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Large scale graph processing using distributed computing frameworks is
becoming pervasive and efficient in the industry. In this work, we present a
highly scalable and configurable distributed algorithm for building connected
components, called Union Find Shuffle (UFS) with Path Compression. The scale
and complexity of the algorithm are a function of the number of partitions into
which the data is initially partitioned, and the size of the connected
components. We discuss the complexity and the benchmarks compared to similar
approaches. We also present current benchmarks of our production system,
running on commodity out-of-the-box cloud Hadoop infrastructure, where the
algorithm was deployed over a year ago, scaled to around 75 Billion nodes and
60 Billions linkages (and growing). We highlight the key aspects of our
algorithm which enable seamless scaling and performance even in the presence of
skewed data with large connected components in the size of 10 Billion nodes
each.
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Using the $1.9 pb^{-1}$ of data collected with the CMD-2 detector at VEPP-2M
the decay mode $\phi \to \eta \gamma$, $\eta \to \pi^+\pi^-\pi^0$ has been
studied. The obtained branching ratio is B($\phi \to \eta \gamma) = (1.18 \pm
0.03 \pm 0.06) %$.
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Deploying Deep Neural Networks (DNNs) on microcontrollers (TinyML) is a
common trend to process the increasing amount of sensor data generated at the
edge, but in practice, resource and latency constraints make it difficult to
find optimal DNN candidates. Neural Architecture Search (NAS) is an excellent
approach to automate this search and can easily be combined with DNN
compression techniques commonly used in TinyML. However, many NAS techniques
are not only computationally expensive, especially hyperparameter optimization
(HPO), but also often focus on optimizing only a single objective, e.g.,
maximizing accuracy, without considering additional objectives such as memory
consumption or computational complexity of a DNN, which are key to making
deployment at the edge feasible. In this paper, we propose a novel NAS strategy
for TinyML based on Multi-Objective Bayesian optimization (MOBOpt) and an
ensemble of competing parametric policies trained using Augmented Random Search
(ARS) Reinforcement Learning (RL) agents. Our methodology aims at efficiently
finding tradeoffs between a DNN's predictive accuracy, memory consumption on a
given target system, and computational complexity. Our experiments show that we
outperform existing MOBOpt approaches consistently on different data sets and
architectures such as ResNet-18 and MobileNetV3.
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Light has a fascinating property: it always travels the path that takes the
least time between any two points. This is the motivating property behind
optical phenomena such as Reflection and Refraction. The unreasonable economic
efficiency of light is captured by a single proposition: the Principle of Least
Action (PLA) in Optics. The PLA can be difficult for students to comprehend
because unlike reflection and refraction, which emerge from optimizing a
one-dimensional function, the PLA emerges from optimizing an
infinite-dimensional functional. Furthermore, students may be confused by the
formulation of the Lagrangian, or the counterintuitive paths generated by the
PLA. To address these difficulties, this paper presents three simulations which
demonstrate the PLA in Optics. Simulations have proven to be effective
pedagogical tools in making mathematical abstractions such as the Action
accessible to undergraduate students. The three simulations in this paper are
as follows: light reflecting in equal angles, light refracting through
different mediums, and light traveling the path of least time in an arbitrary
refractive profile. We then consider the famous Brachistochrone problem as a
special case of the third simulation. The interactive simulations discussed in
the paper, along with supplemental discussion questions, video tutorials, and
fully commented code, are available here.
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We address the question of whether individual nonmagnetic impurities can
induce zero-energy states in time-reversal-invariant topological
superconductors, and define a class of symmetries which guarantee the existence
of such states for a specific value of the impurity strength. These symmetries
allow the definition of a position-space topological Z_2 invariant, which is
related to the standard bulk topological Z_2 invariant. Our general results are
applied to the time-reversal-invariant p-wave phase of the doped
Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can
drive a topologically trivial system into the nontrivial phase.
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Let $f_c(z) = z^2+c$ for $c \in \mathbb{C}$. We show there exists a uniform
bound on the number of points in $\mathbb{P}^1(\mathbb{C})$ that can be
preperiodic for both $f_{c_1}$ and $f_{c_2}$ with $c_1\not= c_2$ in
$\mathbb{C}$. The proof combines arithmetic ingredients with complex-analytic;
we estimate an adelic energy pairing when the parameters lie in
$\bar{\mathbb{Q}}$, building on the quantitative arithmetic equidistribution
theorem of Favre and Rivera-Letelier, and we use distortion theorems in complex
analysis to control the size of the intersection of distinct Julia sets. The
proof is effective, and we provide explicit constants for each of the results.
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There are, by now, several arguments that superstrata, which represent
D1-D5-P bound states that depend upon arbitrary functions of two variables and
that preserve four supersymmetries, exist in string theory, and that their
gravitational back-reaction results in smooth horizonless solutions. In this
paper we examine the shape and density modes of the superstratum and give
strong evidence that the back-reacted supergravity solution allows for
fluctuation modes whose quantization reproduces the entropy growth of black
holes as a function of the charges. In particular, we argue that the shape
modes of the superstratum that lie purely within the non-compact space-time
directions account for at least $1/\sqrt{6}$ of the entropy of the D1-D5-P
black hole and propose a way in which the rest of the entropy could be captured
by superstratum fluctuations. We complete the picture by conjecturing a
relationship between bound states of multiple superstrata and momentum
excitations of different twisted sectors of the dual CFT.
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Based on archive photographic photometry and recent CCD photometric data for
red novae V4332 Sgr and V838 Mon, we established their stellar composition,
exploded components, and the nature of explosions. Low temperature in the
outburst maximum is due to quasi-adiabatic expansion of a massive stellar
envelope after the central energy surge preceded the outburst.
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The recently reported superconductivity 9-15 K in Nd0.8Sr0.2NiO2/SrTiO3
heterostructures that were fabricated by a soft-chemical topotactic reduction
approach based on precursor Nd0.8Sr0.2NiO3 thin films deposited on SrTiO3
substrates, has excited an immediate surge of research interest. To explore an
alternative physical path instead of chemical reduction for realizing
superconductivity in this compound, using pulsed laser deposition, we
systematically fabricated 63 Nd0.8Sr0.2NiOx (NSNO) thin films at a wide range
of oxygen partial pressures on various different oxide substrates. Transport
measurements did not find any signature of superconductivity in all the 63
thin-film samples. With reducing the oxygen content in the NSNO films by
lowering the deposition oxygen pressure, the NSNO films are getting more
resistive and finally become insulating. Furthermore, we tried to cap a
20-nm-thick amorphous LaAlO3 layer on a Nd0.8Sr0.2NiO3 thin film deposited at a
high oxygen pressure of 150 mTorr to create oxygen vacancies on its surface and
did not succeed in higher conductivity either. Our experimental results
together with the recent report on the absence of superconductivity in
synthesized bulk Nd0.8Sr0.2NiO2 crystals suggest that the chemical reduction
approach could be unique for yielding superconductivity in NSNO/SrTiO3
heterostructures. However, SrTiO3 substrates could be reduced to generate
oxygen vacancies during the chemical reduction process as well, which may thus
partially contribute to conductivity.
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Rational word languages can be defined by several equivalent means: finite
state automata, rational expressions, finite congruences, or monadic
second-order (MSO) logic. The robust subclass of aperiodic languages is defined
by: counter-free automata, star-free expressions, aperiodic (finite)
congruences, or first-order (FO) logic. In particular, their algebraic
characterization by aperiodic congruences allows to decide whether a regular
language is aperiodic.
We lift this decidability result to rational transductions, i.e.,
word-to-word functions defined by finite state transducers. In this context,
logical and algebraic characterizations have also been proposed. Our main
result is that one can decide if a rational transduction (given as a
transducer) is in a given decidable congruence class. We also establish a
transfer result from logic-algebra equivalences over languages to equivalences
over transductions. As a consequence, it is decidable if a rational
transduction is first-order definable, and we show that this problem is
PSPACE-complete.
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We analyze lepton flavor violating $\tau \to \mu \gamma$ and $\mu \to e
\gamma$ processes in SUSY GUT model in which sfermions have special mass
spectrum. It is assumed that only third generation sfermions which are
contained in ${\bf 10}(Q, U^c, E^c)$ of SU(5) can have a different mass from
the others. This mass spectrum is led from $E_6$ GUT model with horizontal
symmetries. It is shown that branching ratios of $\tau \to \mu \gamma$ and $\mu
\to e \gamma$ depend strongly on a right-handed stau mass. The weak scale
stability requires the light stau, so large decay rates can be expected in this
scenario. When stau is around 150 GeV and $\tan \beta \sim 10$, the branching
ratios can be larger than $Br(\tau \to \mu \gamma) \simeq 10^{-8}$ and $Br(\mu
\to e \gamma) \simeq 5\times 10^{-12}$, which are within reach of future
experiments. In addition, this model has an interesting feature that the final
state charged lepton tends to have the right-handed chirality.
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Image restoration aims to restore high-quality images from degraded
counterparts and has seen significant advancements through deep learning
techniques. The technique has been widely applied to mobile devices for tasks
such as mobile photography. Given the resource limitations on mobile devices,
such as memory constraints and runtime requirements, the efficiency of models
during deployment becomes paramount. Nevertheless, most previous works have
primarily concentrated on analyzing the efficiency of single modules and
improving them individually. This paper examines the efficiency across
different layers. We propose a roadmap that can be applied to further
accelerate image restoration models prior to deployment while simultaneously
increasing PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity
Index). The roadmap first increases the model capacity by adding more
parameters to partial convolutions on FLOPs non-sensitive layers. Then, it
applies partial depthwise convolution coupled with decoupling
upsampling/downsampling layers to accelerate the model speed. Extensive
experiments demonstrate that our approach decreases runtime by up to 13% and
reduces the number of parameters by up to 23%, while increasing PSNR and SSIM
on several image restoration datasets. Source Code of our method is available
at \href{https://github.com/xiangyu8/MOFA}{https://github.com/xiangyu8/MOFA}.
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If X is a geodesic metric space and $x_1,x_2,x_3\in X$, a {\it geodesic
triangle} $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$,
$[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-\emph{hyperbolic}
$($in the Gromov sense$)$ if any side of $T$ is contained in a
$\delta$-neighborhood of the union of the two other sides, for every geodesic
triangle $T$ in $X$. We denote by $\delta(X)$ the sharp hyperbolicity constant
of $X$, i.e. $\delta(X):=\inf\{\delta\ge 0: \, X \, \text{ is
$\delta$-hyperbolic}\,\}\,. $ The main result of this paper is the inequality
$\delta(G) \le \delta(\mathcal L(G))$ for the line graph $\mathcal L(G)$ of
every graph $G$. We prove also the upper bound $\delta(\mathcal L(G)) \le 5
\delta(G)+ 3 l_{max}$, where $l_{max}$ is the supremum of the lengths of the
edges of $G$. Furthermore, if every edge of $G$ has length $k$, we obtain
$\delta(G) \le \delta(\mathcal L(G)) \le 5 \delta(G)+ 5k/2$.
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We study finite temperature transport in the Luttinger-Abrikosov-Beneslavskii
phase -- an interacting, scale invariant, non-Fermi liquid phase found in
quadratic semimetals. We develop a kinetic equation formalism to describe the
d.c. transport properties, which are dominated by collisions, and compute the
shear viscosity $\eta$. The ratio of shear viscosity to entropy density
$\eta/s$ is a measure of the strength of interaction between the excitations of
a quantum fluid. As a consequence of the quantum critical nature of the system,
$\eta / s$ is a universal number and we find it to be consistent with a bound
proposed from gauge-gravity duality.
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We discuss Beta operators with Jacobi weights on $C[0,1]$ for
$\alpha,\beta\geq-1$, thus including the discussion of three limiting cases.
Emphasis is on the moments and their asymptotic behavior. Extended
Voronovskaya-type results and a discussion concerning the over-iteration of the
operators are included.
|
We show that the usual picture of supersoft X-ray binary evolution as driven
by conservative thermal-timescale mass transfer cannot explain the short
orbital periods of RX J0537.7-7034 (3.5 hr) and 1E 0035.4-7230 (4.1 hr).
Non-conservative evolution may produce such periods, but requires very
significant mass loss, and is highly constrained.
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Molecular cloud observations show that clouds have non-thermal velocity
dispersions that scale with the cloud size as $\sigma\propto R^{1/2}$ at
constant surface density, and for varying surface density scale with both the
cloud`s size and surface density, $\sigma^2 \propto R \Sigma$. The energy
source driving these chaotic motions remains poorly understood. We describe the
velocity dispersions observed in a cloud population formed in a
kiloparsec-scale numerical simulation of a magnetized, supernova-driven,
self-gravitating, interstellar medium, including diffuse heating and radiative
cooling. We compare the relationships between velocity dispersion, size, and
surface density measured in the simulated cloud population to those found in
observations of Galactic molecular clouds. We find that external supernova
explosions can not drive turbulent motions of the observed magnitudes within
dense clouds. On the other hand, self-gravity also induces non-thermal motions
as gravitationally bound clouds begin to collapse in our model, and by doing so
their internal velocity dispersions recover the observed relations. Energy
conservation suggests that the observed behavior is consistent with the kinetic
energy being proportional to the gravitational energy. However, the clouds in
our model show no sign of reaching a stable equilibrium state at any time, even
for strongly magnetized clouds. We conclude that gravitationally bound
molecular clouds are always in a state of gravitational collapse and their
properties are a natural result of this chaotic collapse. In order to agree
with observed star formation efficiencies, this process must be terminated by
the early destruction of the clouds, presumably from internal stellar feedback.
|
We present a comparison of the parameters of accretion disc outflows and the
jet of the broad-line radio galaxy 3C 111 on sub-pc scales. We make use of
published X-ray observations of ultra-fast outflows (UFOs) and new 43GHz VLBA
images to track the jet knots ejection. We find that the superluminal jet
coexists with the mildly relativistic outflows on sub-pc scales, possibly
indicating a transverse stratification of a global flow. The two are roughly in
pressure equilibrium, with the UFOs potentially providing additional support
for the initial jet collimation. The UFOs are much more massive than the jet,
but their kinetic power is probably about an order of magnitude lower, at least
for the observations considered here. However, their momentum flux is
equivalent and both of them are powerful enough to exert a concurrent feedback
impact on the surrounding environment. A link between these components is
naturally predicted in the context of MHD models for jet/outflow formation.
However, given the high radiation throughput of AGNs, radiation pressure should
also be taken into account. From the comparison with the long-term 2-10keV RXTE
light curve we find that the UFOs are preferentially detected during periods of
increasing flux. We also find the possibility to place the UFOs within the
known X-ray dips-jet ejection cycles, which has been shown to be a strong proof
of the disc-jet connection, in analogue with stellar-mass black holes. However,
given the limited number of observations presently available, these relations
are only tentative and additional spectral monitoring is needed to test them
conclusively.
|
We prove existence and stability of smooth entire strictly convex spacelike
hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is
based on barrier constructions and local a priori estimates.
|
Universal blind quantum computing allows users with minimal quantum resources
to delegate a quantum computation to a remote quantum server, while keeping
intrinsically hidden input, algorithm, and outcome. State-of-art experimental
demonstrations of such a protocol have only involved one client. However, an
increasing number of multi-party algorithms, e.g. federated machine learning,
require the collaboration of multiple clients to carry out a given joint
computation. In this work, we propose and experimentally demonstrate a
lightweight multi-client blind quantum computation protocol based on a novel
linear quantum network configuration (Qline). Our protocol originality resides
in three main strengths: scalability, since we eliminate the need for each
client to have its own trusted source or measurement device, low-loss, by
optimizing the orchestration of classical communication between each client and
server through fast classical electronic control, and compatibility with
distributed architectures while remaining intact even against correlated
attacks of server nodes and malicious clients.
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We introduce the mean curvature flow of curves in the Minkowski plane
$\mathbf R^{1,1}$ and give a classification of all the self-similar solutions.
In addition, we describe five other exact solutions to the flow.
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We assume a flat brane located at y=0, surrounded by an AdS space, and
consider the 5D Einstein equations when the energy flux component of the
energy-momentum tensor is related to the Hubble parameter through a constant Q.
We calculate the metric tensor, as well as the Hubble parameter on the brane,
when Q is small. As a special case, if the brane is tensionless, the influence
from Q on the Hubble parameter is absent. We also consider the emission of
gravitons from the brane, by means of the Boltzmann equation. Comparing the
energy conservation equation derived herefrom with the energy conservation
equation for a viscous fluid on the brane, we find that the entropy change for
the fluid in the emission process has to be negative. This peculiar effect is
related to the fluid on the brane being a non-closed thermodynamic system. The
negative entropy property for non-closed systems is encountered in other areas
in physics also, in particular, in connection with the Casimir effect at finite
temperature.
|
RV variable stars are important in astrophysics. The Large Sky Area
Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey has
provided ~ 6.5 million stellar spectra in its Data Release 4 (DR4). During the
survey, ~ 4.7 million unique sources were targeted and ~ 1 million stars
observed repeatedly. The probabilities of stars being RV variables are
estimated by comparing the observed radial velocity variations with the
simulated ones. We build a catalog of 80,702 RV variable candidates with
probability greater than 0.60 by analyzing the duplicate-observed multi-epoch
sources covered by the LAMOST DR4. Simulations and cross-identifications show
that the purity of the catalog is higher than 80%. The catalog consists of 77%
binary systems and 7% pulsating stars as well as 16% pollution by single stars.
3,138 RV variables are classified through cross-identifications with published
results in literatures. By using the 3,138 sources common to both LAMOST and a
collection of published RV variable catalogs we are able to analyze LAMOST's RV
variable detection rate. The efficiency of the method adopted in this work
relies not only on the sampling frequency of observations but also periods and
amplitudes of RV variables. With the progress of LAMOST, Gaia and other
surveys, more and more RV variables would will be confirmed and classified.
This catalog is valuable for other large-scale surveys, especially for RV
variable searches. The catalog will be released according to the LAMOST Data
Policy via http://dr4.lamost.org.
|
The multiphase flow of droplets is widespread, both at the industrial and the
microscale, for both biological and non-biological applications alike. But the
ensemble interactions of such systems are inherently nonlinear and complex,
compounded by interfacial effects, making it a difficult many-body problem for
theory. In comparison, the self-assembly dynamics of solid particles in flow
have long been described and successfully exploited in the field of inertial
microfluidics, where particle crystals can be realized from inertial forces and
hydrodynamic interactions. Here, we report novel self-assembly dynamics of
liquid drops in confined microfluidic channels that contrast starkly with the
established paradigm of inertial microfluidics: higher inertia leads to better
spatial ordering. Instead, we find that the conventional straight wall channel
geometry not only fails to achieve regular spatial ordering for drops but
actually exacerbates it with increasing inertia. Conversely, an asymmetric
serpentine geometry is able to achieve long-range, periodic spatial ordering
over length scales that are at least 3 orders of magnitude greater than the
drop diameter, particularly at low inertia. Experimentally, we are able to
decouple droplet generation from ordering, enabling independent variation of
number density, confinement, inertia, and surfactant concentration. We find the
inertia-dependent emergence of preferred drop separations and show for the
first time that Marangoni effects can influence the longitudinal ordering of
multidrop arrays. These results present a largely unexplored direction for
inertial microfluidics but also show the potential of its unification with
droplet microfluidics. In particular, the utility of passively restoring
uniform drop spacing on-chip is a key requirement for the streamlined
integration of incubation and drop-by-drop interrogation capabilities.
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We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier
derivatives of various encodings of Turing machines into linear logic. We show
that these derivatives calculate the rate of change of probabilities naturally
arising in the Sweedler semantics of linear logic proofs. The resulting theory
is applied to the problem of synthesising Turing machines by gradient descent.
|
Self-organizing networks such as Neural Gas, Growing Neural Gas and many
others have been adopted in actual applications for both dimensionality
reduction and manifold learning. Typically, in these applications, the
structure of the adapted network yields a good estimate of the topology of the
unknown subspace from where the input data points are sampled. The approach
presented here takes a different perspective, namely by assuming that the input
space is a manifold of known dimension. In return, the new type of growing
self-organizing network presented gains the ability to adapt itself in way that
may guarantee the effective and stable recovery of the exact topological
structure of the input manifold.
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Orthogonal time frequency space (OTFS) modulation can effectively convert a
doubly dispersive channel into an almost non-fading channel in the
delay-Doppler domain. However, one critical issue for OTFS is the very high
complexity of equalizers. In this letter, we first reveal the doubly block
circulant feature of OTFS channel represented in the delay-Doppler domain. By
exploiting this unique feature, we further propose zero-forcing (ZF) and
minimum mean squared error (MMSE) equalizers that can be efficiently
implemented with the two-dimensional fast Fourier transform. The complexity of
our proposed equalizers is gracefully reduced from
$\mathcal{O}\left(\left(NM\right)^{3}\right)$ to
$\mathcal{O}\left(NM\mathrm{log_{2}}\left(NM\right)\right)$, where $N$ and $M$
are the number of OTFS symbols and subcarriers, respectively. Analysis and
simulation results show that compared with other existing linear equalizers for
OTFS, our proposed linear equalizers enjoy a much lower computational
complexity without any performance loss.
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The microlensing optical depth to Baade's Window constrains the minimum total
mass in baryonic matter within the Solar circle to be greater than 3.9 x
10^{10} solar masses, assuming the inner Galaxy is barred with viewing angle of
roughly 20 degrees. From the kinematics of solar neighbourhood stars, the local
surface density of dark matter is about 30 +/- 15 solar masses per square
parsec. We construct cuspy haloes normalised to the local dark matter density
and calculate the circular-speed curve of the halo in the inner Galaxy. This is
added in quadrature to the rotation curve provided by the stellar and ISM
discs, together with a bar sufficiently massive so that the baryonic matter in
the inner Galaxy reproduces the microlensing optical depth. Such models violate
the observational constraint provided by the tangent-velocity data in the inner
Galaxy (typically at radii 2-4 kpc). The high baryonic contribution required by
the microlensing is consistent with implications from hydrodynamical modelling
and the pattern speed of the Galactic bar. We conclude that the cuspy haloes
favoured by the Cold Dark Matter cosmology (and its variants) are inconsistent
with the observational data on the Galaxy.
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We study the impact of the Sommerfeld enhancement on the thermal relic
density of the lightest neutralino in the case of large co-annihilation effects
with a scalar particle. The proper way of including the Sommerfeld effect in
this case is discussed, and the appropriate formulas for a general scenario
with a set of particles with arbitrary masses and (off-)diagonal interactions
are provided. We implement these results to compute the relic density in the
neutralino sfermion co-annihilation regions in the mSUGRA framework. We find
non-negligible effects in whole sfermion co-annihilation regimes. For stau
co-annihilations the correction to the relic density is of the order of several
per cent, while for stop co-annihilations is much larger, reaching a factor of
5 in some regions of the parameter space. A numerical package for computing the
neutralino relic density including the Sommerfeld effect in a general MSSM
setup is made public available.
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Two-dimensional semiconductor moir\'e materials have emerged as a highly
controllable platform to simulate and explore quantum condensed matter.
Compared to real solids, electrons in semiconductor moir\'e materials are less
strongly attracted to the moir\'e lattice sites, making the nonlocal
contributions to the magnetic interactions as important as the Anderson
super-exchange. It provides a unique platform to study the effects of competing
magnetic interactions. Here, we report the observation of strongly frustrated
magnetic interactions in a Wigner-Mott insulating state at 2/3 filling of the
moir\'e lattice in angle-aligned WSe2/WS2 heterobilayers. Magneto-optical
measurements show that the net exchange interaction is antiferromagnetic for
filling factors below 1 with a strong suppression at 2/3 filling. The
suppression is lifted upon screening of the long-range Coulomb interactions and
melting of the Wigner-Mott insulator by a nearby metallic gate. The results can
be qualitatively captured by a honeycomb-lattice spin model with an
antiferromagnetic nearest-neighbor coupling and a ferromagnetic second-neighbor
coupling. Our study establishes semiconductor moir\'e materials as a model
system for the lattice-spin physics and frustrated magnetism.
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In the Internet of Things (IoT), heterogeneous devices connect to each other
and to external systems to exchange data and provide services. Given the
diversity of devices, it is becoming increasingly common to establish
collaborative relationships between devices to provide composite services.
However, due to the high degree of heterogeneity in the IoT context, one of the
most significant challenges is to develop software applications that can run on
a wide variety of devices and can communicate and collaborate with an even
wider array of systems. A common middleware infrastructure for these devices
will therefore have a significant impact on the design, deployment, and use of
services in IoT systems by allowing developers to focus on the applications
rather than the low-level implementation details each device.
|
We study the identity testing problem in the context of spin systems or
undirected graphical models, where it takes the following form: given the
parameter specification of the model $M$ and a sampling oracle for the
distribution $\mu_{\hat{M}}$ of an unknown model $\hat{M}$, can we efficiently
determine if the two models $M$ and $\hat{M}$ are the same? We consider
identity testing for both soft-constraint and hard-constraint systems. In
particular, we prove hardness results in two prototypical cases, the Ising
model and proper colorings, and explore whether identity testing is any easier
than structure learning.
For the ferromagnetic (attractive) Ising model, Daskalakis et al. (2018)
presented a polynomial time algorithm for identity testing. We prove hardness
results in the antiferromagnetic (repulsive) setting in the same regime of
parameters where structure learning is known to require a super-polynomial
number of samples. In particular, for $n$-vertex graphs of maximum degree $d$,
we prove that if $|\beta| d = \omega(\log{n})$ (where $\beta$ is the inverse
temperature parameter), then there is no polynomial running time identity
testing algorithm unless $RP=NP$. We also establish computational lower bounds
for a broader set of parameters under the (randomized) exponential time
hypothesis. Our proofs utilize insights into the design of gadgets using random
graphs in recent works concerning the hardness of approximate counting by Sly
(2010). In the hard-constraint setting, we present hardness results for
identity testing for proper colorings. Our results are based on the presumed
hardness of #BIS, the problem of (approximately) counting independent sets in
bipartite graphs. In particular, we prove that identity testing is hard in the
same range of parameters where structure learning is known to be hard.
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We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG)
for hyperbolic equations with random and singular coefficients. Due to the
singu- lar nature of the solution, the standard gPC-SG methods may suffer from
a poor or even non convergence. Taking advantage of the fact that the discrete
solution, by the central type finite difference or finite volume approximations
in space and time for example, is smoother, we first discretize the equation by
a smooth finite difference or finite volume scheme, and then use the gPC-SG
approximation to the discrete system. The jump condition at the interface is
treated using the immersed upwind methods introduced in [8, 12]. This yields a
method that converges with the spectral accuracy for finite mesh size and time
step. We use a linear hyperbolic equation with discontinuous and random
coefficient, and the Liouville equation with discontinuous and random
potential, to illustrate our idea, with both one and second order spatial
discretizations. Spectral convergence is established for the first equation,
and numerical examples for both equations show the desired accu- racy of the
method.
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The multi-sensory setups consisting of the laser scanners and cameras are
popular as the measurements complement each other and provide necessary
robustness for applications. Under dynamic conditions or when in motion, a
direct transformation (spatial calibration) and time offset between sensors
(temporal calibration) is needed to determine the correspondence between
measurements. We propose an open-source spatiotemporal calibration framework
for a camera and a 3D laser scanner. Our solution is based on commonly
available chessboard markers requiring one-minute calibration before the
operation that offers accurate and repeatable results. The framework is based
on batch optimization of point-to-plane constraints with a time offset
calibration possible by a novel continuous representation of the plane
equations based on a minimal representation in the Lie algebra and the use of
B-splines. The framework's properties are evaluated in simulation while
correctness is verified with two distinct sensory setups with Velodyne VLP-16
and SICK MRS6124 3D laser scanners.
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We consider a nonlinear sigma model coupled to the metric of a conic space.
We obtain restrictions for a nonlinear sigma model to be a source of the conic
space. We then study nonlinear sigma model in the conic space background. We
find coordinate transformations which reduce the chiral fields equations in the
conic space background to field equations in Minkowski spacetime. This enables
us to apply the same methods for obtaining exact solutions in Minkowski
spacetime to the case of a conic spacetime. In the case the solutions depend on
two spatial coordinates we employ Ivanov's geometrical ansatz. We give a
general analysis and also present classes of solutions in which there is
dependence on three and four coordinates. We discuss with special attention the
intermediate instanton and meron solutions and their analogous in the conic
space. We find differences in the total actions and topological charges of
these solutions and discuss the role of the deficit angle.
|
We develop a minimal model to describe growing dense active matter such as
biological tissues, bacterial colonies and biofilms, that are driven by a
competition between particle division and steric repulsion. We provide a
detailed numerical analysis of collective and single particle dynamics. We show
that the microscopic dynamics can be understood as the superposition of an
affine radial component due to the global growth, and of a more complex
non-affine component which displays features typical of driven soft glassy
materials, such as aging, compressed exponential decay of time correlation
functions, and a crossover from superdiffusive behaviour at short scales to
subdiffusive behaviour at larger scales. This analogy emerges because particle
division at the microscale leads to a global expansion which then plays a role
analogous to shear flow in soft driven glasses. We conclude that growing dense
active matter and sheared dense suspensions can generically be described by the
same underlying physics.
|
The brittleness of an aluminide diffusion coating protecting a Ren\'e 125
Ni-based polycrystalline superalloy was investigated over a wide range of
temperatures in its as-received and thermally aged form. Isothermal and thermal
cycled aging were performed on the coated system at a maximum temperature of
1100 {\deg}C. Microstructure evolutions and damage initiation within the
coating were characterized. Interrupted tensile tests and thermomechanical
fatigue tests were conducted to document critical stress-strain conditions
leading to the coating cracking and lifetime for the case of thermo-mechanical
fatigue loading. Advanced digital image correlation and acoustic emission
techniques were used to detect coating cracking. Isothermal oxidation or cyclic
oxidation led to improved strain-to-failure due to metallurgical evolutions and
also longer fatigue life under thermomechanical fatigue conditions.
|
We consider two types of $p$-centro affine flows on smooth, centrally
symmetric, closed convex planar curves, $p$-contracting, respectively,
$p$-expanding. Here $p$ is an arbitrary real number greater than 1. We show
that, under any $p$-contracting flow, the evolving curves shrink to a point in
finite time and the only homothetic solutions of the flow are ellipses centered
at the origin. Furthermore, the normalized curves with enclosed area $\pi$
converge, in the Hausdorff metric, to the unit circle modulo SL(2). As a
$p$-expanding flow is, in a certain way, dual to a contracting one, we prove
that, under any $p$-expanding flow, curves expand to infinity in finite time,
while the only homothetic solutions of the flow are ellipses centered at the
origin. If the curves are normalized as to enclose constant area $\pi$, they
display the same asymptotic behavior as the first type flow and converge, in
the Hausdorff metric, and up to SL(2) transformations, to the unit circle. At
the end, we present a new proof of $p$-affine isoperimetric inequality, $p\geq
1$, for smooth, centrally symmetric convex bodies in $\mathbb{R}^2$.
|
B. Schumacher and M. Westmoreland have established a quantum analog of a
well-known classical information theory result on a role of relative entropy as
a measure of non-optimality in (classical) data compression. In this paper, we
provide an alternative, simple and constructive proof of this result by
constructing quantum compression codes (schemes) from classical data
compression codes. Moreover, as the quantum data compression/coding task can be
effectively reduced to a (quasi-)classical one, we show that relevant results
from classical information theory and data compression become applicable and
therefore can be extended to the quantum domain.
|
Undirected hyperbolic graph models have been extensively used as models of
scale-free small-world networks with high clustering coefficient. Here we
presented a simple directed hyperbolic model, where nodes randomly distributed
on a hyperbolic disk are connected to a fixed number m of their nearest spatial
neighbours. We introduce also a canonical version of this network (which we
call "network with varied connection radius"), where maximal length of outgoing
bond is space-dependent and is determined by fixing the average out-degree to
m. We study local bond length, in-degree and reciprocity in these networks as a
function of spatial coordinates of the nodes, and show that the network has a
distinct core-periphery structure. We show that for small densities of nodes
the overall in-degree has a truncated power law distribution. We demonstrate
that reciprocity of the network can be regulated by adjusting an additional
temperature-like parameter without changing other global properties of the
network.
|
In this article, we study the behavior of the stability of pullback of a
vector bundle under a finite morphism from a (not necessarily smooth) stacky
curve to an orbifold curve. We establish a categorical equivalence between
proper formal orbifold curves and proper orbifold curves in the sense of
Deligne-Mumford stacks. Using this identification, we define the notion of
slope $P$-(semi)stability of vector bundles on proper formal orbifold curves
$(X,P)$. We establish some equivalent conditions for a stacky genuinely
ramified morphism, analogous to the case of curves. Finally, we show that for a
cover of an orbifold curve arising as a cartesian pullback via a genuinely
ramified morphism of smooth projective connected curves, the orbifold slope
stability is preserved under the pullback.
|
The relation between fermion mixing and horizontal symmetry is discussed.
|
We study geometric aspects of the Laughlin fractional quantum Hall (FQH)
states using a description of these states in terms of a matrix quantum
mechanics model known as the Chern-Simons matrix model (CSMM). This model was
proposed by Polychronakos as a regularization of the noncommutative
Chern-Simons theory description of the Laughlin states proposed earlier by
Susskind. Both models can be understood as describing the electrons in a FQH
state as forming a noncommutative fluid, i.e., a fluid occupying a
noncommutative space. Here we revisit the CSMM in light of recent work on
geometric response in the FQH effect, with the goal of determining whether the
CSMM captures this aspect of the physics of the Laughlin states. For this model
we compute the Hall viscosity, Hall conductance in a non-uniform electric
field, and the Hall viscosity in the presence of anisotropy (or intrinsic
geometry). Our calculations show that the CSMM captures the guiding center
contribution to the known values of these quantities in the Laughlin states,
but lacks the Landau orbit contribution. The interesting correlations in a
Laughlin state are contained entirely in the guiding center part of the
state/wave function, and so we conclude that the CSMM accurately describes the
most important aspects of the physics of the Laughlin FQH states, including the
Hall viscosity and other geometric properties of these states which are of
current interest.
|
A giant tunneling electroresistance effect may be achieved in a ferroelectric
tunnel junction by exploiting the magnetoelectric effect at the interface
between a ferroelectric barrier and magnetic La1-xSrxMnO3 electrode. Using
first-principles density functional theory we demonstrate that a few magnetic
monolayers of La1-xSrxMnO3 near the interface act, in response to ferroelectric
polarization reversal, as an atomic scale spin-valve by filtering
spin-dependent current. This effect produces more than an order of magnitude
change in conductance, and thus constitutes a giant resistive switching effect.
|
We show that if a surgery on a knot in a product sutured manifold yields the
same product sutured manifold, then this knot is a 0-- or 1--crossing knot. The
proof uses techniques from sutured manifold theory.
|
A number of approaches to gravitation have much in common with the gauge
theories of the standard model of particle physics. In this paper, we develop
the Hamiltonian formulation of a class of gravitational theories that may be
regarded as spontaneously-broken gauge theories of the complexified Lorentz
group $SO(1,3)_C$ with the gravitational field described entirely by a gauge
field valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued in
the group's fundamental representation. The theories have one free parameter
$\beta$ which appears in a similar role to the inverse of the Barbero-Immirzi
parameter of Einstein-Cartan theory. However, contrary to that parameter, it is
shown that the number of degrees of freedom crucially depends on the value of
$\beta$. For non-zero values of $\beta$, it is shown that three complex degrees
of freedom propagate on general backgrounds, and for the specific values
$\beta=\pm i$ an extension to General Relativity is recovered in a
symmetry-broken regime. For the value $\beta=0$, the theory propagates no local
degrees of freedom. A non-zero value of $\beta$ corresponds to the self-dual
and anti-self-dual gauge fields appearing asymmetrically in the action,
therefore in these models, the existence of gravitational degrees of freedom is
tied to chiral asymmetry in the gravitational sector.
|
In this paper, we investigate ${\mathcal F}$-hypercyclicity of linear, not
necessarily continuous, operators on Fr\' echet spaces. The notion of lower
$(m_{n})$-hypercyclicity seems to be new and not considered elsewhere even for
linear continuous operators acting on Fr\' echet spaces. We pay special
attention to the study of $q$-frequent hypercyclicity, where $q\geq 1$ is an
arbitrary real number. We present several new concepts and results for lower
and upper densities in a separate section, providing also a great number of
illustrative examples and open problems.
|
Solar flare is one of the most important solar activities which emit all
electromagnetic waves in gigantic burst. The radio emission can be used to
determine the physical properties of the solar flares. The e-CALLISTO worldwide
network is designed to detect the radio emission of the solar flares and this
study used the spectroscopic data from the e-CALLISTO system. Among the five
types of solar radio bursts, this study was focused on type II radio bursts.
The spectroscopic analysis estimated the shock speed of type II radio bursts
using the uniform electron density model and the nonuniform electron density
model of the sun. The shock speed is proportional to the electron density (Ne)
and inversely proportional to the rate of change in electron density with
altitude (dNe/dr). The determined shock speed at the altitude of one solar
radius is 2131 km/s for uniform model and 766 km/s for non-uniform model.
Although the uniform electron density model is widely used we attempted the
non-uniform electron density since in the active region of the sun, the
electron densities are non-uniform. The estimated shock speeds of uniform
density model is relatively high so that it is reasonable to use non-uniform
electron density model for shock speed estimation of type II radio bursts.
|
Dimuonium (the bound system of two muons, $\mu^+\mu^-$-atom) has not been
observed yet. In this paper we discuss the electromagnetic production of
dimuonium at RHIC and LHC in relativistic heavy ion collisions. The production
of parastates is analyzed in the equivalent photon approximation. For the
treatment of orthostates, we develop a three photon formalism. We determine the
production rates at RHIC and LHC with an accuracy of a few percent and discuss
problems related to the observation of dimuonium.
|
The helicity dependence of the inclusive $\pi^-$ photoproduction reaction
from the deuteron in the $\Delta$(1232)-resonance region is investigated with
inclusion of final-state nucleon-nucleon rescattering ($NN$-FSI). For the
elementary $\pi$-production operator an effective Lagrangian model which
includes the standard pseudovector Born terms and a contribution from the
$\Delta$-resonance is used. The half-off-shell $NN$-scattering matrix is
obtained from a separable representation of a realistic $NN$-interaction. The
differential polarized cross-section difference for parallel and antiparallel
helicity states is predicted and compared with experiment. We find that the
effect of $NN$-FSI is much less important in the helicity difference than in
the previously studied unpolarized differential cross section. Furthermore, the
contribution of $\vec d(\vec\gamma,\pi^-)pp$ to the deuteron spin asymmetry is
explicitly evaluated with inclusion of $NN$-FSI. It has been found that the
effect of $NN$-FSI is much larger in the asymmetry than in the total cross
section, and this leads to an appreciable reduction of the spin asymmetry in
the $\Delta$-region. Inclusion of such effect also leads to improved and quite
satisfactory agreement with existing experimental data.
|
Recent studies of the Q^2 dependence of ep scattering in the large x region
and in the Q^2 range: 1 < Q^2 <leq 30 Gev^2, confirm the validity of the
phenomenon of quark-hadron duality - the similarity of the deep inelastic
(parton) and resonance (hadron) spectra - for values of the invariant mass, W^2
> 2.4 GeV^2 At lower values of W^2, duality is found to be significantly
violated by an amount that cannot be parametrized in terms of the first few
terms of a series of power corrections. We present a dynamical model that
explains the Q^2 dependence of the data: at low W^2, non-partonic components
given by color neutral clusters dominate the cross section and the Q^2
dependence is governed by their mass spectrum, predicted within the
preconfiment property of Q CD; at large W^2 the structure function is
determined by a convolution of the cluster mass spectrum with the parton
distributions.
|
Non-orthogonal multiple access (NOMA) enables power-domain multiplexing via
successive interference cancellation (SIC) and has been viewed as a promising
technology for 5G communication. The full benefit of NOMA depends on resource
allocation, including power allocation and channel assignment, for all users,
which, however, leads to mixed integer programs. In the literature, the optimal
power allocation has only been found in some special cases, while the joint
optimization of power allocation and channel assignment generally requires
exhaustive search. In this paper, we investigate resource allocation in
downlink NOMA systems. As the main contribution, we analytically characterize
the optimal power allocation with given channel assignment over multiple
channels under different performance criteria. Specifically, we consider the
maximin fairness, weighted sum rate maximization, sum rate maximization with
quality of service (QoS) constraints, energy efficiency maximization with
weights or QoS constraints in NOMA systems. We also take explicitly into
account the order constraints on the powers of the users on each channel, which
are often ignored in theexisting works, and show that they have a significant
impact on SIC in NOMA systems. Then, we provide the optimal power allocation
for the considered criteria in closed or semi-closed form. We also propose a
low-complexity efficient method to jointly optimize channel assignment and
power allocation in NOMA systems by incorporating the matching algorithm with
the optimal power allocation. Simulation results show that the joint resource
optimization using our optimal power allocation yields better performance than
the existing schemes.
|
The propagation of light in nonlinear media is well described by a $2$D
nonlinear Schr\"odinger equation (NLSE) within the paraxial approximation,
which is equivalent to the Gross-Pitaesvskii equation (GPE), the mean-field
description for the dynamics of Bose-Einstein condensates (BECs). Due to this
similarity, many theoretical and experimental investigations of phenomena which
have already been studied and realized in BECs have been recently analysed in
alternative experimental platforms such as hot atomic vapours. In this work, we
study the formation of droplets of light in these media, attempting to
establish a mapping between the experimental parameters normally used in BEC
experiments and those needed to observe the analogous phenomenon in hot atomic
vapours. We obtain the energy functional for the susceptibility of the medium
in the $\chi^{(3)}$ , $\chi^{(3)}+\chi^{(5)}$ and saturating regimes for a
two-level atomic configuration considering the focusing (attractive) regime. We
apply a Gaussian variational approach and check its predictions through
numerical simulations of the NLSE for each regime. Finally, we study the
real-time dynamics of the system for both the $\chi^{(3)}+\chi^{(5)}$ and
saturating nonlinearities, focusing our attention on the behaviour of the
breathing mode and on the analysis of droplet formation for realistic
experimental conditions.
|
Given a $K$-type $\pi$, it is known that its spin norm (due to first-named
author) is lower bounded by its lambda norm (due to Vogan). That is,
$\|\pi\|_{\rm spin}\geq \|\pi\|_{\rm lambda}$. This note aims to describe for
which $\pi$ one can actually have equality. We apply the result to tempered
Dirac series. In the case of real groups, we obtain that the tempered Dirac
series are divided into $\#W^1$ parts among all tempered modules with real
infinitesimal characters.
|
Wireless access points on unmanned aerial vehicles (UAVs) are being
considered for mobile service provisioning in commercial networks. To be able
to efficiently use these devices in cellular networks it is necessary to first
have a qualitative and quantitative understanding of how their design
parameters reflect on the service quality experienced by the end user. In this
paper we model a network of UAVs operating at a certain height above ground to
provide wireless service within coverage areas shaped by their directional
antennas, with the UAVs using the existing terrestrial base station network for
wireless backhaul. We provide an analytical expression for the coverage
probability experienced by a typical user as a function of the UAV parameters.
Using our derivations we demonstrate the existence of an optimum UAV height
which maximises the end user coverage probability. We then explore a scenario
where the UAVs adjust their individual heights to meet their backhaul
requirements while at the same time attempting to maximise the coverage
probability of the end user on the ground.
|
We develop a detailed microscopic analysis of electron transport in normal
diffusive conductors in the presence of proximity induced superconducting
correlation. We calculated the linear conductance of the system, the profile of
the electric field and the densities of states. In the case of transparent
metallic boundaries the temperature dependent conductance has a non-monotoneous
``reentrant'' structure. We argue that this behavior is due to nonequilibrium
effects occuring in the normal metal in the presence of both superconducting
correlations and the electric field there. Low transparent tunnel barriers
suppress the nonequilibrium effects and destroy the reentrant behavior of the
conductance. If the wire contains a loop, the conductance shows Aharonov-Bohm
oscillations with the period $\Phi_0=h/2e$ as a function of the magnetic flux
$\Phi$ inside the loop. The amplitude of these oscillations also demonstrates
the reentrant behavior vanishing at $T=0$ and decaying as $1/T$ at relatively
large temperatures. The latter behavior is due to low energy correlated
electrons which penetrate deep into the normal metal and ``feel'' the effect of
the magnetic flux $\Phi$. We point out that the density of states and thus the
``strengh'' of the proximity effect can be tuned by the value of the flux
inside the loop. Our results are fully consistent with recent experimental
findings.
|
Inspired by a concept in comparative genomics, we investigate properties of
randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$
left vertices, n right vertices, t edges, and each vertex of degree at least
one. We give asymptotic results for the number of such graphs and the number of
$(i,j)$ trees they contain. We compute the thresholds for the emergence of a
giant component and for the graph to be connected.
|
In this paper, we first give a necessary and sufficient condition for a
factor code with an unambiguous symbol to admit a subshift of finite type
restricted to which it is one-to-one and onto. We then give a necessary and
sufficient condition for the standard factor code on a spoke graph to admit a
subshift of finite type restricted to which it is finite-to-one and onto. We
also conjecture that for such a code, this finite-to-one property is equivalent
to the existence of a stationary Markov chain that achieves the capacity of the
corresponding deterministic channel.
|
We consider a model that approximates vortex rings in the axisymmetric 3D
Euler equation by the movement of almost rigid bodies described by Newtonian
mechanics. We assume that the bodies have a circular cross-section and that the
fluid is irrotational and interacts with the bodies through the pressure
exerted at the boundary. We show that this kind of system can be described
through an ODE in the positions of the bodies and that in the limit, where the
bodies shrink to massless filaments, the system converges to an ODE system
similar to the point vortex system. In particular, we can show that in a
suitable set-up, the bodies perform a leapfrogging motion.
|
We analyze relevant signals expected at the LHC for a left sneutrino as the
lightest supersymmetric particle (LSP). The discussion is carried out in the
`$\mu$ from $\nu$' supersymmetric standard model ($\mu \nu$SSM), where the
presence of $R$-parity breaking couplings involving right-handed neutrinos
solves the $\mu$ problem and reproduces neutrino data. The sneutrinos are pair
produced via a virtual $W$, $Z$ or $\gamma$ in the $s$ channel. From the prompt
decay of a pair of left sneutrinos LSPs of any family, a significant diphoton
signal plus missing transverse energy (MET) from neutrinos can be present in
the mass range 118-132 GeV, with 13 TeV center-of-mass energy and an integrated
luminosity of 100 fb$^{-1}$. In addition, in the case of a pair of tau left
sneutrinos LSPs, given the large value of the tau Yukawa coupling diphoton plus
leptons and/or multileptons can appear. We find that the number of expected
events for the multilepton signal, together with properly adopted search
strategies, is sufficient to give a significant evidence for a sneutrino of
mass in the range 130-310 GeV, even with the integrated luminosity of 20
fb$^{-1}$. In the case of the signal producing diphoton plus leptons, an
integrated luminosity of 100 fb$^{-1}$ is needed to give a significant evidence
in the mass range 95-145 GeV. Finally, we discuss briefly the presence of
displaced vertices and the associated range of masses.
|
Despite several (accepted) standards, core notions typically employed in
information technology or system engineering architectures lack the precise and
exact foundations encountered in logic, algebra, and other branches of
mathematics.
In this contribution we define the syntactical aspects of the term
architecture in a mathematically rigorous way. We motivate our particular
choice by demonstrating (i) how commonly understood and expected properties of
an architecture--as defined by various standards--can be suitably identified or
derived within our formalization, (ii) how our concept is fully compatible with
real life (business) architectures, and (iii) how our definition complements
recent foundational work in this area (Wilkinson 2018, Dickersen 2020).
We furthermore develop a rigorous notion of architectural similarity based on
the notion of homomorphisms allowing the class of architectures to be regarded
as a category, Arch. We demonstrate the applicability of our concepts to theory
by deriving theorems on the classification of certain types of architectures.
|
We present a measurement of the anisotropic void-galaxy cross-correlation
function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a
joint fit to the data for redshift space distortions (RSD) due to galaxy
peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect,
for the first time using a velocity field reconstruction technique to remove
the complicating effects of RSD in the void centre positions themselves. Fits
to the void-galaxy function give a 1% measurement of the AP parameter
combination $D_A(z)H(z)/c = 0.4367\pm 0.0045$ at redshift $z=0.57$, where $D_A$
is the angular diameter distance and $H$ the Hubble parameter, exceeding the
precision obtainable from baryon acoustic oscillations (BAO) by a factor of
~3.5 and free of systematic errors. From voids alone we also obtain a 10%
measure of the growth rate, $f\sigma_8(z=0.57)=0.501\pm0.051$. The parameter
degeneracies are orthogonal to those obtained from galaxy clustering. Combining
void information with that from BAO and galaxy RSD in the same CMASS sample, we
measure $D_A(0.57)/r_s=9.383\pm 0.077$ (at 0.8% precision),
$H(0.57)r_s=(14.05\pm 0.14)\;10^3$ kms$^{-1}$Mpc$^{-1}$ (1%) and
$f\sigma_8=0.453\pm0.022$ (4.9%), consistent with cosmic microwave background
(CMB) measurements from Planck. These represent a factor \sim2 improvement in
precision over previous results through the inclusion of void information.
Fitting a flat cosmological constant $\Lambda$CDM model to these results in
combination with Planck CMB data, we find up to an 11% reduction in
uncertainties on $H_0$ and $\Omega_m$ compared to use of the corresponding BOSS
consensus values. Constraints on extended models with non-flat geometry and a
dark energy of state that differs from $w=-1$ show an even greater improvement.
|
We propose a method to evaluate spectral functions on the lattice based on a
variational method. On a lattice with a finite spatial extent, spectral
functions consist of discrete spectra only. Adopting a variational method, we
calculate the locations and the heights of spectral functions at low-lying
discrete spectra. We first test the method in the case of analytically solvable
free Wilson quarks at zero and finite temperatures and confirm that the method
well reproduces the analytic results for low-lying spectra. We find that we can
systematically improve the results by increasing the number of trial states. We
then apply the method to calculate the charmonium spectral functions for S and
P-wave states at zero-temperature in quenched QCD and compare the results with
those obtained using the conventional maximum entropy method (MEM). The results
for the ground state are consistent with the location and the area of the first
peak in spectral functions from the MEM, while the variational method leads to
a mass which is closer to the experimental value for the first excited state.
We also investigate the temperature dependence of the spectral functions for
S-wave states below and above $T_c$. We obtain no clear evidences for
dissociation of $J/\psi$ and $\eta_c$ up to 1.4$T_c$.
|
We prove existence and uniqueness of travelling waves for a
reaction-diffusion system coupling a classical reaction-diffusion equation in a
strip with a diffusion equation on a line. To do this we use a continuation
method which leads to further insight into the system. In particular, the
transition occurs through a singular perturbation which seems new in this
context, connecting the system with a Wentzell type boundary value problem.
|
We study the growth of aligned domains in nematic liquid crystals. Results
are obtained solving the Beris-Edwards equations of motion using the lattice
Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a
consequence of the flow induced by the changing order parameter field
(backflow). The generalization of the results to the growth of a cylindrical
domain, which involves the dynamics of a defect ring, is discussed.
|
We analyse the effects of doping Holmium impurities into the full-Heusler
ferromagnetic alloy Co$_2$MnSi. Experimental results, as well as theoretical
calculations within Density Functional Theory in the "Local Density
Approximation plus Hubbard U" framework show that the holmium moment is aligned
antiparallely to that of the transition metal atoms. According to the
electronic structure calculations, substituting Ho on Co sites introduces a
finite density of states in the minority spin gap, while substitution on the Mn
sites preserves the half-metallic character.
|
Naturally small neutrino masses can arise in some grand unified models. The
mechanism of neutrino mass generation in these models typically requires the
existence of neutral heavy leptons. We study the low-energy phenomenology of
these new fermions. Concentrating on loop corrections due to neutral heavy
leptons, we examine how the flavour-conserving leptonic decays of the Z boson,
universality breaking in these decays, and the W boson mass depend on the mass
and mixings of the neutral heavy leptons. Working within the framework of a
superstring-inspired SU(2)_L x U(1)_Y model, we show that these
flavour-conserving processes have some virtues over the traditionally
considered flavour-violating decays.
|
We present a scheme for entangling the atoms of an optical lattice to reduce
the quantum projection noise of a clock measurement. The divalent clock atoms
are held in a lattice at a ``magic'' wavelength that does not perturb the clock
frequency -- to maintain clock accuracy -- while an open-shell J=1/2 ``head''
atom is coherently transported between lattice sites via the lattice
polarization. This polarization-dependent ``Archimedes' screw'' transport at
magic wavelength takes advantage of the vanishing vector polarizability of the
scalar, J=0, clock states of bosonic isotopes of divalent atoms. The on-site
interactions between the clock atoms and the head atom are used to engineer
entanglement and for clock readout.
|
On every compact and orientable three-manifold, we construct total foliations
(three codimension 1 foliations that are transverse at every point). This
construction can be performed on any homotopy class of plane fields with
vanishing Euler class.
As a corollary we obtain similar results on bi-contact structures.
|
In the recent paper \cite{LoD1}, we classified closed geodesics on Finsler
manifolds into rational and irrational two families, and gave a complete
understanding on the index growth properties of iterates of rational closed
geodesics. This study yields that a rational closed geodesic can not be the
only closed geodesic on every irreversible or reversible (including Riemannian)
Finsler sphere, and that there exist at least two distinct closed geodesics on
every compact simply connected irreversible or reversible (including
Riemannian) Finsler 3-dimensional manifold. In this paper, we study the index
growth properties of irrational closed geodesics on Finsler manifolds. This
study allows us to extend results in \cite{LoD1} on rational and in
\cite{DuL1}, \cite{Rad4} and \cite{Rad5} on completely non-degenerate closed
geodesics on spheres and $\CP^2$ to every compact simply connected Finsler
manifold. Then we prove the existence of at least two distinct closed geodesics
on every compact simply connected irreversible or reversible (including
Riemannian) Finsler 4-dimensional manifold.
|
Bootstrap Your Own Latent (BYOL) is a self-supervised learning approach for
image representation. From an augmented view of an image, BYOL trains an online
network to predict a target network representation of a different augmented
view of the same image. Unlike contrastive methods, BYOL does not explicitly
use a repulsion term built from negative pairs in its training objective. Yet,
it avoids collapse to a trivial, constant representation. Thus, it has recently
been hypothesized that batch normalization (BN) is critical to prevent collapse
in BYOL. Indeed, BN flows gradients across batch elements, and could leak
information about negative views in the batch, which could act as an implicit
negative (contrastive) term. However, we experimentally show that replacing BN
with a batch-independent normalization scheme (namely, a combination of group
normalization and weight standardization) achieves performance comparable to
vanilla BYOL ($73.9\%$ vs. $74.3\%$ top-1 accuracy under the linear evaluation
protocol on ImageNet with ResNet-$50$). Our finding disproves the hypothesis
that the use of batch statistics is a crucial ingredient for BYOL to learn
useful representations.
|
A simple protocol for complete and deterministic Bell state measurement is
proposed. It consists of measurements of nonlocal spin product operators with
the help of shared entanglement as an ancillary resource. The protocol realizes
not only nonlocal Bell state measurement between a pair of distant qubits but
also a complete Bell filter that transmits either one of the Bell states
indicated by the measurement outcome. These schemes will be useful in quantum
technologies where nonlocal Bell state measurement is indispensable.
|
We present a comprehensive density-functional theory study addressing the
adsorption, dissociation and successive diffusion of water molecules on the two
regular terminations of SrTiO3(001). Combining the obtained supercell-geometry
converged energetics within a first-principles thermodynamics framework we are
able to reproduce the experimentally observed hydroxilation of the
SrO-termination already at lowest background humidity, whereas the
TiO2-termination stays free of water molecules in the regime of low water
partial pressures. This different behavior is traced back to the effortless
formation of energetically very favorable hydroxyl-pairs on the prior
termination. Contrary to the prevalent understanding our calculations indicate
that at low coverages also the less water-affine TiO2-termination can readily
decompose water, with the often described molecular state only stabilized
towards higher coverages.
|
Suppose that $\m{U} = (U_1, \ldots , U_d) $ has a Uniform$([0,1]^d)$
distribution, that $\m{Y} = (Y_1 , \ldots , Y_d) $ has the distribution $G$ on
$\RR_+^d$, and let $\m{X} = (X_1 , \ldots , X_d) = (U_1 Y_1 , \ldots , U_d Y_d
)$. The resulting class of distributions of $\m{X}$ (as $G$ varies over all
distributions on $\RR_+^d$) is called the {\sl Scale Mixture of Uniforms} class
of distributions, and the corresponding class of densities on $\RR_+^d$ is
denoted by $\{\cal F}_{SMU}(d)$. We study maximum likelihood estimation in the
family ${\cal F}_{SMU}(d)$. We prove existence of the MLE, establish Fenchel
characterizations, and prove strong consistency of the almost surely unique
maximum likelihood estimator (MLE) in ${\cal F}_{SMU}(d)$. We also provide an
asymptotic minimax lower bound for estimating the functional $f \mapsto
f(\m{x})$ under reasonable differentiability assumptions on $f\in{\cal F}_{SMU}
(d)$ in a neighborhood of $\m{x}$. We conclude the paper with discussion,
conjectures and open problems pertaining to global and local rates of
convergence of the MLE.
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As a superconducting thin film becomes disordered and subject to an
increasing magnetic field, a point is reached when it undergoes a transition
from a superconducting to an insulating state. We use the Bogoliubov-De-Gennes
equations and a novel Monte-Carlo approach to study this transition
numerically, starting from a microscopic hamiltonian. The key effect of
disorder is to create 'islands' of strong superconductivity, coupled by regions
that are only weakly superconducting. In the case of weak disorder, an
increasing magnetic field eventually destroys the superconducting state
throughout the material, leading to an insulator. On the other hand, when
disorder is strong, superconductivity persists in the islands, and the effect
of a magnetic field is to suppress the coupling between them, resulting in
strong superconducting phase fluctuations, again leading to an insulating
state. These findings may be relevant to the high-temperature superconductors,
where intrinsic disorder may play a role.
|
This paper has been withdrawn by the authors. We consider the
attraction-repulsion chemotaxis system (3 complicated PDEs system) under
homogeneous Neumann boundary conditions in a bounded domain {\Omega} with
smooth boundary, then the classical solutions to the system are
uniformly-in-time bounded. After the local existence and uniqueness of
solutions was proved, some priory estimates and proves will be established for
the global existence of solutions (see the complete abstract in the PDF version
of paper).
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This paper is devoted to the study of the solution of a stochastic convex
black box optimization problem. Where the black box problem means that the
gradient-free oracle only returns the value of objective function, not its
gradient. We consider non-smooth and smooth setting of the solution to the
black box problem under adversarial stochastic noise. For two techniques
creating gradient-free methods: smoothing schemes via $L_1$ and $L_2$
randomizations, we find the maximum allowable level of adversarial stochastic
noise that guarantees convergence. Finally, we analyze the convergence behavior
of the algorithms under the condition of a large value of noise level.
|
The Golberger- Treiman discrepancy is related to the asymptotic behaviour of
the pionic form factor of the nucleon obtained from baryonic QCD sum rules. The
result is .015<=Delta_{GT}<=.022
|
It is known that theory of MOND with spherical symmetry cannot account for
the convergence $\kappa$-map of Bullet Cluster 1E0657-558. In this paper, we
try to set up a Finslerian MOND, a generalization of MOND in Finsler spacetime.
We use $Ric=0$ to obtain the gravitational vacuum field equation in a
four-dimensional Finsler spacetime. To leading order in the post-Newtonian
approximation, we obtain the explicit form of the Finslerian line element. It
is simply the Schwarzschild's metric except for the Finslerian rescaling
coefficient $f(v)$ of the radial coordinate $r$, i.e. $R=f(v(r))r$. By setting
$f(v(r))=(1-\sqrt{a_0r^2/GM})^{-1}$, we obtain the famous MOND in a Finslerian
framework. Taking a dipole and a quadrupole term into consideration, we give
the convergence $\kappa$ in gravitational lensing astrophysics in our model.
Numerical analysis shows that our prediction is to a certain extent in
agreement with the observations of Bullet Cluster 1E0657-558. With the
theoretical temperature $T$ taking the observed value 14.8 keV, the mass
density profile of the main cluster obtained in our model is the same order as
that given by the best-fit King $\beta$-model.
|
Let $\operatorname{K}_0(\operatorname{Var}_k)$ denote the Grothendieck ring
of $k$-varieties over an algebraically closed field $k$. Larsen and Lunts asked
if two $k$-varieties having the same class in $\operatorname{K}_0
(\operatorname{Var}_k)$ are piecewise isomorphic. Gromov asked if a birational
self-map of a $k$-variety can be extended to a piecewise automorphism. We show
that these two questions are equivalent over any algebraically closed field. If
these two questions admit a positive answer, then we prove that its underlying
abelian group is a free abelian group. Furthermore, if $\mathfrak B$ denotes
the multiplicative monoid of birational equivalence classes of irreducible
$k$-varieties then we also prove that the associated graded ring of the
Grothendieck ring is the monoid ring $\mathbb Z[\mathfrak B]$.
|
Dynamical breaking of chiral symmetry in effective models of QCD is studied.
Introducing a cut-off function or a non-local interaction, the Noether current
must be modified and thus the Ward-Takahashi identity and the PCAC relation are
modified accordingly. We point out that the pion decay constant must be defined
consistently with the Noether current so that the low-energy relations are
satisfied. We define the proxy of the Noether current for general effective
models, which is consistent with loop expansion of the
Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion
decay constant in terms of the Bethe-Salpeter amplitude is derived.
The effective Pagels-Stokar formula is proposed which is useful to estimate
the decay constant without solving the Bethe-Salpeter equation.
|
Argumentation accommodates various rhetorical devices, such as questions,
reported speech, and imperatives. These rhetorical tools usually assert
argumentatively relevant propositions rather implicitly, so understanding their
true meaning is key to understanding certain arguments properly. However, most
argument mining systems and computational linguistics research have paid little
attention to implicitly asserted propositions in argumentation. In this paper,
we examine a wide range of computational methods for extracting propositions
that are implicitly asserted in questions, reported speech, and imperatives in
argumentation. By evaluating the models on a corpus of 2016 U.S. presidential
debates and online commentary, we demonstrate the effectiveness and limitations
of the computational models. Our study may inform future research on argument
mining and the semantics of these rhetorical devices in argumentation.
|
Characterizing quantum nonlocality in networks is a challenging, but
important problem. Using quantum sources one can achieve distributions which
are unattainable classically. A key point in investigations is to decide
whether an observed probability distribution can be reproduced using only
classical resources. This causal inference task is challenging even for simple
networks, both analytically and using standard numerical techniques. We propose
to use neural networks as numerical tools to overcome these challenges, by
learning the classical strategies required to reproduce a distribution. As
such, the neural network acts as an oracle, demonstrating that a behavior is
classical if it can be learned. We apply our method to several examples in the
triangle configuration. After demonstrating that the method is consistent with
previously known results, we give solid evidence that the distribution
presented in [N. Gisin, Entropy 21(3), 325 (2019)] is indeed nonlocal as
conjectured. Finally we examine the genuinely nonlocal distribution presented
in [M.-O. Renou et al., PRL 123, 140401 (2019)], and, guided by the findings of
the neural network, conjecture nonlocality in a new range of parameters in
these distributions. The method allows us to get an estimate on the noise
robustness of all examined distributions.
|
We present phase-resolved near-infrared photometry and spectroscopy of the
classical nova V1500 Cyg to explore whether cyclotron emission is present in
this system. While the spectroscopy do not indicate the presence of discrete
cyclotron harmonic emission, the light curves suggest that a sizable fraction
of its near-infrared fluxes are due to this component. The light curves of
V1500 Cyg appear to remain dominated by emission from the heated face of the
secondary star in this system. We have used infrared spectroscopy and
photometry to search for other potential magnetic systems amongst old classical
novae. We have found that the infrared light curves of V1974 Cyg superficially
resemble those of V1500 Cyg, suggesting a highly irradiated companion. The old
novae V446 Her and QV Vul have light curves with large amplitude variations
like those seen in polars, suggesting they might have magnetic primaries. We
extract photometry for seventy nine old novae from the 2MASS Point Source
Catalog and use those data to derive the mean, un-reddened infrared colors of
quiescent novae. We also extract WISE data for these objects and find that
forty five of them were detected. Surprisingly, a number of these systems were
detected in the WISE 22 mum band. While two of those objects produced
significant dust shells (V705 Cas and V445 Pup), the others did not. It appears
that line emission from their ionized ejected shells is the most likely
explanation for those detections.
|
Random linear systems over the Galois Field modulo 2 have an interest in
connection with problems ranging from computational optimization to complex
networks. They are often approached using random matrices with
Poisson-distributed or finite column/row-sums. This technical note considers
the typical rank of random matrices belonging to a specific ensemble wich has
genuinely power-law distributed column-sums. For this ensemble, we find a
formula for calculating the typical rank in the limit of large matrices as a
function of the power-law exponent and the shape of the matrix, and
characterize its behavior through "phase diagrams" with varying model
parameters.
|
Quasiperiodic lattices have recently been shown to be a non-trivial
topological phase of matter. Charge pumping -- one of the hallmarks of
topological states of matter -- was recently realized for photons in a
one-dimensional (1D) off-diagonal Harper model implemented in a photonic
waveguide array. The topologically nontrivial 1D Fibonacci quasicrystal (QC) is
expected to facilitate a similar phenomenon, but its discrete nature and lack
of pumping parameter hinder the experimental study of such topological effects.
In this work we overcome these obstacles by utilizing a family of topologically
equivalent QCs which ranges from the Fibonacci QC to the Harper model.
Implemented in photonic waveguide arrays, we observe the topological properties
of this family, and perform a topological pumping of photons across a Fibonacci
QC.
|
In this work we introduce the development of a three--phase incompressible
Navier--Stokes/Cahn--Hilliard numerical method to simulate three--phase flows,
present in many industrial operations. The numerical method is then applied to
successfully solve oil transport problems, such as those found in the oil and
gas industry. The three--phase model adopted in this work is a Cahn--Hilliard
diffuse interface model, which was derived by Boyer and Lapuerta et al. 2006.
The Cahn--Hilliard model is coupled to the entropy--stable incompressible
Navier--Stokes equations model derived by Manzanero et al. 2019. The spatial
discretization uses a high--order discontinuous Galerkin spectral element
method which yields highly accurate results in arbitrary geometries, while an
implicit--explicit (IMEX) method is adopted as temporal discretization. The
developed numerical tool is tested for two and three dimensional problems,
including a convergence study, a two--dimensional jet, a three--dimensional
annular flow, and realistic geometries like T--shaped pipe intersections.
|
Bohr's complementarity principle has long been a fundamental concept in
quantum mechanics, positing that, within a given experimental setup, a quantum
system (or quanton) can exhibit either its wave-like character, denoted as $W$,
or its particle-like character, denoted as $P$, but not both simultaneously.
Modern interpretations of Bohr's complementarity principle acknowledge the
coexistence of these aspects in the same experiment while introducing the
constraint $W + P \le \alpha$. Notably, estimations of $W$ or $P$ frequently
rely on indirect retrodiction methods, a practice that has led to the claim of
the violation of Bohr's complementarity principle. By taking a different route,
recent advancements demonstrate that complementarity relations can be
rigorously derived from the axioms of quantum mechanics under specific quantum
state preparation conditions. To reconcile these observations and eliminate
potential paradoxes or violations, we propose an updated formulation of Bohr's
complementarity principle, which is stated as follows: \textit{For a given
quantum state preparation $\rho_t$ at a specific instant of time $t$, the wave
and particle behaviors of a quanton are constrained by a complementarity
relation $W(\rho_t) + P(\rho_t) \le \alpha(d)$, which is derived directly from
the axioms of quantum mechanics.}
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Combining spin textures in ultra-thin films with conventional superconductors
has emerged as a powerful and versatile platform for designing topologically
non-trivial superconducting phases as well as spin-triplet Cooper pairs. As a
consequence, two-dimensional magnet-superconductor hybrids (2D MSHs) are
promising candidate systems to realize devices for topology-based quantum
technologies and superconducting spintronics. So far, studies have focused
mostly on systems hosting collinear ferromagnets or antiferromagnets. However,
topologically non-trivial phases have been predicted to emerge in MSH systems
with non-collinear spin textures as well. In this article, we present the
experimental discovery of topological superconductivity in the MSH system
Fe/Ta(110) where a magnetic spiral is realized in the Fe monolayer on the
surface of the s-wave superconductor Ta. By combining low-temperature
spin-polarized scanning tunneling microscopy measurements with theoretical
modeling, we are able to conclude that the system is in a topological
nodal-point superconducting phase with low-energy edge modes. Due to the
non-collinear spin texture in our MSH system, these edge modes exhibit a
magnetization direction-dependent dispersion. Furthermore, we identify direct
signatures of Rashba spin-orbit coupling in the experimentally measured
differential tunneling conductance. The present work realizes a non-collinear
spin texture-based path to topological superconductivity.
|
The classical De Jonquieres and MacDonald formulas describe the virtual
number of divisors with prescribed multiplicities in a linear system on an
algebraic curve. We establish an essentially optimal result concerning the
enumerative validity of these formulas in the case of a general curve of genus
g.
|
An ever increasing number of battlefield devices that are capable of
collecting, processing, storing, and communicating information are rapidly
becoming interconnected. The staggering number of connected devices on the
battlefield greatly increases the possibility that an adversary could find ways
to exploit hardware or software vulnerabilities, degrading or denying
Warfighters the assured and secure use of those devices. Autonomous software
agents will become necessities to manage, defend, and react to cyber threats in
the future battlespace. The number of connected devices increases
disproportionately to the number of cyber experts that could be available
within an operational environment. In this paper, an autonomous agent
capability and a scenario of how it could operate are proposed. The goal of
developing such capability is to increase the security posture of the Internet
of Battlefield Things and meet the challenges of an increasingly complex
battlefield. This paper describes an illustrative scenario in a notional use
case and discusses the challenges associated with such autonomous agents. We
conclude by offering ideas for potential research into developing autonomous
agents suitable for cyber defense in a battlefield environment.
|
Phishing and spam detection is long standing challenge that has been the
subject of much academic research. Large Language Models (LLM) have vast
potential to transform society and provide new and innovative approaches to
solve well-established challenges. Phishing and spam have caused financial
hardships and lost time and resources to email users all over the world and
frequently serve as an entry point for ransomware threat actors. While
detection approaches exist, especially heuristic-based approaches, LLMs offer
the potential to venture into a new unexplored area for understanding and
solving this challenge. LLMs have rapidly altered the landscape from business,
consumers, and throughout academia and demonstrate transformational potential
for the potential of society. Based on this, applying these new and innovative
approaches to email detection is a rational next step in academic research. In
this work, we present IPSDM, our model based on fine-tuning the BERT family of
models to specifically detect phishing and spam email. We demonstrate our
fine-tuned version, IPSDM, is able to better classify emails in both unbalanced
and balanced datasets. This work serves as an important first step towards
employing LLMs to improve the security of our information systems.
|
The symplectic-Hamiltonian formulation and recursion operator of the
fifth-order Mikhailov-Novikov-Wang system are given.
|
The low -\beta magnet systems are located in the LHC insertion regions around
the four interaction points. They are the key elements in the beams
focusing/defocusing process and will allow proton collisions at a luminosity of
up to 10**34/cm**2s. Large radiation dose deposited at the proximity of the
beam collisions dictate stringent requirements for the design and operation of
the systems. The hardware commissioning phase of the LHC was completed in the
winter of 2010 and permitted to validate this system safe operation. This paper
presents the analysis used to qualify and quantify the safe operation of the
low -\beta magnet systems in the Large Hadron Collider (LHC) for the first
years of operation.
|
The aging and gradual brightening of the Sun will challenge Earth's
habitability in the next few billion years. If life exists elsewhere in the
Universe, the aging of its host star similarly poses an existential threat. One
solution, which we dub a Lazarus star, is for an advanced civilization to
remove (or star-lift) mass from their host star at a rate that offsets the
increase in luminosity, keeping the flux on the habitable planet(s) constant
and extending the lifetime of their star. While this idea has existed since
1985 when it was first proposed by Criswell, numerical investigations of
star-lifting have been lacking. Here, we use the stellar evolution code MESA to
find mass vs. age and $\dot{M}$ vs. age relations which would hold the flux on
surrounding planets constant. We explore initial mass ranging from $0.2{\rm
M}_{\odot}$ to $1.2{\rm M}_{\odot}$. For most stars with a mass initially below
about $ 0.4 {\rm M}_{\odot}$, we find that star-lifting increases their
main-sequence lifetimes up to $500$ Gyr until they approach the hydrogen
burning limit and star-lifting is no longer possible. For more massive stars,
star-lifting increase main-sequence lifetimes by 1 Gyr to 100 Gyr, though they
still enter the red-giant phase. For example, a Sun-like star has a
main-sequence lifetime which can be increased by up to 3 Gyr. This requires a
mass-loss rate of about $0.05 {\rm M}_{\mathrm{Ceres}}$ per year. We compare
star-lifting to other survival strategies and briefly discuss methods for
detecting these engineered stars.
|
Extremal length is a classical tool in 1-dimensional complex analysis for
building conformal invariants. We propose a higher-dimensional generalization
for complex manifolds and provide some ideas on how to estimate and calculate
it. We also show how to formulate certain natural geometric inequalities
concerning moduli spaces in terms of a complex analogue of the classical
Riemannian notion of systole.
|
In \cite{Lee:2006:schrod-converg}, when the spatial variable $x$ is
localized, Lee observed that the Schr\"odinger maximal operator
$e^{it\Delta}f(x)$ enjoys certain localization property in $t$ for frequency
localized functions. In this note, we give an alternative proof of this
observation by using the method of stationary phase, and then include two
applications: the first is on is on the equivalence of the local and the global
Schr\"odinger maximal inequalities; secondly the local Schr\"odinger maximal
inequality holds for $f\in H^{3/8+}$, which implies that $e^{it\Delta}f$
converges to $f$ almost everywhere if $f\in H^{3/8+}$. These results are not
new. In this note we would like to explore them from a slightly different
perspective, where the analysis of the stationary phase plays an important
role.
|
Hard of hearing or profoundly deaf people make use of cued speech (CS) as a
communication tool to understand spoken language. By delivering cues that are
relevant to the phonetic information, CS offers a way to enhance lipreading. In
literature, there have been several studies on the dynamics between the hand
and the lips in the context of human production. This article proposes a way to
investigate how a neural network learns this relation for a single speaker
while performing a recognition task using attention mechanisms. Further, an
analysis of the learnt dynamics is utilized to establish the relationship
between the two modalities and extract automatic segments. For the purpose of
this study, a new dataset has been recorded for French CS. Along with the
release of this dataset, a benchmark will be reported for word-level
recognition, a novelty in the automatic recognition of French CS.
|
Optical spectral variability of quasars and BL Lac Objects is compared by
means of the spectral variability parameter beta (Trevese & Vagnetti 2002).
Both kinds of objects change their spectral slopes alpha, becoming bluer when
brighter, but BL Lac Objects have smaller beta values and are clearly separated
from quasars in the alpha-beta plane. Models accounting for the origin of the
variability are discussed for both classes of objects.
|
We measure the gas-phase oxygen abundances in 4 Lyman Break Analogs (LBAs)
using auroral emission lines to derive direct abundances. The direct method
oxygen abundances of these objects are generally consistent with the
empirically-derived strong-line method values, confirming that these objects
are low oxygen abundance outliers from the Mass-Metallicity (MZ) relation
defined by star forming SDSS galaxies. We find slightly anomalous excitation
conditions (Wolf-Rayet features) that could potentially bias the empirical
estimates towards high values if caution is not exercised in the selection of
the strong-line calibration used. The high rate of star formation and low
oxygen abundance of these objects is consistent with the predictions of the
Fundamental Metallicity Relation (FMR), in which the infall of relatively
unenriched gas simultaneously triggers an episode of star formation and dilutes
ISM of the host galaxy.
|
Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.