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Causal disentanglement seeks a representation of data involving latent
variables that relate to one another via a causal model. A representation is
identifiable if both the latent model and the transformation from latent to
observed variables are unique. In this paper, we study observed variables that
are a linear transformation of a linear latent causal model. Data from
interventions are necessary for identifiability: if one latent variable is
missing an intervention, we show that there exist distinct models that cannot
be distinguished. Conversely, we show that a single intervention on each latent
variable is sufficient for identifiability. Our proof uses a generalization of
the RQ decomposition of a matrix that replaces the usual orthogonal and upper
triangular conditions with analogues depending on a partial order on the rows
of the matrix, with partial order determined by a latent causal model. We
corroborate our theoretical results with a method for causal disentanglement
that accurately recovers a latent causal model.
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While instruction-tuned language models have demonstrated impressive
zero-shot generalization, these models often struggle to generate accurate
responses when faced with instructions that fall outside their training set.
This paper presents Instructive Decoding (ID), a simple yet effective approach
that augments the efficacy of instruction-tuned models. Specifically, ID
adjusts the logits for next-token prediction in a contrastive manner, utilizing
predictions generated from a manipulated version of the original instruction,
referred to as a noisy instruction. This noisy instruction aims to elicit
responses that could diverge from the intended instruction yet remain
plausible. We conduct experiments across a spectrum of such noisy instructions,
ranging from those that insert semantic noise via random words to others like
'opposite' that elicit the deviated responses. Our approach achieves
considerable performance gains across various instruction-tuned models and
tasks without necessitating any additional parameter updates. Notably,
utilizing 'opposite' as the noisy instruction in ID, which exhibits the maximum
divergence from the original instruction, consistently produces the most
significant performance gains across multiple models and tasks.
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We check The Vaisman condition of geometric quantization for R-matrix type
Poisson pencil on a coadjoint orbit of a compact Lie group. It is shown that
this condition isn't satisfied.
|
It is well established that the notion of min-entropy fails to satisfy the
\emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon
Entropy. Such a property would help to analyze how min-entropy is split among
smaller blocks. Problems of this kind arise for example when constructing
extractors and dispersers.
We show that any sequence of variables exhibits a very strong strong
block-source structure (conditional distributions of blocks are nearly flat)
when we \emph{spoil few correlated bits}. This implies, conditioned on the
spoiled bits, that \emph{splitting-recombination properties} hold. In
particular, we have many nice properties that min-entropy doesn't obey in
general, for example strong chain rules, "information can't hurt" inequalities,
equivalences of average and worst-case conditional entropy definitions and
others. Quantitatively, for any sequence $X_1,\ldots,X_t$ of random variables
over an alphabet $\mathcal{X}$ we prove that, when conditioned on $m = t\cdot
O( \log\log|\mathcal{X}| + \log\log(1/\epsilon) + \log t)$ bits of auxiliary
information, all conditional distributions of the form $X_i|X_{<i}$ are
$\epsilon$-close to be nearly flat (only a constant factor away). The argument
is combinatorial (based on simplex coverings).
This result may be used as a generic tool for \emph{exhibiting block-source
structures}. We demonstrate this by reproving the fundamental converter due to
Nisan and Zuckermann (\emph{J. Computer and System Sciences, 1996}), which
shows that sampling blocks from a min-entropy source roughly preserves the
entropy rate. Our bound implies, only by straightforward chain rules, an
additive loss of $o(1)$ (for sufficiently many samples), which qualitatively
meets the first tighter analysis of this problem due to Vadhan
(\emph{CRYPTO'03}), obtained by large deviation techniques.
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It is shown that "nonintegrable phases of Wilson line integrals" are not true
dynamical variables in Chern-Simons field theory.
|
User engagement prediction plays a critical role for designing interaction
strategies to grow user engagement and increase revenue in online social
platforms. Through the in-depth analysis of the real-world data from the
world's largest professional social platforms, i.e., LinkedIn, we find that
users expose diverse engagement patterns, and a major reason for the
differences in user engagement patterns is that users have different intents.
That is, people have different intents when using LinkedIn, e.g., applying for
jobs, building connections, or checking notifications, which shows quite
different engagement patterns. Meanwhile, user intents and the corresponding
engagement patterns may change over time. Although such pattern differences and
dynamics are essential for user engagement prediction, differentiating user
engagement patterns based on user dynamic intents for better user engagement
forecasting has not received enough attention in previous works. In this paper,
we proposed a Dynamic Intent Guided Meta Network (DIGMN), which can explicitly
model user intent varying with time and perform differentiated user engagement
forecasting. Specifically, we derive some interpretable basic user intents as
prior knowledge from data mining and introduce prior intents in explicitly
modeling dynamic user intent. Furthermore, based on the dynamic user intent
representations, we propose a meta predictor to perform differentiated user
engagement forecasting. Through a comprehensive evaluation on LinkedIn
anonymous user data, our method outperforms state-of-the-art baselines
significantly, i.e., 2.96% and 3.48% absolute error reduction, on
coarse-grained and fine-grained user engagement prediction tasks, respectively,
demonstrating the effectiveness of our method.
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The space density of the various classes of cataclysmic variables (CVs) could
only be weakly constrained in the past. Reasons were the small number of
objects in complete X-ray flux-limited samples and the difficulty to derive
precise distances to CVs. The former limitation still exists. Here the impact
of Gaia parallaxes and implied distances on the space density of X-ray selected
complete, flux-limited samples is studied. The samples are described in the
literature, those of non-magnetic CVs are based on ROSAT (RBS - ROSAT Bright
Survey & NEP -- North Ecliptic Pole), that of the Intermediate Polars stems
from Swift/BAT. All CVs appear to be rarer than previously thought, although
the new values are all within the errors of past studies. Upper limits at 90\%
confidence for the space densities of non-magnetic CVs are $\rho_{\rm RBS} <
1.1 \times 10^{-6}$ pc$^{-3}$, and $\rho_{\rm RBS+NEP} < 5.1 \times 10^{-6}$
p$^{-3}$, for an assumed scale height of $h=260$ pc and $\rho_{\rm IPs} < 1.3
\times 10^{-7}$ p$^{-3}$ for the long-period Intermediate Polars at a scale
height of 120 pc. Most of the distances to the IPs were under-estimated in the
past. The upper limits to the space densities are only valid in the case where
CVs do not have lower X-ray luminosities than the lowest-luminosity member of
the sample. These results need consolidation by larger sample sizes, soon to be
established through sensitive X-ray all-sky surveys to be performed with
eROSITA on the Spektrum-X-Gamma mission.
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We construct a simple symplectic map to study the dynamics of eccentric
orbits in non-spherical potentials. The map offers a dramatic improvement in
speed over traditional integration methods, while accurately representing the
qualitative details of the dynamics. We focus attention on planar,
non-axisymmetric power-law potentials, in particular the logarithmic potential.
We confirm the presence of resonant orbit families (``boxlets'') in this
potential and uncover new dynamics such as the emergence of a stochastic web in
nearly axisymmetric logarithmic potentials. The map can also be applied to
triaxial, lopsided, non-power-law and rotating potentials.
|
Loopable music generation systems enable diverse applications, but they often
lack controllability and customization capabilities. We argue that enhancing
controllability can enrich these models, with emotional expression being a
crucial aspect for both creators and listeners. Hence, building upon LooperGP,
a loopable tablature generation model, this paper explores endowing systems
with control over conveyed emotions. To enable such conditional generation, we
propose integrating musical knowledge by utilizing multi-granular semantic and
musical features during model training and inference. Specifically, we
incorporate song-level features (Emotion Labels, Tempo, and Mode) and bar-level
features (Tonal Tension) together to guide emotional expression. Through
algorithmic and human evaluations, we demonstrate the approach's effectiveness
in producing music conveying two contrasting target emotions, happiness and
sadness. An ablation study is also conducted to clarify the contributing
factors behind our approach's results.
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We prove that the BRST complex of a topological conformal field theory is a
homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We
also suggest a refinement of the original conjecture for topological vertex
operator algebras. We illustrate the usefulness of our main tools, operads and
"string vertices" by obtaining new results on Vassiliev invariants of knots and
double loop spaces.
|
Multilead ECG compression (MlEC) has attracted tremendous attention in
long-term monitoring of the patients heart behavior. This paper proposes a
method denoted by block sparse MlEC (BlS MlEC) in order to exploit between-lead
correlations to compress the signals in a more efficient way. This is due to
the fact that multi-lead ECG signals are multiple observations of the same
source (heart) from different locations. Consequently, they have high
correlation in terms of the support set of their sparse models which leads them
to share dominant common structure. In order to obtain the block sparse model,
the collaborative version of lasso estimator is applied. In addition, we have
shown that raised cosine kernel has advantages over conventional Gaussian and
wavelet (Daubechies family) due to its specific properties. It is demonstrated
that using raised cosine kernel in constructing the sparsifying basis matrix
gives a sparser model which results in higher compression ratio and lower
reconstruction error. The simulation results show the average improvement of
37%, 88% and 90-97% for BlS M-lEC compared to the non-collaborative case with
raised cosine kernel, Gaussian kernel and collaborative case with Daubechies
wavelet kernels, respectively, in terms of reconstruction error while the
compression ratio is considered fixed.
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A phenomenological extension of the well-known brane-world cosmology of
Dvali, Gabadadze and Porrati (eDGP) has recently been proposed. In this model,
a cosmological-constant-like term is explicitly present as a non-vanishing
tension sigma on the brane, and an extra parameter alpha tunes the cross-over
scale r_c, the scale at which higher dimensional gravity effects become non
negligible. Since the Hubble parameter in this cosmology reproduces the same
LCDM expansion history, we study how upcoming weak lensing surveys, such as
Euclid and DES (Dark Energy Survey), can confirm or rule out this class of
models. We perform Markov Chain Monte Carlo simulations to determine the
parameters of the model, using Type Ia Supernov\ae, H(z) data, Gamma Ray Bursts
and Baryon Acoustic Oscillations. We also fit the power spectrum of the
temperature anisotropies of the Cosmic Microwave Background to obtain the
correct normalisation for the density perturbation power spectrum. Then, we
compute the matter and the cosmic shear power spectra, both in the linear and
non-linear regimes. The latter is calculated with the two different approaches
of Hu and Sawicki (2007) (HS) and Khoury and Wyman (2009) (KW). With the eDGP
parameters coming from the Markov Chains, KW reproduces the LCDM matter power
spectrum at both linear and non-linear scales and the LCDM and eDGP shear
signals are degenerate. This result does not hold with the HS prescription:
Euclid can distinguish the eDGP model from LCDM because their expected power
spectra roughly differ by the 3sigma uncertainty in the angular scale range
700<l<3000; on the contrary, the two models differ at most by the 1sigma
uncertainty over the range 500<l<3000 in the DES experiment and they are
virtually indistinguishable.
|
While short range 3D pedestrian detection is sufficient for emergency
breaking, long range detections are required for smooth breaking and gaining
trust in autonomous vehicles. The current state-of-the-art on the KITTI
benchmark performs suboptimal in detecting the position of pedestrians at long
range. Thus, we propose an approach specifically targeting long range 3D
pedestrian detection (LRPD), leveraging the density of RGB and the precision of
LiDAR. Therefore, for proposals, RGB instance segmentation and LiDAR point
based proposal generation are combined, followed by a second stage using both
sensor modalities symmetrically. This leads to a significant improvement in mAP
on long range compared to the current state-of-the art. The evaluation of our
LRPD approach was done on the pedestrians from the KITTI benchmark.
|
We discuss regularity statements for equidistant decompositions of Riemannian
manifolds and for the corresponding quotient spaces. We show that any stratum
of the quotient space has curvature locally bounded from both sides.
|
The demonstration of optical multipath interference from a large number of
quantum emitters is essential for the realization of many paradigmatic
experiments in quantum optics. However, such interference remains still
unexplored as it crucially depends on the sub-wavelength positioning accuracy
and stability of all emitters. We present the observation of controlled
interference of light scattered from strings of up to 53~trapped ions. The
light scattered from ions localized in a harmonic trapping potential is
collected along the ion crystal symmetry axis, which guarantees the spatial
indistinguishability and allows for an efficient scaling of the contributing
ion number. We achieve the preservation of the coherence of scattered light
observable for all the measured string sizes and nearly-optimal enhancement of
phase sensitivity. The presented results will enable realization and control of
directional photon emission, direct detection of enhanced quadrature squeezing
of atomic resonance fluorescence, or optical generation of genuine
multi-partite entanglement of atoms.
|
Excess noise from scattered light poses a persistent challenge in the
analysis of data from gravitational wave detectors such as LIGO. We integrate a
physically motivated model for the behavior of these "glitches" into a standard
Bayesian analysis pipeline used in gravitational wave science. This allows for
the inference of the free parameters in this model, and subtraction of these
models to produce glitch-free versions of the data. We show that this inference
is an effective discriminator of the presence of the features of these
glitches, even when those features may not be discernible in standard
visualizations of the data.
|
We present a study of the statistical properties of three velocity dispersion
and mass estimators, namely biweight, gapper and standard deviation, in the
small number of galaxies regime ($N_{\rm gal} \le 75$).
Using a set of 73 numerically simulated galaxy clusters, we characterise the
statistical bias and the variance for the three estimators, both in the
determination of the velocity dispersion and the dynamical mass of the clusters
via the $\sigma-M$ relation. The results are used to define a new set of
unbiased estimators, that are able to correct for those statistical biases with
a minimal increase of the associated variance. The numerical simulations are
also used to characterise the impact of velocity segregation in the selection
of cluster members, and the impact of using cluster members within different
physical radii from the cluster centre.
The standard deviation is found to be the lowest variance estimator. The
selection of galaxies within the sub-sample of the most massive galaxies in the
cluster introduces a $2\,$\% bias in the velocity dispersion estimate when
calculated using a quarter of the most massive cluster members. We also find a
dependence of the velocity dispersion estimate on the aperture radius as a
fraction of $R_{200}$, consistent with previous results.
The proposed set of unbiased estimators effectively provides a correction of
the velocity dispersion and mass estimates from all those effects in the small
number of cluster members regime. This is tested by applying the new estimators
to a subset of simulated observations. Although for a single galaxy cluster the
statistical and physical effects discussed here are comparable or slightly
smaller than the bias introduced by interlopers, they will be of relevance when
dealing with ensemble properties and scaling relations for large cluster
samples (Abridged).
|
The qualitative difference between the anomalous scaling properties of
hadronic final states in soft and hard processes of high energy collisions is
studied in some detail. It is pointed out that the experimental data of e^+e^-
collisions at $E_{cm}=$91.2 GeV from DELPHI indicate that the dynamical
fluctuations in e^+e^- collisions are isotropical, in contrast to the
anisotropical fluctuations oberserved in hadron-hadron collision experiments.
This assertion is confirmed by the Monte Carlo simulation using the Jetset7.4
event generator.
|
Realizing faster experimental cycle times is important for the future of
quantum simulation. The cycle time determines how often the many-body
wave-function can be sampled, defining the rate at which information is
extracted from the quantum simulation. We demonstrate a system which can
produce a Bose-Einstein condensate of $8 \times 10^4$ $^{168}\text{Er}$ atoms
with approximately 85% condensate fraction in 800 ms and a degenerate Fermi gas
of $^{167}\text{Er}$ in 4 seconds, which are unprecedented times compared to
many existing quantum gas experiments. This is accomplished by several novel
cooling techniques and a tunable dipole trap. The methods used here for
accelerating the production of quantum degenerate gases should be applicable to
a variety of atomic species and are promising for expanding the capabilities of
quantum simulation.
|
Space-time (ST) beams, ultrafast optical wavepackets with customized spatial
and temporal characteristics, present a significant contrast to conventional
spatial-structured light and hold the potential to revolutionize our
understanding and manipulation of light. However, the progress in ST beam
research has been constrained by the absence of a universal framework for their
analysis and generation. Here, we introduce the concept of "two-dimensional ST
duality", establishing a foundational duality between spatial-structured light
and ST beams. We show that breaking the exact balance between paraxial
diffraction and narrow-band dispersion is crucial for guiding the dynamics of
ST wavepackets. Leveraging this insight, we pioneer a versatile
complex-amplitude modulation strategy, enabling the precise crafting of ST
beams with an exceptional fidelity exceeding 97%. Furthermore, we uncover a new
range of ST wavepackets by harnessing the exact one-to-one relationship between
scalar spatial-structured light and ST beams. Our findings suggest a paradigm
shift opportunity in ST beam research and may apply to a broader range of wave
physics systems.
|
We show that the light-front vaccum is not trivial, and the Fock space for
positive energy quanta solutions is not complete. As an example of this non
triviality we have calculated the electromagnetic current for scalar bosons in
the background field method were the covariance is restored through considering
the complete Fock space of solutions. We also show thus that the method of
"dislocating the integration pole" is nothing more than a particular case of
this, so that such an "ad hoc" prescription can be dispensed altogether if we
deal with the whole Fock space. In this work we construct the electromagnetic
current operator for a system composed of two free bosons. The technique
employed to deduce these operators is through the definition of global
propagators in the light front when a background electromagnetic field acts on
one of the particles.
|
Double pants decompositions were introduced in our paper "Double pants
decompositions of 2-surfaces" (Mosc. Math. J. 11 (2011), no. 2, 231-258,
arXiv:1005.0073), together with a flip-twist groupoid acting on these
decompositions. It was shown that flip-twist groupoid acts transitively on a
certain topological class of the decompositions, however, recently Randich
discovered a serious mistake in the proof. In this note we present a new proof
of the result, accessible without reading the initial paper.
|
Large Language Models (LLMs) have recently shown impressive abilities in
handling various natural language-related tasks. Among different LLMs, current
studies have assessed ChatGPT's superior performance across manifold tasks,
especially under the zero/few-shot prompting conditions. Given such successes,
the Recommender Systems (RSs) research community have started investigating its
potential applications within the recommendation scenario. However, although
various methods have been proposed to integrate ChatGPT's capabilities into
RSs, current research struggles to comprehensively evaluate such models while
considering the peculiarities of generative models. Often, evaluations do not
consider hallucinations, duplications, and out-of-the-closed domain
recommendations and solely focus on accuracy metrics, neglecting the impact on
beyond-accuracy facets. To bridge this gap, we propose a robust evaluation
pipeline to assess ChatGPT's ability as an RS and post-process ChatGPT
recommendations to account for these aspects. Through this pipeline, we
investigate ChatGPT-3.5 and ChatGPT-4 performance in the recommendation task
under the zero-shot condition employing the role-playing prompt. We analyze the
model's functionality in three settings: the Top-N Recommendation, the
cold-start recommendation, and the re-ranking of a list of recommendations, and
in three domains: movies, music, and books. The experiments reveal that ChatGPT
exhibits higher accuracy than the baselines on books domain. It also excels in
re-ranking and cold-start scenarios while maintaining reasonable
beyond-accuracy metrics. Furthermore, we measure the similarity between the
ChatGPT recommendations and the other recommenders, providing insights about
how ChatGPT could be categorized in the realm of recommender systems. The
evaluation pipeline is publicly released for future research.
|
Phonon measurements in the A15-type superconductors were complicated in the
past because of the unavailability of large single crystals for inelastic
neutron scattering, e.g., in the case of Nb$_3$Sn, or unfavorable neutron
scattering properties in the case of V$_3$Si. Hence, only few studies of the
lattice dynamical properties with momentum resolved methods were published, in
particular below the superconducting transition temperature $T_c$. Here, we
overcome these problems by employing inelastic x-ray scattering and report a
combined experimental and theoretical investigation of lattice dynamics in
V$_3$Si with the focus on the temperature-dependent properties of low-energy
acoustic phonon modes in several high-symmetry directions. We paid particular
attention to the evolution of the soft phonon mode of the structural phase
transition observed in our sample at $T_s=18.9\,\rm{K}$, i.e., just above the
measured superconducting phase transition at $T_c=16.8\,\rm{K}$. Theoretically,
we predict lattice dynamics including electron-phonon coupling based on
density-functional-perturbation theory and discuss the relevance of the soft
phonon mode with regard to the value of $T_c$. Furthermore, we explain
superconductivityinduced anomalies in the lineshape of several acoustic phonon
modes using a model proposed by Allen et al., [Phys. Rev. B 56, 5552 (1997)].
|
A small number of double-lobed radio galaxies (17 from our own census of the
literature) show an additional pair of low surface brightness `wings', thus
forming an overall `X'-shaped appearance. The origin of the wings in these
radio sources is unclear. They may be the result of back-flowing plasma from
the currently active radio lobes into an asymmetric medium surrounding the
active nucleus, which would make these ideal systems in which to study
thermal/non-thermal plasma interactions in extragalactic radio sources. Another
possibility is that the wings are the aging radio lobes left over after a
(rapid) realignment of the central supermassive black-hole/accretion disk
system due perhaps to a merger. Generally, these models are not well tested;
with the small number of known examples, previous works focused on detailed
case studies of selected sources with little attempt at a systematic study of a
large sample. Using the VLA-FIRST survey database, we are compiling a large
sample of winged and X-shaped radio sources for such studies. As a first step
toward this goal, an initial sample of 100 new candidate objects of this type
are presented in this paper. ...[abridged]
|
The latent class model is a powerful unsupervised clustering algorithm for
categorical data. Many statistics exist to test the fit of the latent class
model. However, traditional methods to evaluate those fit statistics are not
always useful. Asymptotic distributions are not always known, and empirical
reference distributions can be very time consuming to obtain. In this paper we
propose a fast resampling scheme with which any type of model fit can be
assessed. We illustrate it here on the latent class model, but the methodology
can be applied in any situation.
The principle behind the lazy bootstrap method is to specify a statistic
which captures the characteristics of the data that a model should capture
correctly. If those characteristics in the observed data and in model-generated
data are very different we can assume that the model could not have produced
the observed data. With this method we achieve the flexibility of tests from
the Bayesian framework, while only needing maximum likelihood estimates. We
provide a step-wise algorithm with which the fit of a model can be assessed
based on the characteristics we as researcher find important. In a Monte Carlo
study we show that the method has very low type I errors, for all illustrated
statistics. Power to reject a model depended largely on the type of statistic
that was used and on sample size. We applied the method to an empirical data
set on clinical subgroups with risk of Myocardial infarction and compared the
results directly to the parametric bootstrap. The results of our method were
highly similar to those obtained by the parametric bootstrap, while the
required computations differed three orders of magnitude in favour of our
method.
|
We study transfer principles for upper bounds of motivic exponential
functions and for linear combinations of such functions, directly generalizing
the transfer principles from [7] by Cluckers-Loeser and [13, Appendix B] by
Shin-Templier (appendix B by Cluckers-Gordon-Halupczok). These functions come
from rather general oscillatory integrals on local fields, and can be used to
describe e.g. Fourier transforms of orbital integrals. One of our techniques
consists in reducing to simpler functions where the oscillation only comes from
the residue field.
|
During its first 4 months of taking data, Advanced LIGO has detected
gravitational waves from two binary black hole mergers, GW150914 and GW151226,
along with the statistically less significant binary black hole merger
candidate LVT151012. We use our rapid binary population synthesis code COMPAS
to show that all three events can be explained by a single evolutionary channel
-- classical isolated binary evolution via mass transfer including a common
envelope phase. We show all three events could have formed in low-metallicity
environments (Z = 0.001) from progenitor binaries with typical total masses
$\gtrsim 160 M_\odot$, $\gtrsim 60 M_\odot$ and $\gtrsim 90 M_\odot$, for
GW150914, GW151226, and LVT151012, respectively.
|
We report the discovery of a new Small Magellanic Cloud Pulsar Wind Nebula
(PWN) at the edge of the Supernova Remnant (SNR)-DEM S5. The pulsar powered
object has a cometary morphology similar to the Galactic PWN analogs PSR
B1951+32 and 'the mouse'. It is travelling supersonically through the
interstellar medium. We estimate the Pulsar kick velocity to be in the range of
700-2000 km/s for an age between 28-10 kyr. The radio spectral index for this
SNR PWN pulsar system is flat (-0.29 $\pm$ 0.01) consistent with other similar
objects. We infer that the putative pulsar has a radio spectral index of -1.8,
which is typical for Galactic pulsars. We searched for dispersion measures
(DMs) up to 1000 cm/pc^3 but found no convincing candidates with a S/N greater
than 8. We produce a polarisation map for this PWN at 5500 MHz and find a mean
fractional polarisation of P $\sim 23$ percent. The X-ray power-law spectrum
(Gamma $\sim 2$) is indicative of non-thermal synchrotron emission as is
expected from PWN-pulsar system. Finally, we detect DEM S5 in Infrared (IR)
bands. Our IR photometric measurements strongly indicate the presence of
shocked gas which is expected for SNRs. However, it is unusual to detect such
IR emission in a SNR with a supersonic bow-shock PWN. We also find a
low-velocity HI cloud of $\sim 107$ km/s which is possibly interacting with DEM
S5. SNR DEM S5 is the first confirmed detection of a pulsar-powered bow shock
nebula found outside the Galaxy.
|
We develop a formalism for evaluation of the transverse momentum dependence
of cross sections of the radiation processes in medium. The analysis is based
on the light-cone path integral approach to the induced radiation. The results
are applicable in both QED and QCD.
|
We study the Rayleigh scattering induced by a diamond nanocrystal in a
whispering-gallery-microcavity--waveguide coupling system, and find that it
plays a significant role in the photon transportation. On one hand, this study
provides a new insight into future solid-state cavity quantum electrodynamics
toward strong coupling physics. On the other hand, benefitting from this
Rayleigh scattering, novel photon transportation such as dipole induced
transparency and strong photon antibunching can occur simultaneously. As
potential applications, this system can function as high-efficiency photon
turnstiles. In contrast to [B. Dayan \textit{et al.}, \textrm{Science}
\textbf{319},1062 (2008)], the photon turnstiles proposed here are highly
immune to nanocrystal's azimuthal position.
|
The transformations of the sum identities for generalized harmonic and
oscillatory numbers, obtained earlier in our recent report [1], enable us to
derive the new identities expressed in terms of the corresponding square roots
of x. At least one of these identities may be applied to prove the Riemann
Hypothesis by induction. Additionally using this approach, the new series for
Euler's constant gamma has been found.
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We investigate the bias-modulated dynamics of a strongly driven two-level
system using the counter-rotating-hybridized rotating-wave (CHRW) method. This
CHRW method treats the driving field and the bias on equal footing by a unitary
transformation with two parameters $\xi$ and $\zeta$, and is nonperturbative in
driving strength, tunneling amplitude or bias. In addition, this CHRW method is
beyond the traditional rotating-wave approximation (Rabi-RWA) and yet by
properly choosing the two parameters $\xi$ and $\zeta$, the transformed
Hamiltonian takes the RWA form with a renormalized energy splitting and a
renormalized driving strength. The reformulated CHRW method possesses the same
mathematical simplicity as the Rabi-RWA approach and thus allows us to
calculate analytically the dynamics and explore explicitly the effect of the
bias. We show that the CHRW method gives the accurate driven dynamics for a
wide range of parameters as compared to the numerically exact results. When
energy scales of the driving are comparable to the intrinsic energy scale of
the two-level systems, the counter-rotating interactions and static bias
profoundly influence the generalized Rabi frequency. In this regime, where
ordinary perturbation approaches fail, the CHRW works very well and
efficiently. We also demonstrate the dynamics of the system in the
strong-driving and off-resonance cases for which the Rabi-RWA method breaks
down but the CHRW method remains valid. We obtain analytical expressions for
the generalized Rabi frequency and bias-modulated Bloch-Siegert shift as
functions of the bias, tunneling and driving field parameters. The CHRW
approach is a mathematically simple and physically clear method. It can be
applied to treat some complicated problems for which a numerical study is
difficult to perform.
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Nuclear deep inelastic scattering is considered in the framework of a model
in which the current operator explicitly satisfies Poincare invariance and
current conservation. The results considerably differ from the standard ones at
small values of the Bjorken variable $x$. In particular, it is impossible to
extract the neutron structure functions from the deuteron data at x<0.01 and we
predict that the behavior of the deuteron structure functions at low x and
large momentum transfer considerably differs from the behavior of the nucleon
structure functions at such conditions. We also argue that for heavier nuclei
the effect of the final state interaction is important even in the Bjorken
limit.
|
Critical discussion of the recently published results [Muller, A. and
Aschenbach, B. 2007 Class. Quantum Grav. 24, p. 2637; arXiv:0704.3963] on the
non-monotonic orbital velocity profiles of the Keplerian motion of test
particles and l = const motion of test perfect fluid around K(a)dS black holes
is given, and the discrepancies concerned the existence of the non-monotonicity
in dependence of the spacetime parameters are corrected. Moreover a new
non-monotonic behaviour of the Keplerian orbital velocity in the Kerr-antide
Sitter spacetimes is highlighted.
|
The rules associated with propositional logic programs and the stable model
semantics are not expressive enough to let one write concise programs. This
problem is alleviated by introducing some new types of propositional rules.
Together with a decision procedure that has been used as a base for an
efficient implementation, the new rules supplant the standard ones in practical
applications of the stable model semantics.
|
We generalize the Hitchin-Kobayashi correspondence between semistability and
the existence of approximate Hermitian-Yang-Mills structures to the case of
principal Higgs bundles. We prove that a principal Higgs bundle on a compact
Kaehler manifold, with structure group a connected linear algebraic reductive
group, is semistable if and only if it admits an approximate
Hermitian-Yang-Mills structure.
|
A well-known challenge in applying deep-learning methods to omnidirectional
images is spherical distortion. In dense regression tasks such as depth
estimation, where structural details are required, using a vanilla CNN layer on
the distorted 360 image results in undesired information loss. In this paper,
we propose a 360 monocular depth estimation pipeline, OmniFusion, to tackle the
spherical distortion issue. Our pipeline transforms a 360 image into
less-distorted perspective patches (i.e. tangent images) to obtain patch-wise
predictions via CNN, and then merge the patch-wise results for final output. To
handle the discrepancy between patch-wise predictions which is a major issue
affecting the merging quality, we propose a new framework with the following
key components. First, we propose a geometry-aware feature fusion mechanism
that combines 3D geometric features with 2D image features to compensate for
the patch-wise discrepancy. Second, we employ the self-attention-based
transformer architecture to conduct a global aggregation of patch-wise
information, which further improves the consistency. Last, we introduce an
iterative depth refinement mechanism, to further refine the estimated depth
based on the more accurate geometric features. Experiments show that our method
greatly mitigates the distortion issue, and achieves state-of-the-art
performances on several 360 monocular depth estimation benchmark datasets.
|
The effective degrees of freedom of the Quark-Gluon Plasma are studied in the
temperature range $\sim 1-2$ $ T_c$. Employing lattice results for the pressure
and the energy density, we constrain the quasiparticle chiral invariant mass to
be of order 200 MeV and the effective number of bosonic resonant states to be
at most of order $\sim 10$. The chiral mass and the effective number of bosonic
degrees of freedom decrease with increasing temperature and at $T \sim 2$ $T_c$
only quark and gluon quasiparticles survive. Some remarks regarding the role of
the gluon condensation and the baryon number-strangeness correlation are also
presented.
|
The low thermal conductivity of piezoelectric perovskites is a challenge for
high power transducer applications. We report first principles calculations of
the thermal conductivity of ferroelectric PbTiO$_3$ and the cubic nearly
ferroelectric perovskite KTaO$_3$. The calculated thermal conductivity of
PbTiO$_3$ is much lower than that of KTaO$_3$ in accord with experiment.
Analysis of the results shows that the reason for the low thermal conductivity
of PbTiO$_3$ is the presence of low frequency optical phonons associated with
the polar modes. These are less dispersive in PbTiO$_3$, leading to a large
three phonon scattering phase space. These differences between the two
materials are associated with the $A$-site driven ferroelectricity of PbTiO$_3$
in contrast to the $B$-site driven near ferroelectricity of KTaO$_3$. The
results are discussed in the context of modification of the thermal
conductivity of electroactive materials.
|
In this paper we investigate spectral properties of Lapla- cians on Rooms and
Passages domains. In the first part, we use Dirichlet- Neumann bracketing
techniques to show that for the Neumann Lapla- cian in certain Rooms and
Passages domains the second term of the asymptotic expansion of the counting
function is of order $\sqrt{\lambda}$. For the Dirichlet Laplacian our methods
only give an upper estimate of the form $\sqrt{\lambda}$. In the second part of
the paper, we consider the relation- ship between Neumann Laplacians on Rooms
and Passages domains and Sturm-Liouville operators on the skeleton.
|
We discuss a (10+2)D N=(1,1) superalgebra and its projections to M-theory,
type IIA and IIB algebras. From the complete classification of a second-rank
central term valued in the so(10,2) algebra, we find all possible BPS states
coming from this term. We show that, among them, there are two types of
1/2-susy BPS configurations; one corresponds to a super (2+2)-brane while
another one arises from a nilpotent element in so(10,2).
|
This paper presents a novel deep architecture for saliency prediction.
Current state of the art models for saliency prediction employ Fully
Convolutional networks that perform a non-linear combination of features
extracted from the last convolutional layer to predict saliency maps. We
propose an architecture which, instead, combines features extracted at
different levels of a Convolutional Neural Network (CNN). Our model is composed
of three main blocks: a feature extraction CNN, a feature encoding network,
that weights low and high level feature maps, and a prior learning network. We
compare our solution with state of the art saliency models on two public
benchmarks datasets. Results show that our model outperforms under all
evaluation metrics on the SALICON dataset, which is currently the largest
public dataset for saliency prediction, and achieves competitive results on the
MIT300 benchmark.
|
Since a Poisson Structure is a smooth bivector field, we use a ring-valued
sheaf $\OO_{X}$ on a manifold with corners $X$, we can interpret $\OO_{X}(U)$
as the ring of admissible smooth functions where $U$ is an open subset on $X$,
in this way, a poisson structure on $(X, \OO_{X})$ is a sheaf morphism $$ \{-,
-\}: \OO_{X} \times \OO_{X} \longrightarrow \OO_{X} $$ which satisfies the
Leibniz rule an also the Jacobi Identity.
|
Canada's access to neutron beams for neutron scattering was significantly
curtailed in 2018 with the closure of the National Research Universal (NRU)
reactor in Chalk River, Ontario, Canada. New sources are needed for the
long-term; otherwise, access will only become harder as the global supply
shrinks. Compact Accelerator-based Neutron Sources (CANS) offer the possibility
of an intense source of neutrons with a capital cost significantly lower than
spallation sources. In this paper, we propose a CANS for Canada. The proposal
is staged with the first stage offering a medium neutron-flux, linac-based
approach for neutron scattering that is also coupled with a boron neutron
capture therapy (BNCT) station and a positron emission tomography (PET) isotope
station. The first stage will serve as a prototype for a second stage: a higher
brightness, higher cost facility that could be viewed as a national centre for
neutron applications.
|
On the one hand, the correctness of routing protocols in networks is an issue
of utmost importance for guaranteeing the delivery of messages from any source
to any target. On the other hand, a large collection of routing schemes have
been proposed during the last two decades, with the objective of transmitting
messages along short routes, while keeping the routing tables small.
Regrettably, all these schemes share the property that an adversary may modify
the content of the routing tables with the objective of, e.g., blocking the
delivery of messages between some pairs of nodes, without being detected by any
node.
In this paper, we present a simple certification mechanism which enables the
nodes to locally detect any alteration of their routing tables. In particular,
we show how to locally verify the stretch-3 routing scheme by Thorup and Zwick
[SPAA 2001] by adding certificates of $\widetilde{O}(\sqrt{n})$ bits at each
node in $n$-node networks, that is, by keeping the memory size of the same
order of magnitude as the original routing tables. We also propose a new
name-independent routing scheme using routing tables of size
$\widetilde{O}(\sqrt{n})$ bits. This new routing scheme can be locally verified
using certificates on $\widetilde{O}(\sqrt{n})$ bits. Its stretch is3 if using
handshaking, and 5 otherwise.
|
A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb.
Phil. Soc. 32, 446) and its several recent rediscoveries.
|
We describe the latest results obtained by the CMS Collaboration on top quark
spin and polarization properties. The top quark spin asymmetry is measured both
targeting single-top quark production in the $t$-channel and single-top quark
production in association with a Z boson. Additionally, all the independent
coefficients of the spin-dependent part of the top quark-antiquark production
density matrix are measured and the results are extrapolated to the
High-Luminosity LHC scenario.
|
The precision of the parallax measurements by Gaia is unprecedented. As of
Gaia Data Release 2, the number of known nearby open clusters has increased.
Some of the clusters appear to be relatively close to each other and form
aggregates, which makes them interesting objects to study. We study the
aggregates of clusters which share several of the assigned member stars in
relatively narrow volumes of the phase space. Using the most recent list of
open clusters, we compare the cited central parallaxes with the histograms of
parallax distributions of cluster aggregates. The aggregates were chosen based
on the member stars which are shared by multiple clusters. Many of the clusters
in the aggregates have been assigned parallaxes which coincide with the
histograms. However, clusters that share a large number of members in a small
volume of the phase space display parallax distributions which do not coincide
with the values from the literature. This is the result of ignoring a
possibility of assigning multiple probabilities to a single star. We propose
that this small number of clusters should be analysed anew.
|
In this paper we study the Hawking radiation in Reissner-Nordstrom and
Kerr-Newman black holes by considering the charge to be the function of radial
coordinate.
|
As a general rule, it is considered that the global gauge invariance of an
action integral does not cause the occurrence of gauge field. However, in this
paper we demonstrate that when the so-called localized assumption is excluded,
the gauge field will be induced by the global gauge invariance of the action
integral. An example is given to support this conclusion.
|
We present a pipeline of Image to Vector (Img2Vec) for masked image modeling
(MIM) with deep features. To study which type of deep features is appropriate
for MIM as a learning target, we propose a simple MIM framework with serials of
well-trained self-supervised models to convert an Image to a feature Vector as
the learning target of MIM, where the feature extractor is also known as a
teacher model. Surprisingly, we empirically find that an MIM model benefits
more from image features generated by some lighter models (e.g., ResNet-50,
26M) than from those by a cumbersome teacher like Transformer-based models
(e.g., ViT-Large, 307M). To analyze this remarkable phenomenon, we devise a
novel attribute, token diversity, to evaluate the characteristics of generated
features from different models. Token diversity measures the feature
dissimilarity among different tokens. Through extensive experiments and
visualizations, we hypothesize that beyond the acknowledgment that a large
model can improve MIM, a high token-diversity of a teacher model is also
crucial. Based on the above discussion, Img2Vec adopts a teacher model with
high token-diversity to generate image features. Img2Vec pre-trained on
ImageNet unlabeled data with ViT-B yields 85.1\% top-1 accuracy on fine-tuning.
Moreover, we scale up Img2Vec on larger models, ViT-L and ViT-H, and get
$86.7\%$ and $87.5\%$ accuracy respectively. It also achieves state-of-the-art
results on other downstream tasks, e.g., 51.8\% mAP on COCO and 50.7\% mIoU on
ADE20K. Img2Vec is a simple yet effective framework tailored to deep feature
MIM learning, accomplishing superb comprehensive performance on representative
vision tasks.
|
Many robot applications call for autonomous exploration and mapping of
unknown and unstructured environments. Information-based exploration
techniques, such as Cauchy-Schwarz quadratic mutual information (CSQMI) and
fast Shannon mutual information (FSMI), have successfully achieved active
binary occupancy mapping with range measurements. However, as we envision
robots performing complex tasks specified with semantically meaningful objects,
it is necessary to capture semantic categories in the measurements, map
representation, and exploration objective. This work develops a Bayesian
multi-class mapping algorithm utilizing range-category measurements. We derive
a closed-form efficiently computable lower bound for the Shannon mutual
information between the multi-class map and the measurements. The bound allows
rapid evaluation of many potential robot trajectories for autonomous
exploration and mapping. We compare our method against frontier-based and FSMI
exploration and apply it in a 3-D photo-realistic simulation environment.
|
Using a model for self-regulated growth of black holes (BHs) in mergers
involving gas-rich galaxies, we study the relationship between quasars and the
population of merging galaxies and predict the merger-induced star formation
rate density of the Universe. Mergers drive nuclear gas inflows, fueling
starbursts and 'buried quasars' until accretion feedback expels the gas,
rendering a briefly visible optical quasar. Star formation is shut down and
accretion declines, leaving a passively evolving remnant with properties
typical of red, elliptical galaxies. Based on evolution of these events in our
simulations, we demonstrate that the observed statistics of merger rates,
luminosity functions (LFs) and mass functions, SFR distributions, specific
SFRs, quasar and quasar host galaxy LFs, and elliptical/red galaxy LFs are
self-consistent and follow from one another as predicted by the merger
hypothesis. We use our simulations to de-convolve both quasar and merging
galaxy LFs to determine the birthrate of black holes of a given final mass and
merger rates as a function of stellar mass. We use this to predict the merging
galaxy LF in several observed wavebands, color-magnitude relations, mass
functions, absolute and specific SFR distributions and SFR density, and quasar
host galaxy LFs, as a function of redshift from z=0-6. We invert this and
predict e.g. quasar LFs from observed merger LFs or SFR distributions. Our
results agree well with observations, but idealized models of quasar
lightcurves are ruled out by comparison of merger and quasar observations at
>99.9% confidence. Using only observations of quasars, we estimate the
contribution of mergers to the SFR density of the Universe even to high
redshifts z~4.
|
In this brief note, we show how to apply Kummer's and other quadratic
transformation formulas for Gauss' and generalized hypergeometric functions in
order to obtain transformation and summation formulas for series with harmonic
numbers that contain one or two continuous parameters. We also give a
generating function of the sequence $\frac{(a)_n (1-a)_n}{(n!)^2}H_n$ as a
combination of Gauss hypergeometric function and elementary functions.
|
Using an effective hadronic Lagrangian with physical hadron masses and
coupling constants determined either empirically or from SU(4) flavor symmetry,
we study the production cross sections of charm mesons from pion and rho meson
interactions with nucleons. With a cutoff parameter of 1 GeV at interaction
vertices as usually used in studying the cross sections for $J/\psi$ absorption
and charm meson scattering by hadrons, we find that the cross sections for
charm meson production have values of a few tenth of mb and are dominated by
the s channel nucleon pole diagram. Relevance of these reactions to charm meson
production in relativistic heavy ion collisions is discussed.
|
We discuss the gauge dependence of physical parameter's definitions under the
on-shell and pole mass renormalization prescriptions. By two-loop-level
calculations we prove for the first time that the on-shell mass renormalization
prescription makes physical result gauge dependent. On the other hand, such
gauge dependence doesn't appear in the result of the pole mass renormalization
prescription. Our calculation also implies the difference of the physical
results between the two mass renormalization prescriptions cannot be neglected
at two-loop level.
|
Music genre classification has become increasingly critical with the advent
of various streaming applications. Nowadays, we find it impossible to imagine
using the artist's name and song title to search for music in a sophisticated
music app. It is always difficult to classify music correctly because the
information linked to music, such as region, artist, album, or non-album, is so
variable. This paper presents a study on music genre classification using a
combination of Digital Signal Processing (DSP) and Deep Learning (DL)
techniques. A novel algorithm is proposed that utilizes both DSP and DL methods
to extract relevant features from audio signals and classify them into various
genres. The algorithm was tested on the GTZAN dataset and achieved high
accuracy. An end-to-end deployment architecture is also proposed for
integration into music-related applications. The performance of the algorithm
is analyzed and future directions for improvement are discussed. The proposed
DSP and DL-based music genre classification algorithm and deployment
architecture demonstrate a promising approach for music genre classification.
|
We present a theoretical model of the near-surface shear layer (NSSL) of the
Sun. Convection cells deeper down are affected by the Sun's rotation, but this
is not the case in a layer just below the solar surface due to the smallness of
the convection cells there. Based on this idea, we show that the thermal wind
balance equation (the basic equation in the theory of the meridional
circulation which holds inside the convection zone) can be solved to obtain the
structure of the NSSL, matching observational data remarkably well.
|
There is increasing need to assess the impact and the interpretation of dim =
6 and dim = 8 operators within the context of the Standard Model Effective
Field Theory (SMEFT). The observational and mathematical consistency of a
construct based on dim = 6 and dim = 8 operators is critically examined in the
light of known theoretical results. The discussion is based on a general dim =
4 theory X and its effective extension, XEFT; it includes elimination of
redundant operators and their higher order compensation, SMEFT in comparison
with ultraviolet completions incorporating a proliferation of scalar and
mixings, canonical normalization of effective field theories, gauge invariance
and gauge fixing, role of tadpoles when constructing XEFT at NLO, heavy-light
contributions to the low energy limit of theories containing bosons and
fermions, one-loop matching, EFT fits and their interpretation and effective
field theory interpretation of derivative-coupled field theories.
|
Recent determinations of the radial distributions of mono-metallicity
populations (MMPs, i.e., stars in narrow bins in [Fe/H] within wider
[$\alpha$/Fe] ranges) by the SDSS-III/APOGEE DR12 survey cast doubts on the
classical thin - thick disk dichotomy. The analysis of these observations lead
to the non-$[\alpha$/Fe] enhanced populations splitting into MMPs with
different surface densities according to their [Fe/H]. By contrast,
$[\alpha$/Fe] enhanced (i.e., old) populations show an homogeneous behaviour.
We analyze these results in the wider context of disk formation within
non-isolated halos embedded in the Cosmic Web, resulting in a two-phase mass
assembly. By performing hydrodynamical simulations in the context of the $\rm
\Lambda CDM$ model, we have found that the two phases of halo mass assembly (an
early, fast phase, followed by a slow one, with low mass assembly rates) are
very relevant to determine the radial structure of MMP distributions, while
radial mixing has only a secondary role, depending on the coeval dynamical
and/or destabilizing events. Indeed, while the frequent dynamical violent
events occuring at high redshift remove metallicity gradients, and imply
efficient stellar mixing, the relatively quiescent dynamics after the
transition keeps [Fe/H] gaseous gradients and prevents newly formed stars to
suffer from strong radial mixing. By linking the two-component disk concept
with the two-phase halo mass assembly scenario, our results set halo
virialization (the event marking the transition from the fast to the slow
phases) as the separating event marking periods characterized by different
physical conditions under which thick and thin disk stars were born.
|
Simple dynamics, few available decay channels, and highly controlled
radiative and loop corrections, make pion and muon decays a sensitive means of
exploring details of the underlying symmetries. We review the current status of
the rare decays: pi+ -> e+ nu, pi+ -> e+ nu gamma, pi+ -> pi0 e+ nu, and mu+ ->
e+ nu nu-bar gamma. For the latter we report new preliminary values for the
branching ratio B(E_gamma >10 MeV, theta_(e-gamma) > 30deg) = 4.365 (9)_stat
(42)_syst x 10^{-3}, and the decay parameter eta-bar = 0.006 (17)_stat
(18)_syst, both in excellent agreement with standard model predictions. We
review recent measurements, particularly by the PIBETA and PEN experiments, and
near-term prospects for improvement. These and other similar precise low energy
studies complement modern collider results materially.
|
We consider barotropic instability of shear flows for incompressible fluids
with Coriolis effects. For a class of shear flows, we develop a new method to
find the sharp stability conditions. We study the flow with Sinus profile in
details and obtain the sharp stability boundary in the whole parameter space,
which corrects previous results in the fluid literature. Our new results are
confirmed by more accurate numerical computation. The addition of the Coriolis
force is found to bring fundamental changes to the stability of shear flows.
Moreover, we study dynamical behaviors near the shear flows, including the
bifurcation of nontrivial traveling wave solutions and the linear inviscid
damping. The first ingredient of our proof is a careful classification of the
neutral modes. The second one is to write the linearized fluid equation in a
Hamiltonian form and then use an instability index theory for general
Hamiltonian PDEs. The last one is to study the singular and non-resonant
neutral modes using Sturm-Liouville theory and hypergeometric functions.
|
In this paper, genetic programming reinforcement learning (GPRL) is utilized
to generate human-interpretable control policies for a Chylla-Haase
polymerization reactor. Such continuously stirred tank reactors (CSTRs) with
jacket cooling are widely used in the chemical industry, in the production of
fine chemicals, pigments, polymers, and medical products. Despite appearing
rather simple, controlling CSTRs in real-world applications is quite a
challenging problem to tackle. GPRL utilizes already existing data from the
reactor and generates fully automatically a set of optimized simplistic control
strategies, so-called policies, the domain expert can choose from. Note that
these policies are white-box models of low complexity, which makes them easy to
validate and implement in the target control system, e.g., SIMATIC PCS 7.
However, despite its low complexity the automatically-generated policy yields a
high performance in terms of reactor temperature control deviation, which we
empirically evaluate on the original reactor template.
|
We study the repulsive Fermi polaron in a two-component, two-dimensional
system of fermionic atoms inspired by the results of a recent experiment with
$^{173}$Yb atoms [N. Darkwah Oppong \textit{et al.}, Phys. Rev. Lett.
\textbf{122}, 193604 (2019)]. We use the diffusion Monte Carlo method to report
properties such as the polaron energy and the quasi-particle residue that have
been measured in that experiment. To provide insight on the quasi-particle
character of the problem, we also report results for the effective mass. We
show that the effective range, together with the scattering length, is needed
in order to reproduce the experimental results. Using different model
potentials for the interaction between the Fermi sea and the impurity, we show
that it is possible to establish a regime of universality, in terms of these
two parameters, that includes the whole experimental regime. This illustrates
the relevance of quantum fluctuations and beyond mean-field effects to
correctly describe the Fermi polaron problem.
|
We present BlockBERT, a lightweight and efficient BERT model for better
modeling long-distance dependencies. Our model extends BERT by introducing
sparse block structures into the attention matrix to reduce both memory
consumption and training/inference time, which also enables attention heads to
capture either short- or long-range contextual information. We conduct
experiments on language model pre-training and several benchmark question
answering datasets with various paragraph lengths. BlockBERT uses 18.7-36.1%
less memory and 12.0-25.1% less time to learn the model. During testing,
BlockBERT saves 27.8% inference time, while having comparable and sometimes
better prediction accuracy, compared to an advanced BERT-based model, RoBERTa.
|
Multiple tracers of the same surveyed volume can enhance the signal-to-noise
on a measurement of local primordial non-Gaussianity and the relativistic
projections. Increasing the number of tracers comparably increases the number
of shot noise terms required to describe the stochasticity of the data.
Although the shot noise is white on large scales, it is desirable to
investigate the extent to which it can degrade constraints on the parameters of
interest. In a multi-tracer analysis of the power spectrum, a marginalization
over shot noise does not degrade the constraints on $f_\text{NL}$ by more than
$\sim 30$% so long as halos of mass $M\lesssim 10^{12}M_\odot$ are resolved.
However, ignoring cross shot noise terms induces large systematics on a
measurement of $f_\text{NL}$ at redshift $z<1$ when small mass halos are
resolved. These effects are less severe for the relativistic projections,
especially for the dipole term. In the case of a low and high mass tracer, the
optimal sample division maximizes the signal-to-noise on $f_\text{NL}$ and the
projection effects simultaneously, reducing the errors to the level of $\sim
10$ consecutive mass bins of equal number density. We also emphasize that the
non-Poissonian noise corrections that arise from small-scale clustering effects
cannot be measured with random dilutions of the data. Therefore, they must
either be properly modeled or marginalized over.
|
Tensors are multiway arrays of data, and transverse operators are the
operators that change the frame of reference. We develop the spectral theory of
transverse tensor operators and apply it to problems closely related to
classifying quantum states of matter, isomorphism in algebra, clustering in
data, and the design of high performance tensor type-systems. We prove the
existence and uniqueness of the optimally-compressed tensor product spaces over
algebras, called \emph{densors}. This gives structural insights for tensors and
improves how we recognize tensors in arbitrary reference frames. Using work of
Eisenbud--Sturmfels on binomial ideals, we classify the maximal groups and
categories of transverse operators, leading us to general tensor data types and
categorical tensor decompositions, amenable to theorems like Jordan--H\"older
and Krull--Schmidt. All categorical tensor substructure is detected by
transverse operators whose spectra contain a Stanley--Reisner ideal, which can
be analyzed with combinatorial and geometrical tools via their simplicial
complexes. Underpinning this is a ternary Galois correspondence between tensor
spaces, multivariable polynomial ideals, and transverse operators. This
correspondence can be computed in polynomial time. We give an implementation in
the computer algebra system \textsf{Magma}.
|
The joint task of Dialog Sentiment Classification (DSC) and Act Recognition
(DAR) aims to predict the sentiment label and act label for each utterance in a
dialog simultaneously. However, current methods encode the dialog context in
only one direction, which limits their ability to thoroughly comprehend the
context. Moreover, these methods overlook the explicit correlations between
sentiment and act labels, which leads to an insufficient ability to capture
rich sentiment and act clues and hinders effective and accurate reasoning. To
address these issues, we propose a Bi-directional Multi-hop Inference Model
(BMIM) that leverages a feature selection network and a bi-directional
multi-hop inference network to iteratively extract and integrate rich sentiment
and act clues in a bi-directional manner. We also employ contrastive learning
and dual learning to explicitly model the correlations of sentiment and act
labels. Our experiments on two widely-used datasets show that BMIM outperforms
state-of-the-art baselines by at least 2.6% on F1 score in DAR and 1.4% on F1
score in DSC. Additionally, Our proposed model not only improves the
performance but also enhances the interpretability of the joint sentiment and
act prediction task.
|
In order to fully harness the potential of dielectric elastomer actu-ators
(DEAs) in soft robots, advanced control methods are need-ed. An important
groundwork for this is the development of a control-oriented model that can
adequately describe the underly-ing dynamics of a DEA. A common feature of
existing models is that always custom-made DEAs were investigated. This makes
the modelling process easier, as all specifications and the struc-ture of the
actuator are well known. In the case of a commercial actuator, however, only
the information from the manufacturer is available and must be checked or
completed during the modelling process. The aim of this paper is to explore how
a commercial stacked silicone-based DEA can be modelled and how complex the
model should be to properly replicate the features of the actu-ator. The static
description has demonstrated the suitability of Hooke's law. In the case of
dynamic description, it is shown that no viscoelastic model is needed for
control-oriented modelling. However, if all features of the DEA are considered,
the general-ized Kelvin-Maxwell model with three Maxwell elements shows good
results, stability and computational efficiency.
|
We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229,
3091-3120) to simulate the advection of neutral particles in phase space using
curvilinear coordinates. The ability to utilize these coordinates is important
for non-equilibrium transport problems in general relativity and also in
science and engineering applications with specific geometries. The method
achieves high-order accuracy using Discontinuous Galerkin (DG) discretization
of phase space and strong stability-preserving, Runge-Kutta (SSP-RK) time
integration. Special care in taken to ensure that the method preserves strict
bounds for the phase space distribution function $f$; i.e., $f\in[0,1]$. The
combination of suitable CFL conditions and the use of the high-order limiter
proposed in Zhang & Shu (2010) is sufficient to ensure positivity of the
distribution function. However, to ensure that the distribution function
satisfies the upper bound, the discretization must, in addition, preserve the
divergence-free property of the phase space flow. Proofs that highlight the
necessary conditions are presented for general curvilinear coordinates, and the
details of these conditions are worked out for some commonly used coordinate
systems (i.e., spherical polar spatial coordinates in spherical symmetry and
cylindrical spatial coordinates in axial symmetry, both with spherical momentum
coordinates). Results from numerical experiments --- including one example in
spherical symmetry adopting the Schwarzschild metric --- demonstrate that the
method achieves high-order accuracy and that the distribution function
satisfies the maximum principle.
|
The redshift-space distortion (RSD) in the observed distribution of galaxies
is known as a powerful probe of cosmology. Observations of large-scale RSD have
given tight constraints on the linear growth rate of the large-scale structures
in the universe. On the other hand, the small-scale RSD, caused by galaxy
random motions inside clusters, has not been much used in cosmology, but also
has cosmological information because universes with different cosmological
parameters have different halo mass functions and virialized velocities. We
focus on the projected correlation function $w(r_p)$ and the multipole moments
$\xi_l$ on small scales ($1.4$ to $30\ h^{-1}\rm{Mpc}$). Using simulated galaxy
samples generated from a physically motivated most bound particle (MBP)-galaxy
correspondence scheme in the Multiverse Simulation, we examine the dependence
of the small-scale RSD on the cosmological matter density parameter $\Omega_m$,
the satellite velocity bias with respect to MBPs, $b_v^s$, and the
merger-time-scale parameter $\alpha$. We find that $\alpha=1.5$ gives an
excellent fit to the $w(r_p)$ and $\xi_l$ measured from the SDSS-KIAS value
added galaxy catalog. We also define the ``strength'' of Fingers-of-God as the
ratio of the parallel and perpendicular size of the contour in the two-point
correlation function set by a specific threshold value and show that the
strength parameter helps constraining $(\Omega_m, b_v^s, \alpha)$ by breaking
the degeneracy among them. The resulting parameter values from all measurements
are $(\Omega_m,b_v^s)=(0.272\pm0.013,0.982\pm0.040)$, indicating a slight
reduction of satellite galaxy velocity relative to the MBP. However,
considering that the average MBP speed inside haloes is $0.94$ times the dark
matter velocity dispersion, the main drivers behind the galaxy velocity bias
are gravitational interactions, rather than baryonic effects.
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The observed small value of cosmological constant can be naturally related
with the scale of breaking down supersymmetry in agreement with other
evaluations in particle physics.
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Analyzing Event-Triggered Control's (ETC) sampling behaviour is of paramount
importance, as it enables formal assessment of its sampling performance and
prediction of its sampling patterns. In this work, we formally analyze the
sampling behaviour of stochastic linear periodic ETC (PETC) systems by
computing bounds on associated metrics. Specifically, we consider functions
over sequences of state measurements and intersampling times that can be
expressed as average, multiplicative or cumulative rewards, and introduce their
expectations as metrics on PETC's sampling behaviour. We compute bounds on
these expectations, by constructing appropriate Interval Markov Chains equipped
with suitable reward structures, that abstract stochastic PETC's sampling
behaviour. Our results are illustrated on a numerical example, for which we
compute bounds on the expected average intersampling time and on the
probability of triggering with the maximum possible intersampling time in a
finite horizon.
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We extend the graph convolutional network method for deep learning on graph
data to higher order in terms of neighboring nodes. In order to construct
representations for a node in a graph, in addition to the features of the node
and its immediate neighboring nodes, we also include more distant nodes in the
calculations. In experimenting with a number of publicly available citation
graph datasets, we show that this higher order neighbor visiting pays off by
outperforming the original model especially when we have a limited number of
available labeled data points for the training of the model.
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Azimuthal angle correlations of charged hadrons were measured in $\sqrt
s_{NN}$ = 2.76 TeV PbPb collisions by the CMS experiment. The distributions
exhibit anisotropies that are correlated with the event-by-event orientation of
the reaction plane. Several methods were employed to extract the strength of
the signal: the event-plane, cumulant and Lee-Yang Zeros methods. These methods
have different sensitivity to correlations that are not caused by the
collective motion in the system (non-flow correlations due to jets, resonance
decays, and quantum correlations). The second Fourier coefficient of the
charged hadron azimuthal distributions was measured as a function of transverse
momentum, pseudorapidity and centrality in a broad kinematic range: $0.3 < p_T
< 12.0$ GeV/c, $|\eta| < 2.4$, as a function of collision centrality. In
addition, the third through sixth Fourier components were measured at
midrapidity using selected methods.
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We consider the effect of optical depth of the 2 ^{3}S level on the nebular
recombination spectrum of He I for a spherically symmetric nebula with no
systematic velocity gradients. These calculations, using many improvements in
atomic data, can be used in place of the earlier calculations of Robbins. We
give representative Case B line fluxes for UV, optical, and IR emission lines
over a range of physical conditions: T=5000-20000 K, n_{e}=1-10^{8} cm^{-3},
and tau_{3889}=0-100. A FORTRAN program for calculating emissivities for all
lines arising from quantum levels with n < 11 is also available from the
authors.
We present a special set of fitting formulae for the physical conditions
relevant to low metallicity extragalactic H II regions: T=12,000-20,000 K,
n_{e}=1-300 cm^{-3}, and tau_{3889} < 2.0. For this range of physical
conditions, the Case B line fluxes of the bright optical lines 4471 A, 5876 A,
and 6678 A, are changed less than 1%, in agreement with previous studies.
However, the 7065 A corrections are much smaller than those calculated by
Izotov & Thuan based on the earlier calculations by Robbins. This means that
the 7065 A line is a better density diagnostic than previously thought. Two
corrections to the fitting functions calculated in our previous work are also
given.
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The result by Burnett-Kroll (BK) states that for radiative decays the
interference of ${\cal O}(\omega^{-1})$ in the photon energy $\omega$, vanishes
after sum over polarizations of the involved particles. Using radiative decays
of vector mesons we show that if the vector meson is polarized the ${\cal
O}(\omega^{-1})$ terms are null only for the canonical value of the magnetic
dipole moment of the vector meson, namely ${\bf g}=2$ in Bohr's magneton units.
A subtle cancellation of all ${\cal O}(\omega^{-1})$ terms happens when summing
over all polarizations to recover the Burnett-Kroll result. We also show the
source of these terms and the corresponding cancellation for the unpolarized
case and exhibit a global structure that can make them individually vanish in a
particular kinematical region.
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We analyze the structure and connectivity of the distinct morphologies that
define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF),
we dissect the matter distribution of a cosmological $\Lambda$CDM N-body
computer simulation into cluster, filaments and walls. The MMF is ideally
suited to adress both the anisotropic morphological character of filaments and
sheets, as well as the multiscale nature of the hierarchically evolved cosmic
matter distribution. The results of our study may be summarized as follows:
i).- While all morphologies occupy a roughly well defined range in density,
this alone is not sufficient to differentiate between them given their overlap.
Environment defined only in terms of density fails to incorporate the intrinsic
dynamics of each morphology. This plays an important role in both linear and
non linear interactions between haloes. ii).- Most of the mass in the Universe
is concentrated in filaments, narrowly followed by clusters. In terms of
volume, clusters only represent a minute fraction, and filaments not more than
9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On
average, massive clusters are connected to more filaments than low mass
clusters. Clusters with $M \sim 10^{14}$ M$_{\odot}$ h$^{-1}$ have on average
two connecting filaments, while clusters with $M \geq 10^{15}$ M$_{\odot}$
h$^{-1}$ have on average five connecting filaments. iv).- Density profiles
indicate that the typical width of filaments is 2$\Mpch$. Walls have less well
defined boundaries with widths between 5-8 Mpc h$^{-1}$. In their interior,
filaments have a power-law density profile with slope ${\gamma}\approx -1$,
corresponding to an isothermal density profile.
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Distributed surveillance systems have become popular in recent years due to
security concerns. However, transmitting high dimensional data in
bandwidth-limited distributed systems becomes a major challenge. In this paper,
we address this issue by proposing a novel probabilistic algorithm based on the
divergence between the probability distributions of the visual features in
order to reduce their dimensionality and thus save the network bandwidth in
distributed wireless smart camera networks. We demonstrate the effectiveness of
the proposed approach through extensive experiments on two surveillance
recognition tasks.
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We introduce matchmakereft, a fully automated tool to compute the tree-level
and one-loop matching of arbitrary models onto arbitrary effective theories.
Matchmakereft performs an off-shell matching, using diagrammatic methods and
the background field method when gauge theories are involved. The large
redundancy inherent to the off-shell matching together with explicit gauge
invariance offers a significant number of non-trivial checks of the results
provided. These results are given in the physical basis but several
intermediate results, including the matching in the Green basis before and
after canonical normalization, are given for flexibility and the possibility of
further cross-checks. As a non-trivial example we provide the complete matching
in the Warsaw basis up to one loop of an extension of the Standard Model with a
charge -1 vector-like lepton singlet. Matchmakereft has been built with
generality, flexibility and efficiency in mind. These ingredients allow
matchmakereft to have many applications beyond the matching between models and
effective theories. Some of these applications include the one-loop
renormalization of arbitrary theories (including the calculation of the
one-loop renormalization group equations for arbitrary theories); the
translation between different Green bases for a fixed effective theory or the
check of (off-shell) linear independence of the operators in an effective
theory. All these applications are performed in a fully automated way by
matchmakereft.
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In this paper, we characterize all the distributions $F \in \mathcal{D}'(U)$
such that there exists a continuous weak solution $v \in C(U,\mathbb{C}^{n})$
(with $U \subset \Omega$) to the divergence-type equation
$$L_{1}^{*}v_{1}+...+L_{n}^{*}v_{n}=F,$$ where
$\left\{L_{1},\dots,L_{n}\right\}$ is an elliptic system of linearly
independent vector fields with smooth complex coefficients defined on $\Omega
\subset \mathbb{R}^{N}$. In case where $(L_1,\dots, L_n)$ is the usual gradient
field on $\mathbb{R}^N$, we recover the classical result for the divergence
equation proved by T. De Pauw and W. Pfeffer.
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A method, referred to as the principal correlation decomposition (PCD), is
proposed in this paper to optimally dissect complex flows into mutually
orthogonal modes that are ranked by their correlated energy with an observable.
It is particularly suitable for identifying the observable-correlated flow
structures, while effectively excluding those uncorrelated even though they may
be highly energetic. Therefore, this method is capable of extracting coherent
flow features under very low signal-to-noise ratio (SNR). A numerical
validation is conducted and shows that the new method can robustly identify the
observable-correlated flow events even though the underlying signal is
corrupted by random noise that is four orders of magnitude more energetic.
Moreover, the resolution continues to improve if the flow is sampled for a
longer duration, which is often readily available in experimental measurements.
This method is subsequently used to analyse the unsteady vortex shedding from a
cylinder and a subsonic turbulent jet. This new decomposition represents a
data-driven method of effective order-reduction for highly noisy experimental
and numerical data and is very effective in identifying the source and
descendent events of a given observable. It is expected to find wide
applications in flow observable diagnosis and its control such as noise
control.
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Simulation of the dynamics of dust-gas circumstellar discs is crucial in
understanding the mechanisms of planet formation. The dynamics of small grains
in the disc is stiffly coupled to the gas, while the dynamics of grown solids
is decoupled. Moreover, in some parts of the disc the concentration of the dust
is low (dust to gas mass ratio is about 0.01), while in other parts it can be
much higher. These factors place high requirements on the numerical methods for
disc simulations. In particular, when gas and dust are simulated with two
different fluids, explicit methods require very small timestep (must be less
than dust stopping time $t_{\rm stop}$ during which the velocity of a solid
particle is equalized with respect to the gas velocity) to obtain solution,
while some implicit methods requires high temporal resolution to obtain
acceptable accuracy. Moreover, recent studies underlined that for Smoothed
particle hydrodynamics (SPH) when the gas and the dust are simulated with
different sets of particles only high spatial resolution $h<c_{\rm s} t_{\rm
stop}$ guaranties suppression of numerical overdissipation due to gas and dust
interaction.
To address these problems, we developed a fast algorithm based on the ideas
of (1) implicit integration of linear (Epstein) drag and (2) exact conservation
of local linear momentum. We derived formulas for monodisperse dust-gas in
two-fluid SPH and tested the new method on problems with known analytical
solutions. We found that our method is a promising alternative for the
previously developed two-fluid SPH scheme in case of stiff linear drag thanks
to the fact that spatial resolution condition $h<c_{\rm s} t_{\rm stop}$ is not
required anymore for accurate results.
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The recent LHCb determination of the direct CP asymmetries in the decays $D^0
\to K^+ K^-, \pi^+ \pi^-$ hints at a sizeable breaking of two approximate
symmetries of the SM: CP and U-spin. We aim at explaining the data with BSM
physics and use the framework of flavorful $Z^\prime$ models. Interestingly,
experimental and theoretical constraints very much narrow down the shape of
viable models: Viable, anomaly-free models are electron- and muon-phobic and
feature a light $Z^\prime$ of 10-20 GeV coupling only to right-handed fermions.
The $Z^\prime$ can be searched for in low mass dijets or at the LHC as well as
dark photon searches. A light $Z^\prime$ of $\sim$ 3 GeV or $\sim$ 5-7 GeV can
moreover resolve the longstanding discrepancy in the $J/\psi, \psi^\prime$
branching ratios with pion form factors from fits to $e^+ e^- \to \pi^+ \pi^-$
data, and simultaneously explain the charm CP asymmetries. Smoking gun
signatures for this scenario are $\Upsilon$ and charmonium decays into pions,
taus or invisbles.
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Social networks are usually considered as positive sources of social support,
a role which has been extensively studied in the context of domestic violence.
To victims of abuse, social networks often provide initial emotional and
practical help as well useful information ahead of formal institutions.
Recently, however, attention has been paid to the negative responses of social
networks. In this article, we advance the theoretical debate on social networks
as a source of social support by moving beyond the distinction between positive
and negative ties. We do so by proposing the concepts of relational ambivalence
and consistency, which describe the interactive processes by which people,
intentionally or inadvertently, disregard or align with each other role
relational expectations, therefore undermining or reinforcing individual
choices of action. We analyse the qualitative accounts of nineteen female
victims of domestic violence in Sweden, who described the responses of their
personal networks during and after the abuse. We observe how the relationships
embedded in these networks were described in ambivalent and consistent terms,
and how they played a role in supporting or undermining women in reframing
their loving relationships as abusive; in accounting or dismissing perpetrators
responsibilities for the abuse; in relieving women from role expectations and
obligations or in burdening them with further responsibilities; and in
supporting or challenging their pathways out of domestic abuse. Our analysis
suggests that social isolation cannot be considered a simple result of a lack
of support but of the complex dynamics in which support is offered and accepted
or withdrawn and refused.
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In order to better understand the heave observed on the railway roadbed of
the French high-speed train (TGV) at Chabrillan in southern France, the
swelling behaviour of the involved expansive clayey marl taken from the site by
coring was investigated. The aim the study is to analyse the part of heave
induced by the soil swelling. First, the swell potential was determined by
flooding the soil specimen in an oedometer under its in-situ overburden stress.
On the other hand, in order to assess the swell induced by the excavation
undertaken during the construction of the railway, a second method was applied.
The soil was first loaded to its in situ overburden stress existing before the
excavation. It was then flooded and unloaded to its current overburden stress
(after the excavation). The swell induced by this unloading was considered.
Finally, the experimental results obtained were analyzed, together with the
results from other laboratory tests performed previously and the data collected
from the field monitoring. This study allowed estimating the heave induced by
soil swelling. Subsequently, the part of heave due to landslide could be
estimated which corresponds to the difference between the monitored heave and
the swelling heave.
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Software as a Service (SaaS) is a new software delivery model in which
pre-built applications are delivered to customers as a service. SaaS providers
aim to attract a large number of tenants (users) with minimal system
modifications to meet economics of scale. To achieve this aim, SaaS
applications have to be customizable to meet requirements of each tenant.
However, due to the rapid growing of the SaaS, SaaS applications could have
thousands of tenants with a huge number of ways to customize applications.
Modularizing such customizations still is a highly complex task. Additionally,
due to the big variation of requirements for tenants, no single customization
model is appropriate for all tenants. In this paper, we propose a
multi-dimensional customization model based on metagraph. The proposed mode
addresses the modelling variability among tenants, describes customizations and
their relationships, and guarantees the correctness of SaaS customizations made
by tenants.
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This paper explores the use of a deformation by a root of unity as a tool to
build models with a finite number of states for applications to quantum
gravity. The initial motivation for this work was cosmological breaking of
supersymmetry. We explain why the project was unsuccessful. What is left are
some observations on supersymmetry for q-bosons, an analogy between black holes
in de Sitter and properties of quantum groups, and an observation on a
noncommutative quantum mechanics model with two degrees of freedom, depending
on one parameter. When this parameter is positive, the spectrum has a finite
number of states; when it is negative or zero, the spectrum has an infinite
number of states. This exhibits a desirable feature of quantum physics in de
Sitter space, albeit in a very simple, non-gravitational context.
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The Sun exhibits a well-observed modulation in the number of spots on its
disk over a period of about 11 years. From the dawn of modern observational
astronomy sunspots have presented a challenge to understanding -- their
quasi-periodic variation in number, first noted 175 years ago, stimulates
community-wide interest to this day. A large number of techniques are able to
explain the temporal landmarks, (geometric) shape, and amplitude of sunspot
"cycles," however forecasting these features accurately in advance remains
elusive. Recent observationally-motivated studies have illustrated a
relationship between the Sun's 22-year (Hale) magnetic cycle and the production
of the sunspot cycle landmarks and patterns, but not the amplitude of the
sunspot cycle. Using (discrete) Hilbert transforms on more than 270 years of
(monthly) sunspot numbers we robustly identify the so-called "termination"
events that mark the end of the previous 11-yr sunspot cycle, the
enhancement/acceleration of the present cycle, and the end of 22-yr magnetic
activity cycles. Using these we extract a relationship between the temporal
spacing of terminators and the magnitude of sunspot cycles. Given this
relationship and our prediction of a terminator event in 2020, we deduce that
Sunspot Cycle 25 could have a magnitude that rivals the top few since records
began. This outcome would be in stark contrast to the community consensus
estimate of sunspot cycle 25 magnitude.
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We study the magnetic susceptibility at large 't Hooft coupling by computing
the correlation function of the magnetizations in the strongly coupled Maxwell
theory in large-N limit with finite temperature and chemical potential, within
the framework of the AdS/CFT correspondence. We show that in strong coupling
limit the magnetic susceptibility is independent to the temperature and be
universal, measured in the unit of magnetic permeability of the bulk space. A
comparison with the weak coupling system, the Pauli paramagnetic
susceptibility, is also discussed.
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We study a two-player, zero-sum, stochastic game with incomplete information
on one side in which the players are allowed to play more and more frequently.
The informed player observes the realization of a Markov chain on which the
payoffs depend, while the non-informed player only observes his opponent's
actions. We show the existence of a limit value as the time span between two
consecutive stages vanishes; this value is characterized through an auxiliary
optimization problem and as the solution of an Hamilton-Jacobi equation.
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Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some
fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs
of $G$ is referred to as a (random) {\sl perturbation} of $G$. We consider the
distribution of edge-coloured graphs arising from assigning each edge of the
random perturbation $G \cup \mathbb{G}(n,p)$ a colour, chosen independently and
uniformly at random from a set of colours of size $r := r(n)$. We prove that
such edge-coloured graph distributions a.a.s. admit rainbow Hamilton cycles
whenever the edge-density of the random perturbation satisfies $p := p(n) \geq
C/n$, for some fixed $C > 0$, and $r = (1 + o(1))n$. The number of colours used
is clearly asymptotically best possible. In particular, this improves upon a
recent result of Anastos and Frieze (2019) in this regard. As an intermediate
result, which may be of independent interest, we prove that randomly
edge-coloured sparse pseudo-random graphs a.a.s. admit an almost spanning
rainbow path.
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Large-scale pretrained language models are surprisingly good at recalling
factual knowledge presented in the training corpus. In this paper, we present
preliminary studies on how factual knowledge is stored in pretrained
Transformers by introducing the concept of knowledge neurons. Specifically, we
examine the fill-in-the-blank cloze task for BERT. Given a relational fact, we
propose a knowledge attribution method to identify the neurons that express the
fact. We find that the activation of such knowledge neurons is positively
correlated to the expression of their corresponding facts. In our case studies,
we attempt to leverage knowledge neurons to edit (such as update, and erase)
specific factual knowledge without fine-tuning. Our results shed light on
understanding the storage of knowledge within pretrained Transformers. The code
is available at https://github.com/Hunter-DDM/knowledge-neurons.
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We demonstrate that muon tomography can be used to precisely measure the
properties of various materials. The materials which have been considered have
been extracted from an experimental blast furnace, including carbon (coke) and
iron oxides, for which measurements of the linear scattering density relative
to the mass density have been performed with an absolute precision of 10%. We
report the procedures that are used in order to obtain such precision, and a
discussion is presented to address the expected performance of the technique
when applied to heavier materials. The results we obtain do not depend on the
specific type of material considered and therefore they can be extended to any
application.
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It has been argued that Horava gravity needs to be extended to include terms
that mix spatial and time derivatives in order avoid unacceptable violations of
Lorentz invariance in the matter sector. In an earlier paper we have shown that
including such mixed derivative terms generically leads to 4th instead of 6th
order dispersion relations and this could be (naively) interpreted as a threat
to renormalizability. We have also argued that power-counting renormalizability
is not actually compromised, but instead the simplest power-counting
renormalizable model is not unitary. In this paper we consider the Lifshitz
scalar as a toy theory and we generalize our analysis to include higher order
operators. We show that models which are power-counting renormalizable and
unitary do exist. Our results suggest the existence of a new class of theories
that can be thought of as Horava gravity with mixed derivative terms.
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Generalized Procrustes Analysis (GPA) is the problem of bringing multiple
shapes into a common reference by estimating transformations. GPA has been
extensively studied for the Euclidean and affine transformations. We introduce
GPA with deformable transformations, which forms a much wider and difficult
problem. We specifically study a class of transformations called the Linear
Basis Warps (LBWs), which contains the affine transformation and most of the
usual deformation models, such as the Thin-Plate Spline (TPS). GPA with
deformations is a nonconvex underconstrained problem. We resolve the
fundamental ambiguities of deformable GPA using two shape constraints requiring
the eigenvalues of the shape covariance. These eigenvalues can be computed
independently as a prior or posterior. We give a closed-form and optimal
solution to deformable GPA based on an eigenvalue decomposition. This solution
handles regularization, favoring smooth deformation fields. It requires the
transformation model to satisfy a fundamental property of free-translations,
which asserts that the model can implement any translation. We show that this
property fortunately holds true for most common transformation models,
including the affine and TPS models. For the other models, we give another
closed-form solution to GPA, which agrees exactly with the first solution for
models with free-translation. We give pseudo-code for computing our solution,
leading to the proposed DefGPA method, which is fast, globally optimal and
widely applicable. We validate our method and compare it to previous work on
six diverse 2D and 3D datasets, with special care taken to choose the
hyperparameters from cross-validation.
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We introduce a weak concept of Morita equivalence, in the birational context,
for Poisson modules on complex normal Poisson projective varieties. We show
that Poisson modules, on projective varieties with mild singularities, are
either rationally Morita equivalent to a flat partial holomorphic sheaf, or a
sheaf with a meromorphic flat connection or a co-Higgs sheaf. As an
application, we study the geometry of rank two meromorphic rank two
$\mathfrak{sl}_2$-Poisson modules which can be interpreted as a Poisson
analogous to transversally projective structures for codimension one
holomorphic foliations. Moreover, we describe the geometry of the symplectic
foliation induced by the Poisson connection on the projectivization of the
Poisson module.
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Complementarity principle is one of the central concepts in quantum mechanics
which restricts joint measurement for certain observables. Of course, later
development shows that joint measurement could be possible for such observables
with the introduction of a certain degree of unsharpness or fuzziness in the
measurement. In this paper, we show that the optimal degree of unsharpness,
which guarantees the joint measurement of all possible pairs of dichotomic
observables, determines the degree of nonlocality in quantum mechanics as well
as in more general no-signaling theories.
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We investigate properties of group gradings on matrix rings $M_n(R)$, where
$R$ is an associative unital ring and $n$ is a positive integer. More
precisely, we introduce very good gradings and show that any very good grading
on $M_n(R)$ is necessarily epsilon-strong. We also identify a condition that is
sufficient to guarantee that $M_n(R)$ is an epsilon-crossed product, i.e.
isomorphic to a crossed product associated with a unital twisted partial
action. In the case where $R$ has IBN, we are able to provide a
characterization of when $M_n(R)$ is an epsilon-crossed product. Our results
are illustrated by several examples.
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