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Quantum algorithms for unstructured search problems rely on the preparation
of a uniform superposition, traditionally achieved through Hadamard gates.
However, this incidentally creates an auxiliary search space consisting of
nonsensical answers that do not belong in the search space and reduce the
efficiency of the algorithm due to the need to neglect, un-compute, or
destructively interfere with them. Previous approaches to removing this
auxiliary search space yielded large circuit depth and required the use of
ancillary qubits. We have developed an optimized general solver for a circuit
that prepares a uniform superposition of any N states while minimizing depth
and without the use of ancillary qubits. We show that this algorithm is
efficient, especially in its use of two wire gates, and that it has been
verified on an IonQ quantum computer and through application to a quantum
unstructured search algorithm.
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The color of galaxies is a fundamental property, easily measured, that
constrains models of galaxies and their evolution. Dust attenuation and star
formation history (SFH) are the dominant factors affecting the color of
galaxies. Here we explore the empirical relation between SFH, attenuation, and
color for a wide range of galaxies, including early types. These galaxies have
been observed by GALEX, SDSS, and Spitzer, allowing the construction of
measures of dust attenuation from the ratio of infrared (IR) to ultraviolet
(UV) flux and measures of SFH from the strength of the 4000A break. The
empirical relation between these three quantities is compared to models that
separately predict the effects of dust and SFH on color. This comparison
demonstrates the quantitative consistency of these simple models with the data
and hints at the power of multiwavelength data for constraining these models.
The UV color is a strong constraint; we find that a Milky Way extinction curve
is disfavored, and that the UV emission of galaxies with large 4000A break
strengths is likely to arise from evolved populations. We perform fits to the
relation between SFH, attenuation, and color. This relation links the
production of starlight and its absorption by dust to the subsequent reemission
of the absorbed light in the IR. Galaxy models that self-consistently treat
dust absorption and emission as well as stellar populations will need to
reproduce these fitted relations in the low-redshift universe.
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Magnetic skyrmions are topologically protected nanoscale objects, which are
promising building blocks for novel magnetic and spintronic devices. Here, we
investigate the dynamics of a skyrmion driven by a spin wave in a magnetic
nanowire. It is found that (i) the skyrmion is first accelerated and then
decelerated exponentially; (ii) it can turn L-corners with both right and left
turns; and (iii) it always turns left (right) when the skyrmion number is
positive (negative) in the T- and Y-junctions. Our results will be the basis of
skyrmionic devices driven by a spin wave.
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Blockchains have popularized automated market makers (AMMs). An AMM exchange
is an application running on a blockchain which maintains a pool of
crypto-assets and automatically trades assets with users governed by some
pricing function that prices the assets based on their relative demand/supply.
AMMs have created an important challenge commonly known as the Miner
Extractable Value (MEV). In particular, the miners who control the contents and
ordering of transactions in a block can extract value by front-running and
back-running users' transactions, leading to arbitrage opportunities that
guarantee them risk-free returns.
In this paper, we consider how to design AMM mechanisms that eliminate MEV
opportunities. Specifically, we propose a new AMM mechanism that processes all
transactions contained within a block in a batch. We show that our new
mechanism satisfies two tiers of guarantees. First, for legacy blockchains
where each block is proposed by a single (possibly rotating) miner, we prove
that our mechanism satisfies arbitrage resilience, i.e., a miner cannot gain
risk-free profit. Moreover, we also guarantee fair treatment among all
transactions within the same block, such that the miner is unable to sell off
favorable positions in the block to users or arbitragers. Second, for
blockchains where the block proposal process is decentralized and offers
sequencing-fairness, we prove a stronger notion called incentive compatibility
-- roughly speaking, we guarantee that any individual user's best response is
to follow the honest strategy.
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The spectral line datacubes obtained from the Square Kilometre Array (SKA)
and its precursors, such as the Australian SKA Pathfinder (ASKAP), will be
sufficiently large to necessitate automated detection and parametrisation of
sources. Matched filtering is widely acknowledged as the best possible method
for the automated detection of sources. This paper presents the Characterised
Noise Hi (CNHI) source finder, which employs a novel implementation of matched
filtering. This implementation is optimised for the 3-D nature of the planned
Wide-field ASKAP Legacy L-band All- sky Blind surveY's (WALLABY) Hi spectral
line observations. The CNHI source finder also employs a novel sparse
representation of 3-D objects, with a high compression rate, to implement Lutz
one-pass algorithm on datacubes that are too large to process in a single pass.
WALLABY will use ASKAP's phenomenal 30 square degree field of view to image
\sim 70% of the sky. It is expected that WALLABY will find 500 000 Hi galaxies
out to z \sim 0.2.
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Load balancing is the process of improving the Performance of a parallel and
distributed system through is distribution of load among the processors [1-2].
Most of the previous work in load balancing and distributed decision making in
general, do not effectively take into account the uncertainty and inconsistency
in state information but in fuzzy logic, we have advantage of using crisps
inputs. In this paper, we present a new approach for implementing dynamic load
balancing algorithm with fuzzy logic, which can face to uncertainty and
inconsistency of previous algorithms, further more our algorithm shows better
response time than round robin and randomize algorithm respectively 30.84
percent and 45.45 percent.
|
Viscously damped particles driven past an evenly spaced array of potential
energy wells or barriers may become kinetically locked in to the array, or else
may escape from the array. The transition between locked-in and free-running
states has been predicted to depend sensitively on the ratio between the
particles' size and the separation between wells. This prediction is confirmed
by measurements on monodisperse colloidal spheres driven through arrays of
holographic optical traps.
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In this paper we investigate explicit numerical approximations for stochastic
differential delay equations (SDDEs) under a local Lipschitz condition by
employing the adaptive Euler-Maruyama (EM) method. Working in both finite and
infinite horizons, we achieve strong convergence results by showing the
boundedness of the pth moments of the adaptive EM solution. We also obtain the
order of convergence infinite horizon. In addition, we show almost sure
exponential stability of the adaptive approximate solution for both SDEs and
SDDEs.
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We discuss the role of gluon poles and the gauge invariance for the hadron
tensors of Drell-Yan and direct photon production processes with the
transversely polarized hadron. These hadron tensors are needed to construct the
corresponding single spin asymmetries. For the Drell-Yan process, we perform
our analysis within both the Feynman and axial-type (contour) gauges for
gluons. In both the Feynman and contour gauges, we demonstrate that the gauge
invariance leads to the need of the new (non-standard) diagrams. Moreover, in
the Feynman gauge, we argue the absence of gluon poles in the correlators
$\langle\bar\psi\gamma_\perp A^+\psi\rangle$ related traditionally to
$dT(x,x)/dx$. As a result, these terms disappear from the final QED gauge
invariant Drell-Yan hadron tensor. For the direct photon production, by using
the contour gauge for gluon fields, we find that there are new twist-$3$ terms
present in the hadron tensor of the considering process in addition to the
standard twist-$3$ terms.
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Vincular and covincular patterns are generalizations of classical patterns
allowing restrictions on the indices and values of the occurrences in a
permutation. In this paper we study the integer sequences arising as the
enumerations of permutations simultaneously avoiding a vincular and a
covincular pattern, both of length 3, with at most one restriction. We see
familiar sequences, such as the Catalan and Motzkin numbers, but also some
previously unknown sequences which have close links to other combinatorial
objects such as lattice paths and integer partitions. Where possible we include
a generating function for the enumeration. One of the cases considered settles
a conjecture by Pudwell (2010) on the Wilf-equivalence of barred patterns. We
also give an alternative proof of the classic result that permutations avoiding
123 are counted by the Catalan numbers.
|
We calculate the contribution of graviton exchange to the running of gauge
couplings at lowest non-trivial order in perturbation theory. Including this
contribution in a theory that features coupling constant unification does not
upset this unification, but rather shifts the unification scale. When
extrapolated formally, the gravitational correction renders all gauge couplings
asymptotically free.
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The cross coproduct braided group $Aut(C) \rcocross B$ is obtained by
Tannaka-Krein reconstruction from $C^B\to C$ for a braided group $B$ in braided
category $C$. We apply this construction to obtain partial solutions to two
problems in braided group theory, namely the tensor problem and the braided
double. We obtain $Aut(C)\rcocross Aut(C)\isom Aut(C)\lcross Aut(C)$ and higher
braided group `spin chains'. The example of the braided group $B(R)\lcross
B(R)\lcross...\lcross B(R)$ is described explicitly by R-matrix relations. We
also obtain $Aut(C)\rcocross Aut(C)^*$ as a dual quasitriangular `codouble'
braided group by reconstruction from the dual category $C^\circ\to C$. General
braided double crossproducts $B\dcross C$ are also considered.
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To find out whether toroidal field can stably exist in galaxies the
current-driven instability of toroidal magnetic fields is considered under the
influence of an axial magnetic field component and under the influence of both
rigid and differential rotation. The MHD equations are solved in a simplified
model with cylindric geometry. We assume the axial field as uniform and the
fluid as incompressible. The stability of a toroidal magnetic field is strongly
influenced by uniform axial magnetic fields. If both field components are of
the same order of magnitude then the instability is slightly supported and
modes with m>1 dominate. If the axial field even dominates the most unstable
modes have again m>1 but the field is strongly stabilized. All modes are
suppressed by a fast rigid rotation where the m=1 mode maximally resists. Just
this mode becomes best re-animated for \Omega > \Omega^A (\Omega^A the Alfven
frequency) if the rotation has a negative shear. -- Strong indication has been
found for a stabilization of the nonaxisymmetric modes for fluids with small
magnetic Prandtl number if they are unstable for Pm=1. For rotating fluids the
higher modes with m>1 do not play an important role in the linear theory. In
the light of our results galactic fields should be marginally unstable against
perturbations with m<= 1. The corresponding growth rates are of the order of
the rotation period of the inner part of the galaxy.
|
The spontaneous decay rates of an excited atom placed near a dielectric
cylinder are investigated. A special attention is paid to the case when the
cylinder radius is small in comparison with radiation wavelength (nanofiber or
photonic wire). In this case, the analytical expressions of the transition
rates for different orientations of dipole are derived. It is shown that the
main contribution to decay rates is due to quasistatic interaction of atom
dipole momentum with nanofiber and the contributions of guided modes are
exponentially small. On the contrary, in the case when the radius of fiber is
only slightly less than radiation wavelength, the influence of guided modes can
be substantial. The results obtained are compared with the case of dielectric
nanospheroid and ideally conducting wire.
|
Quantitative stochastic homogenization of linear elliptic operators is by now
well-understood. In this contribution we move forward to the nonlinear setting
of monotone operators with $p$-growth. This work is dedicated to a quantitative
two-scale expansion result. By treating the range of exponents $2\le p <\infty$
in dimensions $d\le 3$, we are able to consider genuinely nonlinear elliptic
equations and systems such as $-\nabla \cdot A(x)(1+|\nabla u|^{p-2})\nabla
u=f$ (with $A$ random, non-necessarily symmetric) for the first time. When
going from $p=2$ to $p>2$, the main difficulty is to analyze the associated
linearized operator, whose coefficients are degenerate, unbounded, and depend
on the random input $A$ via the solution of a nonlinear equation. One of our
main achievements is the control of this intricate nonlinear dependence,
leading to annealed Meyers' estimates for the linearized operator, which are
key to the optimal quantitative two-scale expansion result we derive (this is
also new in the periodic setting).
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Understanding the feasible power flow region is of central importance to
power system analysis. In this paper, we propose a geometric view of the power
system loadability problem. By using rectangular coordinates for complex
voltages, we provide an integrated geometric understanding of active and
reactive power flow equations on loadability boundaries. Based on such an
understanding, we develop a linear programming framework to 1) verify if an
operating point is on the loadability boundary, 2) compute the margin of an
operating point to the loadability boundary, and 3) calculate a loadability
boundary point of any direction. The proposed method is computationally more
efficient than existing methods since it does not require solving nonlinear
optimization problems or calculating the eigenvalues of the power flow
Jacobian. Standard IEEE test cases demonstrate the capability of the new method
compared to the current state-of-the-art methods.
|
The goal of these notes is to provide an informal introduction to
Gromov-Witten theory with an emphasis on its role in counting curves in
surfaces. These notes are based on a talk given at the Fields Institute during
a week-long conference aimed at introducing graduate students to the subject
which took place during the thematic program on Calabi-Yau Varieties:
Arithmetic, Geometry, and Physics.
|
The Proca theory of the real massive vector field admits non-equilibrium
solutions, where the asymptotic dynamics of the electric field is dominated by
the periodically oscillating Coulomb component. We discuss how such field
configurations are seen in different reference frames, where we find an
intriguing spatial pattern of the vector field and the electromagnetic field
associated with it. Our studies are carried out in the framework of the
classical Proca theory.
|
We study a class of three-point functions on the de Sitter universe and on
the asymptotic cone. A blending of geometrical ideas and analytic methods is
used to compute some remarkable integrals, on the basis of a generalized
star-triangle identity living on the cone and on the complex de Sitter
manifold. We discuss an application of the general results to the study of the
stability of scalar particles on the Sitter universe.
|
By using the direct coexistence method, we have calculated the melting points
of ice Ih at normal pressure for three recently proposed water models, namely,
TIP3P-FB, TIP4P-FB, and TIP4P-D. We obtained Tm = 216 K for TIP3P-FB, Tm = 242
K for TIP4P-FB, and Tm = 247 K for TIP4P-D. We revisited the melting point of
TIP4P/2005 and TIP5P obtaining Tm = 250 and 274 K, respectively. We summarize
the current situation of the melting point of ice Ih for a number of water
models and conclude that no model is yet able to simultaneously reproduce the
melting temperature of ice Ih and the temperature of the maximum in density at
room pressure. This probably points toward our both still incomplete knowledge
of the potential energy surface of water and the necessity of incorporating
nuclear quantum effects to describe both properties simultaneously.
|
Tunneling of fractionally charged quasiparticles across a two-dimensional
electron system on a fractional quantum Hall plateau is expected to be strongly
enhanced at low temperatures. This theoretical prediction is at odds with
recent experimental studies of samples with weakly-pinched
quantum-point-contact constrictions, in which the opposite behavior is
observed. We argue here that this unexpected finding is a consequence of
electron-electron interactions near the point contact.
|
Detailed mobile sensing data from phones, watches, and fitness trackers offer
an unparalleled opportunity to quantify and act upon previously unmeasurable
behavioral changes in order to improve individual health and accelerate
responses to emerging diseases. Unlike in natural language processing and
computer vision, deep representation learning has yet to broadly impact this
domain, in which the vast majority of research and clinical applications still
rely on manually defined features and boosted tree models or even forgo
predictive modeling altogether due to insufficient accuracy. This is due to
unique challenges in the behavioral health domain, including very small
datasets (~10^1 participants), which frequently contain missing data, consist
of long time series with critical long-range dependencies (length>10^4), and
extreme class imbalances (>10^3:1). Here, we introduce a neural architecture
for multivariate time series classification designed to address these unique
domain challenges. Our proposed behavioral representation learning approach
combines novel tasks for self-supervised pretraining and transfer learning to
address data scarcity, and captures long-range dependencies across long-history
time series through transformer self-attention following convolutional neural
network-based dimensionality reduction. We propose an evaluation framework
aimed at reflecting expected real-world performance in plausible deployment
scenarios. Concretely, we demonstrate (1) performance improvements over
baselines of up to 0.15 ROC AUC across five prediction tasks, (2) transfer
learning-induced performance improvements of 16% PR AUC in small data
scenarios, and (3) the potential of transfer learning in novel disease
scenarios through an exploratory case study of zero-shot COVID-19 prediction in
an independent data set. Finally, we discuss potential implications for medical
surveillance testing.
|
The functional space of biquaternions is considered on Minkovskiy space. The
scalar-vector biquaternions representation is used which was offered by W.
Hamilton for quaternions. With introduction of differential operator - a mutual
complex gradient (bigradients), which generalize the notion of a gradient on
biquaternions space, biquaternionic wave (biwave) equations are considered,
their invariance for group of the Lorentz-Puancare transformations is shown and
their generalized solutions are obtained.
Biquaternionic form of generalized Maxwell-Dirac equation is constructed and
its solutions are researched on base of the differential biquaternions algebra.
Its generalized decisions are built with use of scalar potential. The new
equation for these potential are constructed which unites known equations of
quantum mechanics (Klein-Gordon and Schrodinger Eq.). The nonstationary,
steady-state and harmonic on time scalar fields and generated by them the
spinors and spinors fields in biquaternionic form are constructed.
|
Modeling and predicting extreme movements in GDP is notoriously difficult and
the selection of appropriate covariates and/or possible forms of nonlinearities
are key in obtaining precise forecasts. In this paper, our focus is on using
large datasets in quantile regression models to forecast the conditional
distribution of US GDP growth. To capture possible non-linearities, we include
several nonlinear specifications. The resulting models will be huge dimensional
and we thus rely on a set of shrinkage priors. Since Markov Chain Monte Carlo
estimation becomes slow in these dimensions, we rely on fast variational Bayes
approximations to the posterior distribution of the coefficients and the latent
states. We find that our proposed set of models produces precise forecasts.
These gains are especially pronounced in the tails. Using Gaussian processes to
approximate the nonlinear component of the model further improves the good
performance, in particular in the right tail.
|
We prove the rationality and irreducibility of the moduli space of---what we
call---the endomorphism-general instanton vector bundles of arbitrary rank on
the projective space. In particular, we deduce the rationality of the moduli
spaces of rank-two mathematical instantons. This problem was first studied by
Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been
reiterated within the framework of the ICM 2018.
|
The applicability of Doppler radar for gait analysis is investigated by
quantitatively comparing the measured biomechanical parameters to those
obtained using motion capturing and ground reaction forces. Nineteen
individuals walked on a treadmill at two different speeds, where a radar system
was positioned in front of or behind the subject. The right knee angle was
confined by an adjustable orthosis in five different degrees. Eleven gait
parameters are extracted from radar micro-Doppler signatures. Here, new methods
for obtaining the velocities of individual lower limb joints are proposed.
Further, a new method to extract individual leg flight times from radar data is
introduced. Based on radar data, five spatiotemporal parameters related to
rhythm and pace could reliably be extracted. Further, for most of the
considered conditions, three kinematic parameters could accurately be measured.
The radar-based stance and flight time measurements rely on the correct
detection of the time instant of maximal knee velocity during the gait cycle.
This time instant is reliably detected when the radar has a back view, but is
underestimated when the radar is positioned in front of the subject. The
results validate the applicability of Doppler radar to accurately measure a
variety of medically relevant gait parameters. Radar has the potential to
unobtrusively diagnose changes in gait, e.g., to design training in prevention
and rehabilitation. As contact-less and privacy-preserving sensor, radar
presents a viable technology to supplement existing gait analysis tools for
long-term in-home examinations.
|
NASA should design missions to Mars for the purpose of generating "Aha!"
discoveries to jolt scientists contemplating the molecular origins of life.
These missions should be designed with an understanding of the privileged
chemistry that likely created RNA prebiotically on Earth, and universal
chemical principles that constrain the structure of Darwinian molecules
generally.
|
We report the results of a visual inspection of images of the Rapid ASKAP
Continuum Survey (RACS) in search of extended radio galaxies (ERG) that reach
or exceed linear sizes on the order of one Megaparsec. We searched a contiguous
area of 1059deg$^2$ from RA$_{\rm J}$=20$^h$20$^m$ to 06$^h$20$^m$, and
$-50^{\circ}<\rm{Dec}_J<-40^{\circ}$, which is covered by deep multi-band
optical images of the Dark Energy Survey (DES), and in which previously only
three ERGs larger than 1Mpc had been reported. For over 1800 radio galaxy
candidates inspected, our search in optical and infrared images resulted in
hosts for 1440 ERG, for which spectroscopic and photometric redshifts from
various references were used to convert their largest angular size (LAS) to
projected linear size (LLS). This resulted in 178 newly discovered giant radio
sources (GRS) with LLS$>$1Mpc, of which 18 exceed 2Mpc and the largest one is
3.4Mpc. Their redshifts range from 0.02 to $\sim$2.0, but only 10 of the 178
new GRS have spectroscopic redshifts. For the 146 host galaxies the median
$r$-band magnitude and redshift are 20.9 and 0.64, while for the 32 quasars or
candidates these are 19.7 and 0.75. Merging the six most recent large
compilations of GRS results in 458 GRS larger than 1Mpc, so we were able to
increase this number by $\sim39\%$ to now 636.
|
We consider the problem of controlling switched-mode power converters using
model predictive control. Model predictive control requires solving
optimization problems in real time, limiting its application to systems with
small numbers of switches and a short horizon. We propose a technique for using
off-line computation to approximate the model predictive controller. This is
done by dividing the planning horizon into two segments, and using a quadratic
function to approximate the optimal cost over the second segment. The
approximate model predictive algorithm minimizes the true cost over the first
segment, and the approximate cost over the second segment, allowing the user to
adjust the computational requirements by changing the length of the first
segment. We conclude with two simulated examples.
|
We present distance estimates to a set of high-latitude intermediate-velocity
HI clouds. We explore some of the physical parameters that can be determined
from these results, such as cloud mass, infall velocity and height above the
Galactic plane. We also briefly describe some astrophysical applications of
these data and explore future work.
|
Entanglement in multipartite systems can be achieved by the coherent
superposition of product states, generated through a universal unitary
transformation, followed by spontaneous parametric down-conversions and path
identification.
|
There is a parallelism between growth in arithmetic combinatorics and growth
in a geometric context. While, over $\mathbb{R}$ or $\mathbb{C}$, geometric
statements on growth often have geometric proofs, what little is known over
finite fields rests on arithmetic proofs. We discuss strategies for geometric
proofs of growth over finite fields, and show that growth can be defined and
proven in an abstract projective plane -- even one with weak axioms.
|
We present high S/N optical spectra of 10 BL Lac objects detected at GeV
energies by Fermi satellite (3FGL catalog), for which previous observations
suggested that they are at relatively high redshift. The new observations,
obtained at the 10 m Gran Telescopio Canarias, allowed us to find the redshift
for J0814.5+2943 (z = 0.703) and we can set spectroscopic lower limit for
J0008.0+4713 (z>1.659) and J1107.7+0222 (z>1.0735) on the basis of Mg II
intervening absorption features. In addition we confirm the redshifts for
J0505.5+0416 (z=0.423) and for J1450+5200 (z>2.470). Finally we contradict the
previous z estimates for five objects (J0049.7+0237, J0243.5+7119,
J0802.0+1005, J1109.4+2411, and J2116.1+3339).
|
We computationally study the Fermi arc states in a Dirac semimetal, both in a
semi-infinite slab and in the thin-film limit. We use Cd$_3$A$_2$ as a model
system, and include perturbations that break the $C_4$ symmetry and inversion
symmetry. The surface states are protected by the mirror symmetries present in
the bulk states and thus survive these perturbations. The Fermi arc states
persist down to very thin films, thinner than presently measured
experimentally, but are affected by breaking the symmetry of the Hamiltonian.
Our findings are compatible with experimental observations of transport in
Cd$_3$As$_2$, and also suggest that symmetry-breaking terms that preserve the
Fermi arc states nevertheless can have a profound effect in the thin film
limit.
|
We classify parallel and totally geodesic hypersurfaces of the relevant class
of G\"odel-type spacetimes, with particular regard to the homogeneous examples.
|
We show that Nash-Williams' theorem asserting that the countable transfinite
sequences of elements of a better-quasi-ordering ordered by embeddability form
a better-quasi-ordering is provable in the subsystem of second order arithmetic
Pi^1_1-CA_0 but is not equivalent to Pi^1_1-CA_0. We obtain some partial
results towards the proof of this theorem in the weaker subsystem ATR_0 and we
show that the minimality lemmas typical of wqo and bqo theory imply Pi^1_1-CA_0
and hence cannot be used in such a proof.
|
Consider a logistic partially linear model, in which the logit of the mean of
a binary response is related to a linear function of some covariates and a
nonparametric function of other covariates. We derive simple, doubly robust
estimators of coefficient for the covariates in the linear component of the
partially linear model. Such estimators remain consistent if either a nuisance
model is correctly specified for the nonparametric component, or another
nuisance model is correctly specified for the means of the covariates of
interest given other covariates and the response at a fixed value. In previous
works, conditional density models are needed for the latter purposes unless a
scalar, binary covariate is handled. We also propose two specific doubly robust
estimators: one is locally-efficient like in our class of doubly robust
estimators and the other is numerically and statistically simpler and can
achieve reasonable efficiency especially when the true coefficients are close
to 0.
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We study electron transport through double quantum dots (DQD) coupled to a
cavity with a single photon mode. The DQD is connected to two electron
reservoirs, and the total system is under an external perpendicular magnetic
field. The DQD system exhibits a complex multi-level energy spectrum. By
varying the photon energy, several anti-crossings between photon dressed
electron states of the DQD-cavity system are found at low strength of the
magnetic field. The anti-crossings are identified as multiple Rabi resonances
arising from the photon exchange between these states. As the results, a dip in
the current is seen caused by the multiple Rabi resonances. By increasing the
strength of the external magnetic field, a dislocation of the current dip to a
lower photon energy is found and the current dip can be diminished. The
interplay of the strength of the magnetic field and the geometry of the states
the DQD system can weaken the multiple Rabi resonances in which the exchange of
photon between the anti-crossings is decreased. We can therefore confirm that
the electron transport behavior in the DQD-cavity system can be controlled by
manipulating the external magnetic field and the photon cavity parameters.
|
Gravitational lensing can provide pure geometric tests of the structure of
space-time, for instance by determining empirically the angular diameter
distance-redshift relation. This geometric test has been demonstrated several
times using massive clusters which produce a large lensing signal. In this
case, matter at a single redshift dominates the lensing signal, so the analysis
is straightforward. It is less clear how weaker signals from multiple sources
at different redshifts can be stacked to demonstrate the geometric dependence.
We introduce a simple measure of relative shear which for flat cosmologies
separates the effect of lens and source positions into multiplicative terms,
allowing signals from many different source-lens pairs to be combined. Applying
this technique to a sample of groups and low-mass clusters in the COSMOS
survey, we detect a clear variation of shear with distance behind the lens.
This represents the first detection of the geometric effect using weak lensing
by multiple, low-mass systems. The variation of distance with redshift is
measured with sufficient precision to constrain the equation of state of the
universe under the assumption of flatness, equivalent to a detection of a dark
energy component Omega_X at greater than 99% confidence for an
equation-of-state parameter -2.5 < w < -0.1. For the case w = -1, we find a
value for the cosmological constant density parameter Omega_Lambda =
0.85+0.044-0.19 (68% C.L.), and detect cosmic acceleration (q_0 < 0) at the 98%
C.L.. We consider the systematic uncertainties associated with this technique
and discuss the prospects for applying it in forthcoming weak-lensing surveys.
|
Context: R Coronae Borealis (RCB) variables and their non-variable
counterparts, the dustless Hydrogen-Deficient Carbon (dLHdC) stars have been
known to exhibit enhanced s-processed material on their surfaces, especially
Sr, Y, and Ba. No comprehensive work has been done to explore the s-process in
these types of stars, however one particular RCB star, U Aqr, has been under
scrutiny for its extraordinary Sr enhancement. Aims: We aim to identify RCB and
dLHdC stars that have significantly enhanced Sr abundances, such as U Aqr, and
use stellar evolution models to begin to estimate the type of neutron exposure
that occurs in a typical HdC star. Methods: We compare the strength of the Sr
II 4077 $\AA$ spectral line to Ca II H to identify the new subclass of Sr-rich
HdCs. We additionally use the structural and abundance information from
existing RCB MESA models to calculate the neutron exposure parameter, $\tau$
Results: We identify six stars in the Sr-rich class. Two are RCBs, and four are
dLHdCs. We additionally find that the preferred RCB MESA model has a neutron
exposure $\tau$ ~ 0.1 mb$^{-1}$, which is lower than the estimated $\tau$
between 0.15 and 0.6 mb$^{-1}$ for the Sr-rich star U Aqr found in the
literature. We find trends in the neutron exposure corresponding to He-burning
shell temperature, metallicity, and assumed s-processing site. Conclusions: We
have found a sub-class of 6 HdCs known as the Sr-rich class, which tend to lie
in the halo, outside the typical distribution of RCBs and dLHdCs. We find that
dLHdC stars are more likely to be Sr-rich than RCBs, with an occurrence rate of
~13\% for dLHdCs and ~2\% for RCBs. This is one of the first potential
spectroscopic differences between RCBs and dLHdCs, along with dLHdCs having
stronger surface abundances of $^{18}$O.
|
During last two decades it has been discovered that the statistical
properties of a number of microscopically rather different random systems at
the macroscopic level are described by {\it the same} universal probability
distribution function which is called the Tracy-Widom (TW) distribution. Among
these systems we find both purely methematical problems, such as the longest
increasing subsequences in random permutations, and quite physical ones, such
as directed polymers in random media or polynuclear crystal growth. In the
extensive Introduction we discuss in simple terms these various random systems
and explain what the universal TW function is. Next, concentrating on the
example of one-dimensional directed polymers in random potential we give the
main lines of the formal proof that fluctuations of their free energy are
described the universal TW distribution. The second part of the review consist
of detailed appendices which provide necessary self-contained mathematical
background for the first part.
|
High-fidelity 3D scene reconstruction has been substantially advanced by
recent progress in neural fields. However, most existing methods train a
separate network from scratch for each individual scene. This is not scalable,
inefficient, and unable to yield good results given limited views. While
learning-based multi-view stereo methods alleviate this issue to some extent,
their multi-view setting makes it less flexible to scale up and to broad
applications. Instead, we introduce training generalizable Neural Fields
incorporating scene Priors (NFPs). The NFP network maps any single-view RGB-D
image into signed distance and radiance values. A complete scene can be
reconstructed by merging individual frames in the volumetric space WITHOUT a
fusion module, which provides better flexibility. The scene priors can be
trained on large-scale datasets, allowing for fast adaptation to the
reconstruction of a new scene with fewer views. NFP not only demonstrates SOTA
scene reconstruction performance and efficiency, but it also supports
single-image novel-view synthesis, which is underexplored in neural fields.
More qualitative results are available at:
https://oasisyang.github.io/neural-prior
|
We explore theoretically the optical response properties in an optomechanical
system under electromagneti- cally induced transparency condition but with the
mechanical resonator being driven by an additional coherent field. In this
configuration, more complex quantum coherent and interference phenomena occur.
In partic- ular, we find that the probe transmission spectra depend on the
total phase of the applied fields. Our study also provides an efficient way to
control propagation of amplification.
|
We present an approach for recognizing all objects in a scene and estimating
their full pose from an accurate 3D instance-aware semantic reconstruction
using an RGB-D camera. Our framework couples convolutional neural networks
(CNNs) and a state-of-the-art dense Simultaneous Localisation and Mapping
(SLAM) system, ElasticFusion, to achieve both high-quality semantic
reconstruction as well as robust 6D pose estimation for relevant objects. While
the main trend in CNN-based 6D pose estimation has been to infer object's
position and orientation from single views of the scene, our approach explores
performing pose estimation from multiple viewpoints, under the conjecture that
combining multiple predictions can improve the robustness of an object
detection system. The resulting system is capable of producing high-quality
object-aware semantic reconstructions of room-sized environments, as well as
accurately detecting objects and their 6D poses. The developed method has been
verified through experimental validation on the YCB-Video dataset and a newly
collected warehouse object dataset. Experimental results confirmed that the
proposed system achieves improvements over state-of-the-art methods in terms of
surface reconstruction and object pose prediction. Our code and video are
available at https://sites.google.com/view/object-rpe.
|
We establish a formula for the SL(2,C) Casson invariant of spliced sums of
homology spheres along knots. Along the way, we show that the SL(2,C) Casson
invariant vanishes for spliced sums along knots in the 3-sphere.
|
Short-term hydro-generation management poses a non-convex or even
non-continuous optimization problem. For this reason, the problem of
systematically obtaining feasible and economically satisfying solutions has not
yet been completely solved. Two decomposition methods, which, as far as we
know, have not been applied in this field, are here proposed : $\bullet$ the
first is based on a decomposition by prediction method and the coordination is
a primal-dual relaxation algorithm, $\bullet$ handling the dynamic constraints
by duality, the second achieves a price decomposition by an Augmented
Lagrangian technique. Numerical tests show the efficiency of these algorithms.
They will enable the process in use at Electricit{\'e} de France to be
improved.
|
This report addresses state inference for hidden Markov models. These models
rely on unobserved states, which often have a meaningful interpretation. This
makes it necessary to develop diagnostic tools for quantification of state
uncertainty. The entropy of the state sequence that explains an observed
sequence for a given hidden Markov chain model can be considered as the
canonical measure of state sequence uncertainty. This canonical measure of
state sequence uncertainty is not reflected by the classic multivariate state
profiles computed by the smoothing algorithm, which summarizes the possible
state sequences. Here, we introduce a new type of profiles which have the
following properties: (i) these profiles of conditional entropies are a
decomposition of the canonical measure of state sequence uncertainty along the
sequence and makes it possible to localize this uncertainty, (ii) these
profiles are univariate and thus remain easily interpretable on tree
structures. We show how to extend the smoothing algorithms for hidden Markov
chain and tree models to compute these entropy profiles efficiently.
|
We initiate the recently proposed $\boldsymbol{w}$-ensemble one-particle
reduced density matrix functional theory ($\boldsymbol{w}$-RDMFT) by deriving
the first functional approximations and illustrate how excitation energies can
be calculated in practice. For this endeavour, we first study the symmetric
Hubbard dimer, constituting the building block of the Hubbard model, for which
we execute the Levy-Lieb constrained search. Second, due to the particular
suitability of $\boldsymbol{w}$-RDMFT for describing Bose-Einstein condensates,
we demonstrate three conceptually different approaches for deriving the
universal functional in a homogeneous Bose gas for arbitrary pair interaction
in the Bogoliubov regime. Remarkably, in both systems the gradient of the
functional is found to diverge repulsively at the boundary of the functional's
domain, extending the recently discovered Bose-Einstein condensation force to
excited states. Our findings highlight the physical relevance of the
generalized exclusion principle for fermionic and bosonic mixed states and the
curse of universality in functional theories.
|
The Shack-Hartmann wavefront sensor is widely used to measure aberrations
induced by atmospheric turbulence in adaptive optics systems. However if there
exists strong atmospheric turbulence or the brightness of guide stars is low,
the accuracy of wavefront measurements will be affected. In this paper, we
propose a compressive Shack-Hartmann wavefront sensing method. Instead of
reconstructing wavefronts with slope measurements of all sub-apertures, our
method reconstructs wavefronts with slope measurements of sub-apertures which
have spot images with high signal to noise ratio. Besides, we further propose
to use a deep neural network to accelerate wavefront reconstruction speed.
During the training stage of the deep neural network, we propose to add a
drop-out layer to simulate the compressive sensing process, which could
increase development speed of our method. After training, the compressive
Shack-Hartmann wavefront sensing method can reconstruct wavefronts in high
spatial resolution with slope measurements from only a small amount of
sub-apertures. We integrate the straightforward compressive Shack-Hartmann
wavefront sensing method with image deconvolution algorithm to develop a
high-order image restoration method. We use images restored by the high-order
image restoration method to test the performance of our the compressive
Shack-Hartmann wavefront sensing method. The results show that our method can
improve the accuracy of wavefront measurements and is suitable for real-time
applications.
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Nonequilibrium processes of small systems such as molecular machines are
ubiquitous in biology, chemistry and physics, but are often challenging to
comprehend. In the past two decades, several exact thermodynamic relations of
nonequilibrium processes, collectively known as fluctuation theorems, have been
discovered and provided critical insights. These fluctuation theorems are
generalizations of the second law, and can be unified by a differential
fluctuation theorem. Here we perform the first experimental test of the
differential fluctuation theorem, using an optically levitated nanosphere in
both underdamped and overdamped regimes, and in both spatial and velocity
spaces. We also test several theorems that can be obtained from it directly,
including a generalized Jarzynski equality that is valid for arbitrary initial
states, and the Hummer-Szabo relation. Our study experimentally verifies these
fundamental theorems, and initiates the experimental study of stochastic
energetics with the instantaneous velocity measurement.
|
Correlated outcomes are common in many practical problems. In some settings,
one outcome is of particular interest, and others are auxiliary. To leverage
information shared by all the outcomes, traditional multi-task learning (MTL)
minimizes an averaged loss function over all the outcomes, which may lead to
biased estimation for the target outcome, especially when the MTL model is
mis-specified. In this work, based on a decomposition of estimation bias into
two types, within-subspace and against-subspace, we develop a robust transfer
learning approach to estimating a high-dimensional linear decision rule for the
outcome of interest with the presence of auxiliary outcomes. The proposed
method includes an MTL step using all outcomes to gain efficiency, and a
subsequent calibration step using only the outcome of interest to correct both
types of biases. We show that the final estimator can achieve a lower
estimation error than the one using only the single outcome of interest.
Simulations and real data analysis are conducted to justify the superiority of
the proposed method.
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OpenAI's ChatGPT initiated a wave of technical iterations in the space of
Large Language Models (LLMs) by demonstrating the capability and disruptive
power of LLMs. OpenAI has prompted large organizations to respond with their
own advancements and models to push the LLM performance envelope. OpenAI has
prompted large organizations to respond with their own advancements and models
to push the LLM performance envelope. OpenAI's success in spotlighting AI can
be partially attributed to decreased barriers to entry, enabling any individual
with an internet-enabled device to interact with LLMs. What was previously
relegated to a few researchers and developers with necessary computing
resources is now available to all. A desire to customize LLMs to better
accommodate individual needs prompted OpenAI's creation of the GPT Store, a
central platform where users can create and share custom GPT models.
Customization comes in the form of prompt-tuning, analysis of reference
resources, browsing, and external API interactions, alongside a promise of
revenue sharing for created custom GPTs. In this work, we peer into the window
of the GPT Store and measure its impact. Our analysis constitutes a large-scale
overview of the store exploring community perception, GPT details, and the GPT
authors, in addition to a deep-dive into a 3rd party storefront indexing
user-submitted GPTs, exploring if creators seek to monetize their creations in
the absence of OpenAI's revenue sharing.
|
We introduce a switching mechanism in the asymptotic occupations of quantum
states induced by the combined effects of a periodic driving and a weak
coupling to a heat bath. It exploits one of the ubiquitous avoided crossings in
driven systems and works even if both involved Floquet states have small
occupations. It is independent of the initial state and the duration of the
driving. As a specific example of this general switching mechanism we show how
an asymmetric double well potential can be switched between the lower and the
upper well by a periodic driving that is much weaker than the asymmetry.
|
In this paper a new method for information hiding in club music is
introduced. The method called StegIbiza is based on using the music tempo as a
carrier. The tempo is modulated by hidden messages with a 3-value coding
scheme, which is an adoption of Morse code for StegIbiza. The evaluation of the
system was performed for several music samples (with and without StegIbiza
enabled) on a selected group of testers who had a music background. Finally,
for the worst case scenario, none of them could identify any differences in the
audio with a 1% margin of changed tempo.
|
In the era of the fourth industrial revolution, it is essential to automate
fault detection and diagnosis of machineries so that a warning system can be
developed that will help to take an appropriate action before any catastrophic
damage. Some machines health monitoring systems are used globally but they are
expensive and need trained personnel to operate and analyse. Predictive
maintenance and occupational health and safety culture are not available due to
inadequate infrastructure, lack of skilled manpower, financial crisis, and
others in developing countries. Starting from developing a cost-effective DAS
for collecting fault data in this study, the effect of limited data and
resources has been investigated while automating the process. To solve this
problem, A feature engineering and data reduction method has been developed
combining the concepts from wavelets, differential calculus, and signal
processing. Finally, for automating the whole process, all the necessary
theoretical and practical considerations to develop a predictive model have
been proposed. The DAS successfully collected the required data from the
machine that is 89% accurate compared to the professional manual monitoring
system. SVM and NN were proposed for the prediction purpose because of their
high predicting accuracy greater than 95% during training and 100% during
testing the new samples. In this study, the combination of the simple algorithm
with a rule-based system instead of a data-intensive system turned out to be
hybridization by validating with collected data. The outcome of this research
can be instantly applied to small and medium-sized industries for finding other
issues and developing accordingly. As one of the foundational studies in
automatic FDD, the findings and procedure of this study can lead others to
extend, generalize, or add other dimensions to FDD automation.
|
We analyze the ultimate quantum limit of resolving two identical sources in a
noisy environment. We prove that in the presence of noise causing false
excitation, such as thermal noise, the quantum Fisher information of arbitrary
quantum states for the separation of the objects, which quantifies the
resolution, always converges to zero as the separation goes to zero. Noisy
cases contrast with a noiseless case where it has been shown to be nonzero for
a small distance in various circumstances, revealing the superresolution. In
addition, we show that false excitation on an arbitrary measurement, such as
dark counts, also makes the classical Fisher information of the measurement
approach to zero as the separation goes to zero. Finally, a practically
relevant situation resolving two identical thermal sources, is quantitatively
investigated by using the quantum and classical Fisher information of finite
spatial mode multiplexing, showing that the amount of noise poses a limit on
the resolution in a noisy system.
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Federated Learning (FL) has emerged as a potent framework for training models
across distributed data sources while maintaining data privacy. Nevertheless,
it faces challenges with limited high-quality labels and non-IID client data,
particularly in applications like autonomous driving. To address these hurdles,
we navigate the uncharted waters of Semi-Supervised Federated Object Detection
(SSFOD). We present a pioneering SSFOD framework, designed for scenarios where
labeled data reside only at the server while clients possess unlabeled data.
Notably, our method represents the inaugural implementation of SSFOD for
clients with 0% labeled non-IID data, a stark contrast to previous studies that
maintain some subset of labels at each client. We propose FedSTO, a two-stage
strategy encompassing Selective Training followed by Orthogonally enhanced
full-parameter training, to effectively address data shift (e.g. weather
conditions) between server and clients. Our contributions include selectively
refining the backbone of the detector to avert overfitting, orthogonality
regularization to boost representation divergence, and local EMA-driven pseudo
label assignment to yield high-quality pseudo labels. Extensive validation on
prominent autonomous driving datasets (BDD100K, Cityscapes, and SODA10M)
attests to the efficacy of our approach, demonstrating state-of-the-art
results. Remarkably, FedSTO, using just 20-30% of labels, performs nearly as
well as fully-supervised centralized training methods.
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In the last decade, there has been a growing realization that the current
Internet Protocol is reaching the limits of its senescence. This has prompted
several research efforts that aim to design potential next-generation Internet
architectures. Named Data Networking (NDN), an instantiation of the
content-centric approach to networking, is one such effort. In contrast with
IP, NDN routers maintain a significant amount of user-driven state. In this
paper we investigate how to use this state for covert ephemeral communication
(CEC). CEC allows two or more parties to covertly exchange ephemeral messages,
i.e., messages that become unavailable after a certain amount of time. Our
techniques rely only on network-layer, rather than application-layer, services.
This makes our protocols robust, and communication difficult to uncover. We
show that users can build high-bandwidth CECs exploiting features unique to
NDN: in-network caches, routers' forwarding state and name matching rules. We
assess feasibility and performance of proposed cover channels using a local
setup and the official NDN testbed.
|
n a recent paper we proposed the expansion of the space of variations in
energy calculations by considering the approximate wave function $\psi$ to be a
functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For
the determination of such a wave function functional, a constrained search is
first performed over the subspace of all functions $\chi$ such that
$\psi[\chi]$ satisfies a physical constraint or leads to the known value of an
observable. A rigorous upper bound to the energy is then obtained by
application of the variational principle. To demonstrate the advantages of the
expansion of variational space, we apply the constrained-search--variational
method to the ground state of the negative ion of atomic Hydrogen, the Helium
atom, and its isoelectronic sequence. The method is equally applicable to
excited states, and its extension to such states in conjunction with the
theorem of Theophilou is also described.
|
Measurements of the Hall effect and the resistivity in twinned
YBa2Cu3O7-delta thin films in magnetic fields B oriented parallel to the
crystallographic c-axis and to the twin boundaries reveal a double sign
reversal of the Hall coefficient for B below 1 T. In high transport current
densities, or with B tilted off the twin boundaries by 5 degrees, the second
sign reversal vanishes. The power-law scaling of the Hall conductivity to the
longitudinal conductivity in the mixed state is strongly modified in the regime
of the second sign reversal. Our observations are interpreted as strong,
disorder-type dependent vortex pinning and confirm that the Hall conductivity
in high temperature superconductors is not independent of pinning.
|
We prove that the number of oscillating tableaux of length $n$ with at most
$k$ columns, starting at $\emptyset$ and ending at the one-column shape
$(1^m)$, is equal to the number of standard Young tableaux of size~$n$ with $m$
columns of odd length, all columns of length at most $2k$. This refines a
conjecture of Burrill, which it thereby establishes. We prove as well a
"Knuth-type" extension stating a similar equi-enumeration result between
generalised oscillating tableaux and semistandard tableaux.
|
This paper concerns the physical behaviors of any solutions to the one
dimensional compressible Navier-Stokes equations for viscous and heat
conductive gases with constant viscosities and heat conductivity for fast
decaying density at far fields only. First, it is shown that the specific
entropy becomes not uniformly bounded immediately after the initial time, as
long as the initial density decays to vacuum at the far field at the rate not
slower than $O\left(\frac1{|x|^{\ell_\rho}}\right)$ with $\ell_\rho>2$.
Furthermore, for faster decaying initial density, i.e., $\ell_\rho\geq4$, a
sharper result is discovered that the absolute temperature becomes uniformly
positive at each positive time, no matter whether it is uniformly positive or
not initially, and consequently the corresponding entropy behaves as
$O(-\log(\varrho_0(x)))$ at each positive time, independent of the boundedness
of the initial entropy. Such phenomena are in sharp contrast to the case with
slowly decaying initial density of the rate no faster than $O(\frac1{x^2})$,
for which our previous works \cite{LIXINADV,LIXINCPAM,LIXIN3DK} show that the
uniform boundedness of the entropy can be propagated for all positive time and
thus the temperature decays to zero at the far field. These give a complete
answer to the problem concerning the propagation of uniform boundedness of the
entropy for the heat conductive ideal gases and, in particular, show that the
algebraic decay rate $2$ of the initial density at the far field is sharp for
the uniform boundedness of the entropy. The tools to prove our main results are
based on some scaling transforms, including the Kelvin transform, and a Hopf
type lemma for a class of degenerate equations with possible unbounded
coefficients.
|
Ultrarelativistic heavy ion collisions at the laboratory provide a unique
chance to study quantum chromodynamics (QCD) under extreme temperature
(${\approx}150\,\mathrm{MeV}$) and density
(${\approx}1\,\mathrm{GeV}/\mathrm{fm}^3$) conditions. Over the past decade,
experimental results from LHC have shown further evidence for the formation of
the quark-gluon plasma (QGP), a phase that is thought to permeate the early
Universe and is formed in the high-density neutron-star cores. Various QCD
predictions that model the behavior of the low-$x$ gluon nuclear density, a
poorly explored region, are also tested. Since the photon flux per ion scales
as the square of the emitting electric charge $Z^2$, cross sections of so far
elusive photon-induced processes are extremely enhanced as compared to
nucleon-nucleon collisions. Here, we review recent progress on CMS measurements
of particle production with large transverse momentum or mass, photon-initiated
processes, jet-induced medium response, and heavy quark production. These
high-precision data, along with novel approaches, offer stringent constraints
on initial state, QGP formation and transport parameters, and even
parametrizations beyond the standard model.
|
We calculated the spectrum of normal scalar waves in a planar waveguide with
absolutely soft randomly rough boundaries beyond the perturbation theories in
the roughness heights and slopes, basing on the exact boundary scattering
potential. The spectrum is proved to be a nearly real non-analytic function of
the dispersion $\zeta^2$ of the roughness heights (with square-root
singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is
summarized.
|
Regular nutrient intake monitoring in hospitalised patients plays a critical
role in reducing the risk of disease-related malnutrition (DRM). Although
several methods to estimate nutrient intake have been developed, there is still
a clear demand for a more reliable and fully automated technique, as this could
improve the data accuracy and reduce both the participant burden and the health
costs. In this paper, we propose a novel system based on artificial
intelligence to accurately estimate nutrient intake, by simply processing RGB
depth image pairs captured before and after a meal consumption. For the
development and evaluation of the system, a dedicated and new database of
images and recipes of 322 meals was assembled, coupled to data annotation using
innovative strategies. With this database, a system was developed that employed
a novel multi-task neural network and an algorithm for 3D surface construction.
This allowed sequential semantic food segmentation and estimation of the volume
of the consumed food, and permitted fully automatic estimation of nutrient
intake for each food type with a 15% estimation error.
|
Accurate QED calculation of transition probabilities for the low-lying
two-electron configurations of multicharged ions is presented. The calculation
is performed for the nondegenerate states $(1s2s) 3S1$, $(1s2p_{3/2}) 3P2$ ($M
1$ and $M 2$ transitions, respectively) and for the quasidegenerate states
$(1s2p) 1P1$, $(1s2p) 3P1$ ($E 1$ transitions) decaying to the ground state
$(1s1s) 1S0$. Two-electron ions with nuclear charge numbers $Z=10-92$ are
considered. The line profile approach is employed for the description of the
process in multicharged ions within the framework of QED.
|
It is likely that electricity storage will play a significant role in the
balancing of future energy systems. A major challenge is then that of how to
assess the contribution of storage to capacity adequacy, i.e. to the ability of
such systems to meet demand. This requires an understanding of how to optimally
schedule multiple storage facilities. The present paper studies this problem in
the cases where the objective is the minimisation of expected energy unserved
(EEU) and also a form of weighted EEU in which the unit cost of unserved energy
is higher at higher levels of unmet demand. We also study how the contributions
of individual stores may be identified for the purposes of their inclusion in
electricity capacity markets.
|
Many supermassive black holes (SMBH) of mass $10^{6\sim9}M_{\odot}$ are
observed at the center of each galaxy even in the high redshift ($z\approx7$)
Universe. To explain the early formation and the common existence of SMBH, we
proposed previously the SMBH formation scenario by the gravitational collapse
of the coherent dark matter (DM) composed from the Bose-Einstein Condensed
(BEC) objects. A difficult problem in this scenario is the inevitable angular
momentum which prevents the collapse of BEC. To overcome this difficulty, in
this paper, we consider the very early Universe when the BEC-DM acquires its
proper angular momentum by the tidal torque mechanism. The balance of the
density evolution and the acquisition of the angular momentum determines the
mass of the SMBH as well as the mass ratio of BH and the surrounding dark halo
(DH). This ratio turns out to be
$M_{BH}/M_{DH}\approx10^{-3\sim-5}(M_{tot}/10^{12}\mathrm{M}_{\odot})^{-1/2}$
assuming simple density profiles of the initial DM cloud. This estimate turns
out to be consistent with the observations at $z\approx0$ and $z\approx6$,
although the data scatter is large. Thus the angular momentum determines the
separation of black and dark, \textsl{i.e. }SMBH and DH, in the original DM
cloud.
|
We address the problem of joint sparsity pattern recovery based on low
dimensional multiple measurement vectors (MMVs) in resource constrained
distributed networks. We assume that distributed nodes observe sparse signals
which share the same sparsity pattern and each node obtains measurements via a
low dimensional linear operator. When the measurements are collected at
distributed nodes in a communication network, it is often required that joint
sparse recovery be performed under inherent resource constraints such as
communication bandwidth and transmit/processing power.
We present two approaches to take the communication constraints into account
while performing common sparsity pattern recovery. First, we explore the use of
a shared multiple access channel (MAC) in forwarding observations residing at
each node to a fusion center. With MAC, while the bandwidth requirement does
not depend on the number of nodes, the fusion center has access to only a
linear combination of the observations. We discuss the conditions under which
the common sparsity pattern can be estimated reliably. Second, we develop two
collaborative algorithms based on Orthogonal Matching Pursuit (OMP), to jointly
estimate the common sparsity pattern in a decentralized manner with a low
communication overhead. In the proposed algorithms, each node exploits
collaboration among neighboring nodes by sharing a small amount of information
for fusion at different stages in estimating the indices of the true support in
a greedy manner. Efficiency and effectiveness of the proposed algorithms are
demonstrated via simulations along with a comparison with the most related
existing algorithms considering the trade-off between the performance gain and
the communication overhead.
|
In this review, we present a self-contained introduction to axion-like
particles (ALPs) with a particular focus on their effects on photon
polarization: both theoretical and phenomenological aspects are discussed. We
derive the photon survival probability in the presence of photon--ALP
interaction, the corresponding final photon degree of linear polarization, and
the polarization angle in a wide energy interval. The presented results can be
tested by current and planned missions such as IXPE (already operative), eXTP,
XL-Calibur, NGXP, XPP in the X-ray band and like COSI (approved to launch),
e-ASTROGAM, and AMEGO in the high-energy range. Specifically, we describe
ALP-induced polarization effects on several astrophysical sources, such as
galaxy clusters, blazars, and gamma-ray bursts, and we discuss their real
detectability. In particular, galaxy clusters appear as very good observational
targets in this respect. Moreover, in the very-high-energy (VHE) band, we
discuss a peculiar ALP signature in photon polarization, in principle capable
of proving the ALP existence. Unfortunately, present technologies cannot detect
photon polarization up to such high energies, but the observational capability
of the latter ALP signature in the VHE band could represent an interesting
challenge for the future. As a matter of fact, the aim of this review is to
show new ways to make progress in the physics of ALPs, thanks to their effects
on photon polarization, a topic that has aroused less interest in the past, but
which is now timely with the advent of many new polarimetric missions.
|
In this study, we address the off-road traversability estimation problem,
that predicts areas where a robot can navigate in off-road environments. An
off-road environment is an unstructured environment comprising a combination of
traversable and non-traversable spaces, which presents a challenge for
estimating traversability. This study highlights three primary factors that
affect a robot's traversability in an off-road environment: surface slope,
semantic information, and robot platform. We present two strategies for
estimating traversability, using a guide filter network (GFN) and footprint
supervision module (FSM). The first strategy involves building a novel GFN
using a newly designed guide filter layer. The GFN interprets the surface and
semantic information from the input data and integrates them to extract
features optimized for traversability estimation. The second strategy involves
developing an FSM, which is a self-supervision module that utilizes the path
traversed by the robot in pre-driving, also known as a footprint. This enables
the prediction of traversability that reflects the characteristics of the robot
platform. Based on these two strategies, the proposed method overcomes the
limitations of existing methods, which require laborious human supervision and
lack scalability. Extensive experiments in diverse conditions, including
automobiles and unmanned ground vehicles, herbfields, woodlands, and farmlands,
demonstrate that the proposed method is compatible for various robot platforms
and adaptable to a range of terrains. Code is available at
https://github.com/yurimjeon1892/FtFoot.
|
The interplay between band topology and magnetic order could generate a
variety of time-reversal-breaking gapped topological phases with exotic
topological quantization phenomena, such as quantum anomalous Hall (QAH)
insulators and axion insulators (AxI). Here by combining analytic models and
first-principles calculations, we predict QAH and AxI phases can be realized in
thin film of an intrinsic antiferromagnetic van der Waal material
Mn$_2$Bi$_2$Te$_5$. The phase transition between QAH and AxI is tuned by the
layer magnetization, which would provide a promising platform for chiral
superconducting phases. We further present a simple and unified continuum model
that captures the magnetic topological features, and is generic for
Mn$_2$Bi$_2$Te$_5$ and MnBi$_2$Te$_4$ family materials.
|
Let $\omega$ be an unbounded radial weight on $\mathbb{C}^d$, $d\ge 1$. Using
results related to approximation of $\omega$ by entire maps, we investigate
Volterra type and weighted composition operators defined on the growth space
$\mathcal{A}^\omega(\mathbb{C}^d)$. Special attention is given to the operators
defined on the growth Fock spaces.
|
We develop a fast and scalable computational framework to solve large-scale
and high-dimensional Bayesian optimal experimental design problems. In
particular, we consider the problem of optimal observation sensor placement for
Bayesian inference of high-dimensional parameters governed by partial
differential equations (PDEs), which is formulated as an optimization problem
that seeks to maximize an expected information gain (EIG). Such optimization
problems are particularly challenging due to the curse of dimensionality for
high-dimensional parameters and the expensive solution of large-scale PDEs. To
address these challenges, we exploit two essential properties of such problems:
the low-rank structure of the Jacobian of the parameter-to-observable map to
extract the intrinsically low-dimensional data-informed subspace, and the high
correlation of the approximate EIGs by a series of approximations to reduce the
number of PDE solves. We propose an efficient offline-online decomposition for
the optimization problem: an offline stage of computing all the quantities that
require a limited number of PDE solves independent of parameter and data
dimensions, and an online stage of optimizing sensor placement that does not
require any PDE solve. For the online optimization, we propose a swapping
greedy algorithm that first construct an initial set of sensors using leverage
scores and then swap the chosen sensors with other candidates until certain
convergence criteria are met. We demonstrate the efficiency and scalability of
the proposed computational framework by a linear inverse problem of inferring
the initial condition for an advection-diffusion equation, and a nonlinear
inverse problem of inferring the diffusion coefficient of a log-normal
diffusion equation, with both the parameter and data dimensions ranging from a
few tens to a few thousands.
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Rank-width is a width parameter of graphs describing whether it is possible
to decompose a graph into a tree-like structure by `simple' cuts. This survey
aims to summarize known algorithmic and structural results on rank-width of
graphs.
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Arrays of metallic particles patterned on a substrate have emerged as a
promising design for on-chip plasmonic lasers. In past examples of such
devices, the periodic particles provided feedback at a single resonance
wavelength, and organic dye molecules were used as the gain material. Here, we
introduce a flexible template-based fabrication method that allows a broader
design space for Ag particle-array lasers. Instead of dye molecules, we
integrate colloidal quantum dots (QDs), which offer better photostability and
wavelength tunability. Our fabrication approach also allows us to easily adjust
the refractive index of the substrate and the QD-film thickness. Exploiting
these capabilities, we demonstrate not only single-wavelength lasing but
dual-wavelength lasing via two distinct strategies. First, by using particle
arrays with rectangular lattice symmetries, we obtain feedback from two
orthogonal directions. The two output wavelengths from this laser can be
selected individually using a linear polarizer. Second, by adjusting the
QD-film thickness, we use higher-order transverse waveguide modes in the QD
film to obtain dual-wavelength lasing at normal and off-normal angles from a
symmetric square array. We thus show that our approach offers various design
possibilities to tune the laser output.
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The magnetic structure of the "nonmetallic metal" FeCrAs, a compound with the
characters of both metals and insulators, was examined as a function of
temperature using single-crystal neutron diffraction. The magnetic propagation
vector was found to be $\mathit{k}$ = (1/3, 1/3, 0), and the magnetic
reflections disppeared above $\mathit{T_{N}}$ = 116(1) K. In the ground state,
the Cr sublattice shows an in-plane spiral antiferromagnetic order. The moment
sizes of the Cr ions were found to be small, due to strong magnetic frustration
in the distorted Kagome lattice or the itinerant nature of the Cr magnetism,
and vary between 0.8 and 1.4 $\mu_{B}$ on different sites as expected for a
spin-density-wave (SDW) type order. The upper limit of the moment on the Fe
sublattice is estimated to be less than 0.1 $\mu_{B}$. With increasing
temperature up to 95 K, the Cr moments cant out of the $\mathit{ab}$ plane
gradually, with the in-plane components being suppressed and the out-of-plane
components increasing in contrast. This spin-reorientation of Cr moments can
explain the dip in the $\mathit{c}$-direction magnetic susceptibility and the
kink in the magnetic order parameter at $\mathit{T_{O}}$ ~ 100 K, a second
magnetic transition which was unexplained before. We have also discussed the
similarity between FeCrAs and the model itinerant magnet Cr, which exhibits
spin-flip transitions and SDW-type antiferromagnetism.
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Data extraction and management are crucial components of research and
clinical workflows in Radiation Oncology (RO), where accurate and comprehensive
data are imperative to inform treatment planning and delivery. The advent of
automated data mining scripts, particularly using the Python Environment for
Scripting APIs (PyESAPI), has been a promising stride towards enhancing
efficiency, accuracy, and reliability in extracting data from RO Information
Systems (ROIS) and Treatment Planning Systems (TPS). This review dissects the
role, efficiency, and challenges of implementing PyESAPI in RO data extraction
and management, juxtaposing manual data extraction techniques and explicating
future avenues
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We propose Stereo Direct Sparse Odometry (Stereo DSO) as a novel method for
highly accurate real-time visual odometry estimation of large-scale
environments from stereo cameras. It jointly optimizes for all the model
parameters within the active window, including the intrinsic/extrinsic camera
parameters of all keyframes and the depth values of all selected pixels. In
particular, we propose a novel approach to integrate constraints from static
stereo into the bundle adjustment pipeline of temporal multi-view stereo.
Real-time optimization is realized by sampling pixels uniformly from image
regions with sufficient intensity gradient. Fixed-baseline stereo resolves
scale drift. It also reduces the sensitivities to large optical flow and to
rolling shutter effect which are known shortcomings of direct image alignment
methods. Quantitative evaluation demonstrates that the proposed Stereo DSO
outperforms existing state-of-the-art visual odometry methods both in terms of
tracking accuracy and robustness. Moreover, our method delivers a more precise
metric 3D reconstruction than previous dense/semi-dense direct approaches while
providing a higher reconstruction density than feature-based methods.
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Carbon nanostructures with zigzag edges exhibit unique properties with
exciting potential applications. Such nanostructures are generally synthesized
under vacuum because their zigzag edges are unstable under ambient conditions:
a barrier that must be surmounted to achieve their scalable exploitation. Here,
we prove the viability of chemical protection/deprotection strategies for this
aim, demonstrated on labile chiral graphene nanoribbons (chGNRs). Upon
hydrogenation, the chGNRs survive an exposure to air, after which they are
easily converted back to their original structure via annealing. We also
approach the problem from another angle by synthesizing a chemically stable
oxidized form of the chGNRs that can be converted to the pristine hydrocarbon
form via hydrogenation and annealing. These findings may represent an important
step toward the integration of zigzag-edged nanostructures in devices.
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The collective operation of robots, such as unmanned aerial vehicles (UAVs)
operating as a team or swarm, is affected by their individual capabilities,
which in turn is dependent on their physical design, aka morphology. However,
with the exception of a few (albeit ad hoc) evolutionary robotics methods,
there has been very little work on understanding the interplay of morphology
and collective behavior. There is especially a lack of computational frameworks
to concurrently search for the robot morphology and the hyper-parameters of
their behavior model that jointly optimize the collective (team) performance.
To address this gap, this paper proposes a new co-design framework. Here the
exploding computational cost of an otherwise nested morphology/behavior
co-design is effectively alleviated through the novel concept of ``talent"
metrics; while also allowing significantly better solutions compared to the
typically sub-optimal sequential morphology$\to$behavior design approach. This
framework comprises four major steps: talent metrics selection, talent Pareto
exploration (a multi-objective morphology optimization process), behavior
optimization, and morphology finalization. This co-design concept is
demonstrated by applying it to design UAVs that operate as a team to localize
signal sources, e.g., in victim search and hazard localization. Here, the
collective behavior is driven by a recently reported batch Bayesian search
algorithm called Bayes-Swarm. Our case studies show that the outcome of
co-design provides significantly higher success rates in signal source
localization compared to a baseline design, across a variety of signal
environments and teams with 6 to 15 UAVs. Moreover, this co-design process
provides two orders of magnitude reduction in computing time compared to a
projected nested design approach.
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In materials without spatial inversion symmetry the spin degeneracy of the
conduction electrons can be lifted by an antisymmetric spin-orbit coupling. We
discuss the influence of this spin-orbit coupling on the spin susceptibility of
such superconductors, with a particular emphasis on the recently discovered
heavy Fermion superconductor CePt3Si. We find that, for this compound (with
tetragonal crystal symmetry,) irrespective of the pairing symmetry, the stable
superconducting phases would give a very weak change of the spin susceptibility
for fields along the c-axis and an intermediate reduction for fields in the
basal plane. We also comment on the consequences for the paramagnetic limiting
in this material.
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The validation of any database mining methodology goes through an evaluation
process where benchmarks availability is essential. In this paper, we aim to
randomly generate relational database benchmarks that allow to check
probabilistic dependencies among the attributes. We are particularly interested
in Probabilistic Relational Models (PRMs), which extend Bayesian Networks (BNs)
to a relational data mining context and enable effective and robust reasoning
over relational data. Even though a panoply of works have focused, separately ,
on the generation of random Bayesian networks and relational databases, no work
has been identified for PRMs on that track. This paper provides an algorithmic
approach for generating random PRMs from scratch to fill this gap. The proposed
method allows to generate PRMs as well as synthetic relational data from a
randomly generated relational schema and a random set of probabilistic
dependencies. This can be of interest not only for machine learning researchers
to evaluate their proposals in a common framework, but also for databases
designers to evaluate the effectiveness of the components of a database
management system.
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In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard
analysis and the finitization of soft analysis statements into hard analysis
statements. One of his main examples was a quasi-finitization of the infinite
pigeonhole principle IPP, arriving at the "finitary" infinite pigeonhole
principle FIPP1. That turned out to not be the proper formulation and so we
proposed an alternative version FIPP2. Tao himself formulated yet another
version FIPP3 in a revised version of his essay.
We give a counterexample to FIPP1 and discuss for both of the versions FIPP2
and FIPP3 the faithfulness of their respective finitization of IPP by studying
the equivalences IPP <-> FIPP2 and IPP <-> FIPP3 in the context of reverse
mathematics. In the process of doing this we also introduce a continuous
uniform boundedness principle CUB as a formalization of Tao's notion of a
correspondence principle and study the strength of this principle and various
restrictions thereof in terms of reverse mathematics, i.e., in terms of the
"big five" subsystems of second order arithmetic.
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"KPipe" is a proposed experiment which will study muon neutrino disappearance
for a sensitive test of the $\Delta m^2\sim1 \mathrm{eV}^2$ anomalies, possibly
indicative of one or more sterile neutrinos. The experiment is to be located at
the J-PARC Materials and Life Science Facility's spallation neutron source,
which represents the world's most intense source of charged kaon decay-at-rest
monoenergetic (236 MeV) muon neutrinos. The detector vessel, designed to
measure the charged current interactions of these neutrinos, will be 3 m in
diameter and 120 m long, extending radially at a distance of 32 m to 152 m from
the source. This design allows a sensitive search for $\nu_\mu$ disappearance
associated with currently favored light sterile neutrino models and features
the ability to reconstruct the neutrino oscillation wave within a single,
extended detector. The required detector design, technology, and costs are
modest. The KPipe measurements will be robust since they depend on a known
energy neutrino source with low expected backgrounds. Further, since the
measurements rely only on the measured rate of detected events as a function of
distance, with no required knowledge of the initial flux and neutrino
interaction cross section, the results will be largely free of systematic
errors. The experimental sensitivity to oscillations, based on a shape-only
analysis of the $L/E$ distribution, will extend an order of magnitude beyond
present experimental limits in the relevant high-$\Delta m^2$ parameter space.
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Recent experimental data on the $\Upsilon(4S)\to\Upsilon(1S)\eta$ and
$\Upsilon(4S)\to h_{b}(1P)\eta$ processes seem to contradict the naive
expectation that hadronic transitions with spin-flipping terms should be
suppressed with respect those without spin-flip. We analyze these transitions
using the QCD Multipole Expansion (QCDME) approach and within a constituent
quark model framework that has been applied successfully to the heavy-quark
sectors during the last years. The QCDME formalism requires the computation of
hybrid intermediate states which has been performed in a natural,
parameter-free extension of our constituent quark model based on the Quark
Confining String (QCS) scheme. We show that i) the M1-M1 contribution in the
decay rate of the $\Upsilon(4S)\to\Upsilon(1S)\eta$ is important and its
supression until now is not justified; ii) the role played by the $L=0$ hybrid
states, which enter in the calculation of the M1-M1 contribution, explains the
enhancement in the $\Upsilon(4S)\to\Upsilon(1S)\eta$ decay rate; and iii) the
anomalously large decay rate of the $\Upsilon(4S)\to h_{b}(1P)\eta$ process has
the same physical origin.
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In this article we focus on a general model of random walk on random marked
trees. We prove a recurrence criterion, analogue to the recurrence criterion
proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In
the critical case, we obtain a criterion for the positive/null recurrence.
Several regimes appear, as proved (in a similar model), by Y. Hu and Z. Shi
(2007). We focus on the "diffusive" regime and improve their result in this
case, by obtaining a functional Central Limit Theorem. Our result is also an
extension of a result by Y. Peres and O. Zeitouni (2008), obtained in the
setting of biased random walk in Galton-Watson trees.
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We provide a fast method for computing constraints on impactor pre-impact
orbits, applying this to the late giant impacts in the Solar System. These
constraints can be used to make quick, broad comparisons of different collision
scenarios, identifying some immediately as low-probability events, and
narrowing the parameter space in which to target follow-up studies with
expensive N-body simulations. We benchmark our parameter space predictions,
finding good agreement with existing N-body studies for the Moon. We suggest
that high-velocity impact scenarios in the inner Solar System, including all
currently proposed single impact scenarios for the formation of Mercury, should
be disfavoured. This leaves a multiple hit-and-run scenario as the most
probable currently proposed for the formation of Mercury.
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Ground-based laser interferometric gravitational wave detectors consist of
complex multiple optical cavity systems. An arm-length stabilization (ALS)
system has played an important role in bringing such complex detector into
operational state and enhance the duty cycle. The sensitivity of these
detectors can be improved if the thermal noise of their test mass mirror
coatings is reduced. Crystalline AlGaAs coatings are a promising candidate for
this. However, traditional ALS system with frequency-doubled 532 nm light is no
longer an option with AlGaAs coatings due to the narrow bandgap of GaAs, thus
alternative locking schemes must be developed. In this letter, we describe an
experimental demonstration of a novel ALS scheme which is compatible with
AlGaAs coatings. This ALS scheme will enable the use of AlGaAs coatings and
contribute to improved sensitivity of future detectors.
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In this paper, we study genus $0$ equivariant relative Gromov-Witten
invariants of $\mathbb{P}^1$ whose corresponding relative stable maps are
totally ramified over one point. For fixed number of marked points, we show
that such invariants are piecewise polynomials in some parameter space. The
parameter space can then be divided into polynomial domains, called chambers.
We determine the difference of polynomials between two neighboring chambers. In
some special chamber, which we called the totally negative chamber, we show
that such a polynomial can be expressed in a simple way. The chamber structure
here shares some similarities to that of double Hurwitz numbers.
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We study the problem of the existence of arithmetic progressions of three
cubes over quadratic number fields Q(sqrt(D)), where D is a squarefree integer.
For this purpose, we give a characterization in terms of Q(sqrt(D))-rational
points on the elliptic curve E:y^2=x^3-27. We compute the torsion subgroup of
the Mordell-Weil group of this elliptic curve over Q(sqrt(D)) and we give
partial answers to the finiteness of the free part of E(Q(sqrt(D))). This last
task will be translated to compute if the rank of the quadratic D-twist of the
modular curve X_0(36) is zero or not.
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In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius
pushforward of the structure sheaf on the adjoint varieties in type ${\bf A}_3$
and ${\bf A}_4$. We show that this pushforward sheaf decomposes into a direct
sum of indecomposable bundles and explicitly determine this set that does not
depend of the characteristic. In accordance with the results of
arXiv:0707.0913, this set forms a strong full exceptional collection in the
derived category of coherent sheaves. These computations lead to a natural
conjectural answer in the general case that we state at the end.
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In this paper we are concerned with numerical methods for nonhomogeneous
Helmholtz equations in inhomogeneous media. We design a least squares method
for discretization of the considered Helmholtz equations. In this method, an
auxiliary unknown is introduced on the common interface of any two neighboring
elements and a quadratic subject functional is defined by the jumps of the
traces of the solutions of local Helmholtz equations across all the common
interfaces, where the local Helmholtz equations are defined on elements and are
imposed Robin-type boundary conditions given by the auxiliary unknowns. A
minimization problem with the subject functional is proposed to determine the
auxiliary unknowns. The resulting discrete system of the auxiliary unknowns is
Hermitian positive definite and so it can be solved by the PCG method. Under
some assumptions we show that the generated approximate solutions possess
almost the optimal error estimates with little "wave number pollution".
Moreover, we construct a substructuring preconditioner for the discrete system
of the auxiliary unknowns. Numerical experiments show that the proposed methods
are very effective for the tested Helmholtz equations with large wave numbers.
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Foundation models are rapidly being developed for computational pathology
applications. However, it remains an open question which factors are most
important for downstream performance with data scale and diversity, model size,
and training algorithm all playing a role. In this work, we present the result
of scaling both data and model size, surpassing previous studies in both
dimensions, and introduce two new models: Virchow 2, a 632M parameter vision
transformer, and Virchow 2G, a 1.85B parameter vision transformer, each trained
with 3.1M histopathology whole slide images. To support this scale, we propose
domain-inspired adaptations to the DINOv2 training algorithm, which is quickly
becoming the default method in self-supervised learning for computational
pathology. We achieve state of the art performance on twelve tile-level tasks,
as compared to the top performing competing models. Our results suggest that
data diversity and domain-specific training can outperform models that only
scale in the number of parameters, but, on average, performance benefits from
domain-tailoring, data scale, and model scale.
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We present a full-program induction technique for proving (a sub-class of)
quantified as well as quantifier-free properties of programs manipulating
arrays of parametric size N. Instead of inducting over individual loops, our
technique inducts over the entire program (possibly containing multiple loops)
directly via the program parameter N. Significantly, this does not require
generation or use of loop-specific invariants. We have developed a prototype
tool Vajra to assess the efficacy of our technique. We demonstrate the
performance of Vajra vis-a-vis several state-of-the-art tools on a set of array
manipulating benchmarks.
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This paper rediscovers a classical homogenization result for a prototypical
linear elliptic boundary value problem with periodically oscillating diffusion
coefficient. Unlike classical analytical approaches such as asymptotic
analysis, oscillating test functions, or two-scale convergence, the result is
purely based on the theory of domain decomposition methods and standard finite
elements techniques. The arguments naturally generalize to problems far beyond
periodicity and scale separation and we provide a brief overview on such
applications.
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The gravity model, inspired by Newton's law of universal gravitation, has
long served as a primary tool for interpreting trade flows between countries,
using a country's economic `mass' as a key determinant. Despite its wide
application, the definition of `mass' within this model remains ambiguous. It
is often approximated using indicators like GDP, which may not accurately
reflect a country's true trade potential. Here, we introduce a data-driven,
self-consistent numerical approach that redefines `mass' from a static proxy to
a dynamic attribute inferred directly from flow data. We infer mass
distribution and interaction nature through our method, mirroring Newton's
approach to understanding gravity. Our methodology accurately identifies
predefined embeddings and reconstructs system attributes when applied to
synthetic flow data, demonstrating its strong predictive power and
adaptability. Further application to real-world trade networks yields critical
insights, revealing the spatial spectrum of trade flows and the economic mass
of countries, two key features unexplored in depth by existing models. Our
methodology not only enables accurate reconstruction of the original flow but
also allows for a deep understanding of the unique capabilities of each node
within the network. This study marks a significant shift in the understanding
and application of the gravity model, providing a more comprehensive tool for
analyzing complex systems and uncovering new insights into various fields,
including global trade, traffic engineering, epidemic disease prevention, and
infrastructure design.
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In this paper we obtain a representation as martingale transform operators
for the rearrangement and shift operators introduced by T. Figiel. The
martingale transforms and the underlying sigma algebras are obtained explicitly
by combinatorial means. The known norm estimates for those operators are a
direct consequence of our representation.
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A conducting 1D line or 2D plane inside (or on the surface of) an insulator
is considered.Impurities displace the charges inside the insulator. This
results in a long-range fluctuating electric field acting on the conducting
line (plane). This field can be modeled by that of randomly distributed
electric dipoles. This model provides a random correlated potential with
<U(r)U(r+k)> decaying as 1/k . In the 1D case such correlations give essential
corrections to the localization length but do not destroy Anderson
localization.
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We investigate diagonal forms of degree $d$ over the function field $F$ of a
smooth projective $p$-adic curve: if a form is isotropic over the completion of
$F$ with respect to each discrete valuation of $F$, then it is isotropic over
certain fields $F_U$, $F_P$ and $F_p$. These fields appear naturally when
applying the methodology of patching; $F$ is the inverse limit of the finite
inverse system of fields $\{F_U,F_P,F_p\}$. Our observations complement some
known bounds on the higher $u$-invariant of diagonal forms of degree $d$. We
only consider diagonal forms of degree $d$ over fields of characteristic not
dividing $d!$.
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