3\}$) and the statistical
error is estimated by Rademacher complexity. We derive the bound on the
Rademacher complexity of the non-Lipschitz composition of gradient norm with
$\mathrm{ReLU}^{3}$ network, which is of immense independent interest.
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Spatially extended systems, such as channel or pipe flows, are often
equivariant under continuous symmetry transformations, with each state of the
flow having an infinite number of equivalent solutions obtained from it by a
translation or a rotation. This multitude of equivalent solutions tends to
obscure the dynamics of turbulence. Here we describe the `first Fourier mode
slice', a very simple, easy to implement reduction of SO(2) symmetry. While the
method exhibits rapid variations in phase velocity whenever the magnitude of
the first Fourier mode is nearly vanishing, these near singularities can be
regularized by a time-scaling transformation. We show that after application of
the method, hitherto unseen global structures, for example Kuramoto-Sivashinsky
relative periodic orbits and unstable manifolds of travelling waves, are
uncovered.
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Empirical risk minimization frequently employs convex surrogates to
underlying discrete loss functions in order to achieve computational
tractability during optimization. However, classical convex surrogates can only
tightly bound modular loss functions, sub-modular functions or supermodular
functions separately while maintaining polynomial time computation. In this
work, a novel generic convex surrogate for general non-modular loss functions
is introduced, which provides for the first time a tractable solution for loss
functions that are neither super-modular nor submodular. This convex surro-gate
is based on a submodular-supermodular decomposition for which the existence and
uniqueness is proven in this paper. It takes the sum of two convex surrogates
that separately bound the supermodular component and the submodular component
using slack-rescaling and the Lov{\'a}sz hinge, respectively. It is further
proven that this surrogate is convex , piecewise linear, an extension of the
loss function, and for which subgradient computation is polynomial time.
Empirical results are reported on a non-submodular loss based on the
S{{\o}}rensen-Dice difference function, and a real-world face track dataset
with tens of thousands of frames, demonstrating the improved performance,
efficiency, and scalabil-ity of the novel convex surrogate.
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We present evidence for a spatially-dependent systematic error in the first
data release of ${\it Gaia}$ parallaxes based on comparisons to asteroseismic
parallaxes in the ${\it Kepler}$ field, and present a parametrized model of the
angular dependence of these systematics. We report an error of
$0.059^{+0.004}_{-0.004}$mas on scales of 0.3deg, which decreases for larger
scales to become $0.011^{+0.006}_{-0.004}$mas at 8deg. This is consistent with
the $\sim2\%$ zeropoint offset for the whole sample discussed by Huber et al.,
and is compatible with the effect predicted by the ${\it Gaia}$ team. Our
results are robust to dust prescriptions and choices in temperature scales used
to calculate asteroseismic parallaxes. We also do not find evidence for
significant differences in the signal when using red clump versus red giant
stars. Our approach allows us to quantify and map the correlations in an
astrophysically interesting field, resulting in a parametrized model of the
spatial systematics that can be used to construct a covariance matrix for any
work that relies upon TGAS parallaxes.
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We develop a continuum dislocation description of twist and stretch moire
superlattices in 2D material bilayers. The continuum formulation is based on
the topological constraints introduced by the periodic dislocation network
associated with the moire structure. The approach is based on solving
analytically for the structural distortion and displacement fields that satisfy
the topological constraints, and which minimize the total energy. The total
energy is described by both the strain energy of each individual distorted
layer, and a Peierls-Nabarro like interfacial contribution arising from
stacking disregistry. The dislocation core emerges naturally within the
formalism as a result of the competition between the two contributions. The
approach presented here captures the structure and energetics of twist and
stretch moire superlattices of dislocations with arbitrary direction and
character, without assuming an analytical solution a priori, with no adjustable
parameters, while accounting naturally for dislocation-dislocation image
interactions. In comparisons to atomistic simulations using classical
potentials, the maximum structure deviation is 6%, while the maximum line
energy deviation is 0.019 eV/Angstrom. Several applications of our model are
shown, including predicting the variation of structure with twist angle, and
describing dislocation line tension and junction energies.
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We analyze the interplay between charge-density-wave (CDW) and
pair-density-wave (PDW) orders within the spin-fermion model for the cuprates.
We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm
Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. We show that both
emerge in the spin-fermion model near the onset of antiferromagnetism. We
further argue that the two orders are nearly degenerate due to an approximate
SU(2) particle-hole symmetry of the model. The ${\rm SU}(2)$ symmetry becomes
exact if one neglects the curvature of the Fermi surface in hot regions, in
which case ${\rm U}(1)$ CDW and PDW order parameters become components of an
SO(4)-symmetric PDW/CDW "super-vector". We develop a Ginzburg-Landau theory for
PDW/CDW order parameters and find two possible ground states: a "stripe" state,
and a "checkerboard" state. We show that the ${\rm SO}(4)$ symmetry between CDW
and PDW is broken by two effects. One is the inclusion of Fermi surface
curvature, which selects a PDW order immediately below the instability
temperature. Another is the overlap between different hot regions, which favors
CDW order at low temperatures. For the stripe state, we show that the
competition between the two effects gives rise to a first-order transition from
PDW to CDW inside the ordered state. We also argue that beyond mean-field
theory, the onset temperature for CDW order is additionally enhanced due to
feedback from a preemptive breaking of ${\mathbb Z}_2$ time-reversal symmetry.
We discuss the ground state properties of a pure PDW state and a pure CDW
state, and show that the PDW checkerboard state yields a vortex-anti-vortex
lattice. For the checkerboard state, we considered a situation when both CDW
and PDW orders are present at low $T$ and show that the presence of both
condensates induces a long sought chiral $s+id_{xy}$ superconductivity.
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This work aims at giving Trotter errors in digital quantum simulation (DQS)
of collective spin systems an interpretation in terms of quantum chaos of the
kicked top. In particular, for DQS of such systems, regular dynamics of the
kicked top ensures convergence of the Trotterized time evolution, while chaos
in the top, which sets in above a sharp threshold value of the Trotter step
size, corresponds to the proliferation of Trotter errors. We show the
possibility to analyze this phenomenology in a wide variety of experimental
realizations of the kicked top, ranging from single atomic spins to trapped-ion
quantum simulators which implement DQS of all-to-all interacting spin-1/2
systems. These platforms thus enable in-depth studies of Trotter errors and
their relation to signatures of quantum chaos, including the growth of
out-of-time-ordered correlators.
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We estimate the resource requirements for the quantum simulation of the
ground state energy of the one dimensional quantum transverse Ising model
(TIM), based on the surface code implementation of a fault tolerant quantum
computer. The surface code approach has one of the highest known tolerable
error rates (1%) which makes it currently one of the most practical quantum
computing schemes. Compared to results of the same model using the concatenated
Steane code, the current results indicate that the simulation time is
comparable but the number of physical qubits for the surface code is 2-3 orders
of magnitude larger than that of the concatenation code. Considering that the
error threshold requirements of the surface code is four orders of magnitude
higher than the concatenation code, building a quantum computer with a surface
code implementation appears more promising given current physical hardware
capabilities.
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We discuss classical and quantum computations in terms of corresponding
Hamiltonian dynamics. This allows us to introduce quantum computations which
involve parallel processing of both: the data and programme instructions. Using
mixed quantum-classical dynamics we look for a full cost of computations on
quantum computers with classical terminals.
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Traffic simulations are made more realistic by giving individual drivers
intentions, i.e. an idea of where they want to go. One possible implementation
of this idea is to give each driver an exact pre-computed path, that is, a
sequence of roads this driver wants to follow. This paper shows, in a realistic
road network, how repeated simulations can be used so that drivers can explore
different paths, and how macroscopic quantities such as locations of jams or
network throughput change as a result of this.
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We study mean-field states resulting from the pairing of electrons in
time-reversal broken fractal Hofstadter bands, which arise in two-dimensional
lattices where the unit cell traps magnetic flux $\Phi = (p/q)\Phi_0$
comparable to the flux quantum $\Phi_0 = h/e$. It is established that the
dimension and degeneracy of the irreducible representations of the magnetic
translation group (MTG) furnished by the charge 2e pairing fields have
different properties from those furnished by single particle Bloch states, and
in particular are shown to depend on the parity of the denominator $q$. We
explore this symmetry analysis to formulate a Ginzburg-Landau theory describing
the thermodynamic properties of Hofstadter superconductors at arbitrary
rational flux $\Phi = (p/q)\Phi_0$ in terms of a multicomponent order parameter
that describes the finite momentum pairing of electrons across different Fermi
surface patches. This phenomenological theory leads to a rich phase diagram
characterized by different symmetry breaking patterns of the MTG, which can be
interpreted as distinct classes of vortex lattices. A class of
$\mathbb{Z}_q$-symmetric Hofstadter SCs is identified, in which the MTG breaks
down to a $\mathbb{Z}_q$ subgroup. We study the topological properties of such
$\mathbb{Z}_q$-symmetric Hofstadter SCs and show that the parity of the Chern
numbers is fixed by the parity of $q$. We identify the conditions for the
realization of Bogoliubov Fermi surfaces in the presence of parity and MTG
symmetries, establishing a novel topological invariant capturing the existence
of such charge-neutral gapless excitations. Our findings, which could bear
relevance to the description of re-entrant superconductivity in moir\'e systems
in the Hofstadter regime, establish Hofstadter SC as a fertile setting to
explore symmetry broken and topological orders.
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Particle correlations are extensively studied to obtain information about the
dynamics of hadron production. From 1989 to 2000 the four LEP collaborations
recorded more than 16 million hadronic Z0 decays and several thousand W+W-
events. In Z0 decays, two-particle correlations were analysed in detail to
study Bose-Einstein and Fermi-Dirac correlations for various particle species.
In fully-hadronic W+W- decays, particle correlations were used to study whether
the two W bosons decay independently. A review of selected results is
presented.
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In this paper we consider the oscillatory integrals on Lefschetz thimbles in
the Landau-Ginzburg model as the mirror of a toric Fano manifold. We show these
thimbles represent the same relative homology classes as the characteristic
cycles of the corresponding constructible sheaves under the equivalence of
\cite{GPS18-2}. Then the oscillatory integrals on such thimbles are the same as
the integrals on the characteristic cycles and relate to genus $0$
Gromov-Witten descendant potential for $X$, and this leads to a proof of Gamma
II conjecture for toric Fano manifolds.
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Constraining the composition of super-Earth-to-sub-Neptune-size planets is a
priority to understand the processes of planetary formation and evolution. pi
Men c represents a unique target for the atmospheric and compositional
characterization of such planets because it is strongly irradiated and its bulk
density is consistent with abundant H2O. We searched for hydrogen from
photodissociating H2/H2O in pi Men c's upper atmosphere through H i Ly-alpha
transmission spectroscopy with the Hubble Space Telescope's STIS instrument,
but did not detect it. We set 1 (3) upper limits for the effective
planet-to-star size ratio RLy-alpha/Rearth=0.13 (0.24) and 0.12 (0.20) at
velocities [-215,-91] km/s and [+57,+180] km/s, respectively. We reconstructed
the stellar spectrum, and estimate that Men c receives about 1350 erg cm-2 s-1
of 5-912-Angstroms-energy, enough to cause rapid atmospheric escape. An
interesting scenario to explain the non-detection is that Men c's atmosphere is
dominated by H2O or other heavy molecules rather than H2/He. According to our
models, abundant oxygen results in less extended atmospheres, which transition
from neutral to ionized hydrogen closer to the planet. We compare our
non-detection to other detection attempts, and tentatively identify two
behaviors: planets with densities <2 g cm-3 (and likely hydrogen-dominated
atmospheres) result in H i Ly-alpha absorption, whereas planets with densities
>3 g cm-3 (and plausibly non-hydrogen-dominated atmospheres) do not result in
measurable absorption. Investigating a sample of strongly-irradiated
sub-Neptunes may provide some statistical confirmation if it is shown that they
do not generally develop extended atmospheres.
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Hund's metals are multi-orbital systems with $3d$ or $4d$ electrons
exhibiting both itinerant character and local moments, and they feature
Kondo-like screenings of local orbital and spin moments, with suppressed
coherence temperature driven by Hund's coupling $J_H$. They often exhibit
magnetic order at low temperature, but how the interaction between the
Kondo-like screening and long-range magnetic order is manifested in the
quasiparticle spectrum remains an open question. Here we present spectroscopic
signature of such interaction in a Hund's metal candidate MnSi exhibiting weak
ferromagnetism. Our photoemission measurements reveal renormalized
quasiparticle bands near the Fermi level with strong momentum dependence: the
ferromagnetism manifests through possibly exchange-split bands (Q1) below $T_C$
, while the spin/orbital screenings lead to gradual development of
quasiparticles (Q2) upon cooling. Our results demonstrate how the
characteristic spin/orbital coherence in a Hund's metal could coexist and
compete with the magnetic order to form a weak itinerant ferromagnet, via
quasiparticle bands that are well separated in momentum space and exhibit
distinct temperature dependence. Our results imply that the competition between
the spin/orbital screening and the magnetic order in a Hund's metal bears
intriguing similarity to the Kondo lattice systems.
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We discuss excess noise contributions of a practical balanced homodyne
detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution
(QKD). We point out the key generated from the original realistic model of GMCS
QKD may not be secure. In our refined realistic model, we take into account
excess noise due to the finite bandwidth of the homodyne detector and the
fluctuation of the local oscillator. A high speed balanced homodyne detector
suitable for GMCS QKD in the telecommunication wavelength region is built and
experimentally tested. The 3dB bandwidth of the balanced homodyne detector is
found to be 104MHz and its electronic noise level is 13dB below the shot noise
at a local oscillator level of 8.5*10^8 photon per pulse. The secure key rate
of a GMCS QKD experiment with this homodyne detector is expected to reach
Mbits/s over a few kilometers.
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This is a follow-up tutorial article of our previous article entitled "Robot
Basics: Representation, Rotation and Velocity". For better understanding of the
topics covered in this articles, we recommend the readers to first read our
previous tutorial article on robot basics. Specifically, in this article, we
will cover some more advanced topics on robot kinematics, including robot
motion, forward kinematics, inverse kinematics, and robot dynamics. For the
topics, terminologies and notations introduced in the previous article, we will
use them directly without re-introducing them again in this article. Also
similar to the previous article, math and formulas will also be heavily used in
this article as well (hope the readers are well prepared for the upcoming math
bomb). After reading this article, readers should be able to have a deeper
understanding about how robot motion, kinematics and dynamics. As to some more
advanced topics about robot control, we will introduce them in the following
tutorial articles for readers instead.
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We study the subsets of metric spaces that are negligible for the infimal
length of connecting curves; such sets are called metrically removable. In
particular, we show that every totally disconnected set with finite Hausdorff
measure of codimension 1 is metrically removable, which answers a question
raised by Hakobyan and Herron. The metrically removable sets are shown to be
related to other classes of "thin" sets that appeared in the literature. They
are also related to the removability problems for classes of holomorphic
functions with restrictions on the derivative.
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The notion of duality between the hydrodynamic and kinetic (ghost) variables
of lattice kinetic formulations of the Boltzmann equation is introduced. It is
suggested that this notion can serve as a guideline in the design of matrix
versions of the lattice Boltzmann equation in a physically transparent and
computationally efficient way.
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Permutationally invariant polynomial (PIP) regression has been used to obtain
machine-learned (ML) potential energy surfaces, including analytical gradients,
for many molecules and chemical reactions. Recently, the approach has been
extended to moderate size molecules and applied to systems up to 15 atoms. The
algorithm, including "purification of the basis", is computationally efficient
for energies; however, we found that the recent extension to obtain analytical
gradients, despite being a remarkable advance over previous methods, could be
further improved. Here we report developments to compact further a purified
basis and, more significantly, to use the reverse gradient approach to greatly
speed up gradient evaluation. We demonstrate this for our recent 4-body water
interaction potential. Comparisons of training and testing precision on the
MD17 database of energies and gradients (forces) for ethanol against GP-SOAP,
ANI, sGDML, PhysNet, pKREG, KRR, and other methods, which were recently
assessed by Dral and co-workers, are given. The PIP fits are as precise as
those using these methods, but the PIP computation time for energy and force
evaluation is shown to be 10 to 1000 times faster. Finally, a new PIP PES is
reported for ethanol based on a more extensive dataset of energies and
gradients than in the MD17 database. Diffusion Monte Carlo calculations which
fail on MD17-based PESs are successful using the new PES.
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Combining a classical force field, a tight-binding model, and
first-principles calculations, we have studied structural, electronic, and
optical properties of double-walled carbon nanotube (DWNT) bundles under
hydrostatic pressure. We find that the outer tube acts as a protection shield
for the inner tube and the inner tube increases the structure stability and the
ability to resist the pressure of the outer tube. Moreover, the collapsed
structures of the double-walled carbon nanotube bundle called ``parallel'' and
``in-between'' are more stable than the one called ``herringbone''. The
structural phase transition induces a pseudogap along symmetry line
\textit{$\Gamma $X}. Furthermore, the optical properties change greatly after
the collapse and a strong anisotropy appears in the collapsed structure. This
provides an efficient experimental way to detect structural phase transitions
in DWNT bundles.
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This paper proposes prediction-and-sensing based spectrum sharing, a new
spectrum-sharing model for cognitive radio networks, with a time structure for
each resource block divided into a spectrum prediction-and-sensing phase and a
data transmission phase. Cooperative spectrum prediction is incorporated as a
sub-phase of spectrum sensing in the first phase. We investigate a joint design
of transmit beamforming at the secondary base station (BS) and sensing time.
The primary design goal is to maximize the sum rate of all secondary users
(SUs) subject to the minimum rate requirement for all SUs, the transmit power
constraint at the secondary BS, and the interference power constraints at all
primary users. The original problem is difficult to solve since it is highly
nonconvex. We first convert the problem into a more tractable form, then arrive
at a convex program based on an inner approximation framework, and finally
propose a new algorithm to successively solve this convex program. We prove
that the proposed algorithm iteratively improves the objective while
guaranteeing convergence at least to local optima. Simulation results
demonstrate that the proposed algorithm reaches a stationary point after only a
few iterations with a substantial performance improvement over existing
approaches.
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Subsets and Splits